This document proposes a robust PID tuning strategy for uncertain plants based on the Kharitonov theorem.
1) The Kharitonov theorem is used to define four "vortex polynomials" that characterize the stability of an uncertain plant family.
2) A systematic graphical method is developed to design a PID controller that stabilizes all four vortex polynomials simultaneously. This results in a "Kharitonov region" of stabilizing controller parameters.
3) Additional gain and phase margin specifications are imposed to ensure the robust stability and performance of the closed loop system for the uncertain plant family.
Adaptive backstepping sliding mode control of flexible ball screw drives with...ISA Interchange
This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.
On an LAS-integrated soft PLC system based on WorldFIP fieldbusISA Interchange
Communication efficiency is lowered and real-time performance is not good enough in discrete control based on traditional WorldFIP field intelligent nodes in case that the scale of control in field is large. A soft PLC system based on WorldFIP fieldbus was designed and implemented. Link Activity Scheduler (LAS) was integrated into the system and field intelligent I/O modules acted as networked basic nodes. Discrete control logic was implemented with the LAS-integrated soft PLC system. The proposed system was composed of configuration and supervisory sub-systems and running sub-systems. The configuration and supervisory sub-system was implemented with a personal computer or an industrial personal computer; running subsystems were designed and implemented based on embedded hardware and software systems. Communication and schedule in the running subsystem was implemented with an embedded sub-module; discrete control and system self-diagnosis were implemented with another embedded sub-module. Structure of the proposed system was presented. Methodology for the design of the sub-systems was expounded. Experiments were carried out to evaluate the performance of the proposed system both in discrete and process control by investigating the effect of network data transmission delay induced by the soft PLC in WorldFIP network and CPU workload on resulting control performances. The experimental observations indicated that the proposed system is practically applicable.
Plant-Wide Control: Eco-Efficiency and Control Loop ConfigurationISA Interchange
Since the eco-efficiency of all industrial processes/plants has become increasingly important, engineers need to find a way to integrate the control loop configuration and the measurements of eco-efficiency. A new measure of eco-efficiency, the exergy eco-efficiency factor, for control loop configuration, is proposed in this paper. The exergy eco-efficiency factor is based on the thermodynamic concept of exergy which can be used to analyse a process in terms of its efficiency associated with the control configuration. The combination of control pairing configuration techniques (such as the relative gain array, RGA and Niederlinski index, NI) and the proposed exergy eco-efficiency factor will guide the process designer to reach the optimal control design with low operational cost (i.e., energy consumption). The exergy eco-efficiency factor is implemented in the process simulation case study and the reliability of the proposed method is demonstrated by dynamic simulation results.
A fuzzy logic method is developed for gain scheduling of PID controllers that improves upon existing fuzzy-PID schemes. The method uses a single fuzzy input variable related to the derivative of the PID manipulated variable, eliminating redundant rules. Online tuning improves PID performance while retaining original PID parameters. The fuzzy and PID manipulated variables are related through a differential equation, allowing online replacement and tuning with two parameters. The method is demonstrated on a temperature control process, improving PID performance to the level of model predictive control with only a few tuning tests.
Estimation of region of attraction for polynomial nonlinear systems a numeric...ISA Interchange
This document introduces a numerical method to estimate the region of attraction (ROA) for polynomial nonlinear systems using sum-of-squares programming. The method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. This invariant set provides an estimation of the ROA for the equilibrium point. The paper then proposes an algorithm to select a "shape factor" based on the linearized dynamic model of the system, which is used to enlarge the estimation of the ROA by solving a sum-of-squares optimization problem in each iteration. Numerical examples are provided to demonstrate the efficiency of the proposed method.
This document describes a novel auto-tuning method for cascade control systems. The method uses a simple relay feedback test to simultaneously identify both the inner and outer loop process model parameters. This allows established PID tuning rules to then be applied to tune both loops. The method is simpler than existing approaches and can be directly integrated into commercial auto-tuning systems. It is illustrated through examples to be effective and robust.
Robust PID controller design for non-minimum phase time delay systemsISA Interchange
1. A robust PID controller design method is presented for non-minimum phase systems with uncertain time delays.
2. The gain-phase margin tester method is used to determine a parameter region in the controller parameter plane that guarantees at least a specified gain and phase margin, providing robustness against instability induced by time delays.
3. PID controller parameters are selected from this region to achieve a compromise between robustness and tracking performance even in the presence of uncertain time delays.
Stochastic behavior analysis of complex repairable industrial systemsISA Interchange
The document presents a novel technique called particle swarm optimization-based Lambda-Tau (PSOBLT) for analyzing the stochastic behavior of complex repairable industrial systems using uncertain data. PSOBLT combines Lambda-Tau methodology and particle swarm optimization to model system interactions using Petri nets and optimize the membership functions of reliability indices like failure rate and repair time. The technique reduces uncertainty in behavior analysis results compared to existing methods. The document demonstrates PSOBLT on a paper mill feeding unit to analyze system performance and help managers improve profit through maintenance strategies.
Adaptive backstepping sliding mode control of flexible ball screw drives with...ISA Interchange
This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.
On an LAS-integrated soft PLC system based on WorldFIP fieldbusISA Interchange
Communication efficiency is lowered and real-time performance is not good enough in discrete control based on traditional WorldFIP field intelligent nodes in case that the scale of control in field is large. A soft PLC system based on WorldFIP fieldbus was designed and implemented. Link Activity Scheduler (LAS) was integrated into the system and field intelligent I/O modules acted as networked basic nodes. Discrete control logic was implemented with the LAS-integrated soft PLC system. The proposed system was composed of configuration and supervisory sub-systems and running sub-systems. The configuration and supervisory sub-system was implemented with a personal computer or an industrial personal computer; running subsystems were designed and implemented based on embedded hardware and software systems. Communication and schedule in the running subsystem was implemented with an embedded sub-module; discrete control and system self-diagnosis were implemented with another embedded sub-module. Structure of the proposed system was presented. Methodology for the design of the sub-systems was expounded. Experiments were carried out to evaluate the performance of the proposed system both in discrete and process control by investigating the effect of network data transmission delay induced by the soft PLC in WorldFIP network and CPU workload on resulting control performances. The experimental observations indicated that the proposed system is practically applicable.
Plant-Wide Control: Eco-Efficiency and Control Loop ConfigurationISA Interchange
Since the eco-efficiency of all industrial processes/plants has become increasingly important, engineers need to find a way to integrate the control loop configuration and the measurements of eco-efficiency. A new measure of eco-efficiency, the exergy eco-efficiency factor, for control loop configuration, is proposed in this paper. The exergy eco-efficiency factor is based on the thermodynamic concept of exergy which can be used to analyse a process in terms of its efficiency associated with the control configuration. The combination of control pairing configuration techniques (such as the relative gain array, RGA and Niederlinski index, NI) and the proposed exergy eco-efficiency factor will guide the process designer to reach the optimal control design with low operational cost (i.e., energy consumption). The exergy eco-efficiency factor is implemented in the process simulation case study and the reliability of the proposed method is demonstrated by dynamic simulation results.
A fuzzy logic method is developed for gain scheduling of PID controllers that improves upon existing fuzzy-PID schemes. The method uses a single fuzzy input variable related to the derivative of the PID manipulated variable, eliminating redundant rules. Online tuning improves PID performance while retaining original PID parameters. The fuzzy and PID manipulated variables are related through a differential equation, allowing online replacement and tuning with two parameters. The method is demonstrated on a temperature control process, improving PID performance to the level of model predictive control with only a few tuning tests.
Estimation of region of attraction for polynomial nonlinear systems a numeric...ISA Interchange
This document introduces a numerical method to estimate the region of attraction (ROA) for polynomial nonlinear systems using sum-of-squares programming. The method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. This invariant set provides an estimation of the ROA for the equilibrium point. The paper then proposes an algorithm to select a "shape factor" based on the linearized dynamic model of the system, which is used to enlarge the estimation of the ROA by solving a sum-of-squares optimization problem in each iteration. Numerical examples are provided to demonstrate the efficiency of the proposed method.
This document describes a novel auto-tuning method for cascade control systems. The method uses a simple relay feedback test to simultaneously identify both the inner and outer loop process model parameters. This allows established PID tuning rules to then be applied to tune both loops. The method is simpler than existing approaches and can be directly integrated into commercial auto-tuning systems. It is illustrated through examples to be effective and robust.
Robust PID controller design for non-minimum phase time delay systemsISA Interchange
1. A robust PID controller design method is presented for non-minimum phase systems with uncertain time delays.
2. The gain-phase margin tester method is used to determine a parameter region in the controller parameter plane that guarantees at least a specified gain and phase margin, providing robustness against instability induced by time delays.
3. PID controller parameters are selected from this region to achieve a compromise between robustness and tracking performance even in the presence of uncertain time delays.
Stochastic behavior analysis of complex repairable industrial systemsISA Interchange
The document presents a novel technique called particle swarm optimization-based Lambda-Tau (PSOBLT) for analyzing the stochastic behavior of complex repairable industrial systems using uncertain data. PSOBLT combines Lambda-Tau methodology and particle swarm optimization to model system interactions using Petri nets and optimize the membership functions of reliability indices like failure rate and repair time. The technique reduces uncertainty in behavior analysis results compared to existing methods. The document demonstrates PSOBLT on a paper mill feeding unit to analyze system performance and help managers improve profit through maintenance strategies.
Bi objective redundancy allocation problem for a system with mixed repairable...ISA Interchange
Traditionally, in the redundancy allocation problem (RAP), two general classes of optimization problems are considered; reliability optimization and availability optimization. Contrary to reliability optimization, fewer researchers have studied availability optimization to find out the optimal combination of components type and redundancy levels for each subsystem in a system for maximizing (or minimizing) the objectives. In each problem it is assumed that either the entire components are repairable or they are non-repairable. However, in real world situations, systems usually consist of both repairable and non-repairable components. In this paper a new Mixed Integer Nonlinear Programming (MINLP) model is presented to analyze the availability optimization of a system with a given structure, using both repairable and non-repairable components, simultaneously. To find the solution of the introduced MINLP, an efficient Genetic Algorithm (GA) is also developed. Furthermore, to show the efficiency of the proposed GA, a numerical example is presented. Experimental results demonstrate that the proposed GA has a better performance compared to one of the most recommended algorithm in the literature.
A simple numerical procedure for estimating nonlinear uncertainty propagationISA Interchange
This document presents a numerical method for estimating nonlinear uncertainty propagation. The method approximates the nonlinear function with piecewise linear segments. It then calculates the probability density function of the dependent variable based on the transformations of the linear segments. For functions of a normally distributed independent variable, the mean and confidence intervals of the dependent variable can be calculated using only the error function. A simple example of applying this method to a parabolic function is presented to demonstrate the technique.
A modified narmax model based self-tuner with fault tolerance for unknown non...ISA Interchange
A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input–output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.
Design of a self tuning regulator for temperature control of a polymerization...ISA Interchange
The temperature control of a polymerization reactor described by Chylla and Haase, a control engineering benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. The conventional cascade control provides a robust operation, but often lacks in control performance concerning the required strict temperature tolerances. The self-tuning control concept presented in this contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature in order to follow a predefined trajectory of the reactor temperature. The reaction heat and the heat transfer coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Two simple physically motivated relations are employed, which allow the non-delayed estimation of both quantities. Simulation results under model uncertainties show the effectiveness of the self-tuning control concept.
Cascade control of superheated steam temperature with neuro PID controllerISA Interchange
In this paper, an improved cascade control methodology for superheated processes is developed, in which the primary PID controller is implemented by neural networks trained by minimizing error entropy criterion. The entropy of the tracking error can be estimated recursively by utilizing receding horizon window technique. The measurable disturbances in superheated processes are input to the neuro-PID controller besides the sequences of tracking error in outer loop control system, hence, feedback control is combined with feedforward control in the proposed neuro-PID controller. The convergent condition of the neural networks is analyzed. The implementation procedures of the proposed cascade control approach are summarized. Compared with the neuro-PID controller using minimizing squared error criterion, the proposed neuro-PID controller using minimizing error entropy criterion may decrease fluctuations of the superheated steam temperature. A simulation example shows the advantages of the proposed method.
Modified Smith predictor design for periodic disturbance rejectionISA Interchange
The modified Smith predictor control scheme aims to improve rejection of periodic disturbances while maintaining the superior setpoint response of traditional Smith predictor control. It does this by adding an additional feedback loop containing controllers Gc2 and Gc3 that provide a stabilizing effect. The stability of the overall closed-loop system is analyzed, showing it can stabilize both stable and unstable processes with time delay. Simulation and experimental results demonstrate the effectiveness of the approach.
An opto isolator based linearization technique of a typical thyristor driven ...ISA Interchange
A thyristor driven pump is operated by varying the DC input signal in the firing circuit of thyristor drive. This operation suffers from difficulties due to the nonlinear relation between thyristor output and DC input. In the present paper, an opto-isolator based linearization technique of a typical thyristor driven pump has been proposed. The design, fabrication and the necessary circuit diagram along with theoretical explanations of the resultant output has been described. The operation of the linearized thyristor driven pump has been studied experimentally and the experimental data before and after linearization are reported. The characteristic graphs are found to have very good linearity.
This document provides summaries of several appendices related to PID tuning and control. Appendix A offers a short cut tuning method that can identify process dynamics and tune a controller in about five dead times. It reduces open loop test time by over 80% for processes with large time constants. Appendix B provides a PID checklist to help utilize full PID capabilities and ensure parameters are correctly set. Appendix C derives equations to understand the effects of dynamics and tuning on performance. It provides a guide to change plant dynamics and tuning to achieve objectives.
1) The document describes using genetic algorithms to tune PID, state variable feedback, and LQR controllers for balancing an inverted pendulum on a cart.
2) It presents the mathematical model of the inverted pendulum system and linearizes the model.
3) PID, state variable feedback, and LQR controllers are designed for the system. The controller parameters are then tuned using a genetic algorithm to minimize error.
4) Simulation results show the genetic algorithm approach improves rise time and reduces overshoot compared to controllers without genetic algorithm tuning.
Biomedical Control Systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE ...Mathankumar S
Biomedical control systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE (short Questions & Answers) - ITS DEALS WITH STABILITY OF THE SYSTEM (ROUTH HURWITZ CRITERION, ROUTH ARRAY), ROOT LOCUS TECHNIQUE, ZEROS & POLES,
Improving performance using cascade control and a Smith predictorISA Interchange
The document describes an improved cascade control (ICC) structure that uses a Smith predictor in the outer loop of a cascade control system. This structure can provide better performance than conventional cascade control, single feedback control, or a Smith predictor alone. The ICC structure is applicable to temperature control problems where the inner loop process has little or no delay, while the outer loop process has a significant time delay. Two methods are proposed for tuning the controller parameters in the ICC structure: 1) Using optimization to minimize an integral performance criterion, and 2) An autotuning method that uses relay feedback to identify process models and apply tuning rules. Examples are provided showing the ICC structure can achieve improved disturbance rejection and setpoint tracking compared to alternative control configurations.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Self tuning adaptive control for an industrial weigh belt feederISA Interchange
This document summarizes a study on applying an adaptive control method called an indirect self-tuning regulator to control the feed rate of an industrial weigh belt feeder. The weigh belt feeder exhibits nonlinear behavior due to motor friction, saturation, and sensor noise. The self-tuning regulator uses a recursive least-squares method and pole placement design to adapt the controller parameters online to overcome the nonlinearities. Experimental results on the weigh belt feeder show the adaptive controller provides effective control for different reference inputs compared to a fixed PI controller, demonstrating the benefits of the adaptive approach.
Multivariable Control System Design for Quadruple Tank Process using Quantita...IDES Editor
This paper focus on design of multivariable
controller for Quadruple Tank Process, a two input two
output system with large plant uncertainty using QFT
methodology. In the present work, a new approach using
Quantitative Feedback Theory (QFT) is formulated for
design of a robust two degree of freedom controller for
Quadruple Tank Process. The design is done in frequency
domain. This paper presents a design method for a 2 x 2
multiple input multiple output system. The plant
uncertainties are transformed into equivalent external
disturbance sets, and the design problem becomes one of
the external disturbance attenuation. The objective is to
find compensator functions which guarantee that the
system performance bounds are satisfied over the range
of plant uncertainty. The methodology is successfully
applied to design a two degree of freedom compensator
Quadruple Tank Process.
Autotuning of a new PI-PD Smith predictor based on time domain specificationsISA Interchange
This document presents a new PI-PD Smith predictor controller configuration for processes with long time delays. The controller aims to improve set point tracking and disturbance rejection performance over existing Smith predictor designs. It does this by adding additional controllers - a PI controller (Gc1(s)) for set point tracking, a PD controller (Gc2(s)) to stabilize unstable processes, and a disturbance rejection controller (Gd(s)). Autotuning formulas are developed to identify plant models from relay feedback tests and design the PI-PD controller parameters based on specifications for damping ratio, natural frequency, and settling time. Examples are given to show the effectiveness of the proposed method.
The document describes optimizing an automatic generation control (AGC) scheme for a two-area power system using a particle swarm optimization (PSO) tuned fuzzy PID controller. A linearized model of the two-area power system is presented. A fuzzy PID controller is used to regulate the area control error of each area. The gains of the fuzzy PID controller are optimized using PSO to minimize time-domain performance metrics. Simulation results show the PSO tuned fuzzy PID controller provides better dynamic response than a conventional PSO PID controller, with lower error and faster settling time. Comparisons of tie-line power deviation also show improved performance with the PSO tuned fuzzy approach. The paper concludes the proposed method efficiently tunes fuzzy PID parameters
The document discusses the design of control system compensators using the root locus method (LGR) and frequency response (RF) methods. It covers introducing compensators to improve closed-loop response, different types of compensators (lead, lag, lead-lag), and the process for designing lead compensators using root locus graphs. An example is provided to illustrate how to design a lead compensator to place dominant closed-loop poles at a desired location on the s-plane to meet specifications like damping ratio and natural frequency.
Artificial Intelligent and meta-heuristic Control Based DFIG model Considered...IRJET Journal
This document summarizes a research paper that investigates different control methods for load frequency control in a multi-area power system incorporating wind energy from doubly fed induction generators. The control methods analyzed include PI control, PI control tuned with particle swarm optimization, and fuzzy logic control. MATLAB simulations are conducted on a 4-area power system consisting of both thermal and hydro power plants as well as DFIG-based wind power. Results show that all control methods are able to regulate tie line power and frequency to zero steady state values, but settling times differ between the methods.
Enhancement of Power System Performance by Optimal Placement of Distributed G...IRJET Journal
This document presents a comparative performance analysis of different control schemes for load frequency control in a multi-area power system incorporating wind energy conversion systems using doubly fed induction generators (DFIGs). The control schemes analyzed are PI control, PI control tuned using particle swarm optimization (PSO), and fuzzy logic control. MATLAB simulation results show the tie line power flow and frequency deviations for different control scenarios and cases. The scenarios consider different combinations of thermal, hydro, and DFIG systems across 4 areas. The results indicate that fuzzy logic control provides the fastest system response in the scenario with higher system complexity, while PSO-tuned PI control performs best in the scenario with lower complexity. The analysis focuses on minimizing the settling time as the primary
Optimal design & analysis of load frequency control for two interconnecte...ijctet
This document summarizes a research paper that proposes using Particle Swarm Optimization (PSO) to tune the parameters of PID controllers for Automatic Load Frequency Control (ALFC) in a system of two interconnected power generation areas. It describes modeling the two-area system and the objectives of ALFC to maintain frequency and distribute load. PSO is introduced as a technique to explore the search space to maximize objective functions by updating particle velocities and positions. The paper presents simulation results comparing the tuned PID controller performance to untuned controllers.
The document discusses synchronized phasor measurements in electric power systems and their applications. Precise synchronization of phasor measurements across substations separated by hundreds of miles enables a consistent description of the power system state. GPS provides an ideal synchronization source. Synchronized phasors can improve state estimation algorithms, provide dynamic state estimates, enhance control techniques, and improve protection concepts. The paper describes phasor measurement implementation and several uses including improved state estimation, control, detection of instability, and adaptive relaying.
1) Precise synchronization of phasor measurements across wide areas of the electric grid is important for monitoring system state, control, and protection. GPS provides an ideal synchronization source with accuracy of 1 microsecond or better.
2) Synchronized phasor measurements directly measure the system state vector and dynamic conditions, providing faster response than traditional state estimation. They can improve control schemes and adaptive relaying by providing real-time feedback across the entire system.
3) Detection of instability between two interconnected regions can be achieved using synchronized phasor measurements to predict angular stability based on the equal area criterion for a two-machine system.
Bi objective redundancy allocation problem for a system with mixed repairable...ISA Interchange
Traditionally, in the redundancy allocation problem (RAP), two general classes of optimization problems are considered; reliability optimization and availability optimization. Contrary to reliability optimization, fewer researchers have studied availability optimization to find out the optimal combination of components type and redundancy levels for each subsystem in a system for maximizing (or minimizing) the objectives. In each problem it is assumed that either the entire components are repairable or they are non-repairable. However, in real world situations, systems usually consist of both repairable and non-repairable components. In this paper a new Mixed Integer Nonlinear Programming (MINLP) model is presented to analyze the availability optimization of a system with a given structure, using both repairable and non-repairable components, simultaneously. To find the solution of the introduced MINLP, an efficient Genetic Algorithm (GA) is also developed. Furthermore, to show the efficiency of the proposed GA, a numerical example is presented. Experimental results demonstrate that the proposed GA has a better performance compared to one of the most recommended algorithm in the literature.
A simple numerical procedure for estimating nonlinear uncertainty propagationISA Interchange
This document presents a numerical method for estimating nonlinear uncertainty propagation. The method approximates the nonlinear function with piecewise linear segments. It then calculates the probability density function of the dependent variable based on the transformations of the linear segments. For functions of a normally distributed independent variable, the mean and confidence intervals of the dependent variable can be calculated using only the error function. A simple example of applying this method to a parabolic function is presented to demonstrate the technique.
A modified narmax model based self-tuner with fault tolerance for unknown non...ISA Interchange
A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input–output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.
Design of a self tuning regulator for temperature control of a polymerization...ISA Interchange
The temperature control of a polymerization reactor described by Chylla and Haase, a control engineering benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. The conventional cascade control provides a robust operation, but often lacks in control performance concerning the required strict temperature tolerances. The self-tuning control concept presented in this contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature in order to follow a predefined trajectory of the reactor temperature. The reaction heat and the heat transfer coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Two simple physically motivated relations are employed, which allow the non-delayed estimation of both quantities. Simulation results under model uncertainties show the effectiveness of the self-tuning control concept.
Cascade control of superheated steam temperature with neuro PID controllerISA Interchange
In this paper, an improved cascade control methodology for superheated processes is developed, in which the primary PID controller is implemented by neural networks trained by minimizing error entropy criterion. The entropy of the tracking error can be estimated recursively by utilizing receding horizon window technique. The measurable disturbances in superheated processes are input to the neuro-PID controller besides the sequences of tracking error in outer loop control system, hence, feedback control is combined with feedforward control in the proposed neuro-PID controller. The convergent condition of the neural networks is analyzed. The implementation procedures of the proposed cascade control approach are summarized. Compared with the neuro-PID controller using minimizing squared error criterion, the proposed neuro-PID controller using minimizing error entropy criterion may decrease fluctuations of the superheated steam temperature. A simulation example shows the advantages of the proposed method.
Modified Smith predictor design for periodic disturbance rejectionISA Interchange
The modified Smith predictor control scheme aims to improve rejection of periodic disturbances while maintaining the superior setpoint response of traditional Smith predictor control. It does this by adding an additional feedback loop containing controllers Gc2 and Gc3 that provide a stabilizing effect. The stability of the overall closed-loop system is analyzed, showing it can stabilize both stable and unstable processes with time delay. Simulation and experimental results demonstrate the effectiveness of the approach.
An opto isolator based linearization technique of a typical thyristor driven ...ISA Interchange
A thyristor driven pump is operated by varying the DC input signal in the firing circuit of thyristor drive. This operation suffers from difficulties due to the nonlinear relation between thyristor output and DC input. In the present paper, an opto-isolator based linearization technique of a typical thyristor driven pump has been proposed. The design, fabrication and the necessary circuit diagram along with theoretical explanations of the resultant output has been described. The operation of the linearized thyristor driven pump has been studied experimentally and the experimental data before and after linearization are reported. The characteristic graphs are found to have very good linearity.
This document provides summaries of several appendices related to PID tuning and control. Appendix A offers a short cut tuning method that can identify process dynamics and tune a controller in about five dead times. It reduces open loop test time by over 80% for processes with large time constants. Appendix B provides a PID checklist to help utilize full PID capabilities and ensure parameters are correctly set. Appendix C derives equations to understand the effects of dynamics and tuning on performance. It provides a guide to change plant dynamics and tuning to achieve objectives.
1) The document describes using genetic algorithms to tune PID, state variable feedback, and LQR controllers for balancing an inverted pendulum on a cart.
2) It presents the mathematical model of the inverted pendulum system and linearizes the model.
3) PID, state variable feedback, and LQR controllers are designed for the system. The controller parameters are then tuned using a genetic algorithm to minimize error.
4) Simulation results show the genetic algorithm approach improves rise time and reduces overshoot compared to controllers without genetic algorithm tuning.
Biomedical Control Systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE ...Mathankumar S
Biomedical control systems - THE CONCEPT OF STABILITY & ROOT LOCUS TECHNIQUE (short Questions & Answers) - ITS DEALS WITH STABILITY OF THE SYSTEM (ROUTH HURWITZ CRITERION, ROUTH ARRAY), ROOT LOCUS TECHNIQUE, ZEROS & POLES,
Improving performance using cascade control and a Smith predictorISA Interchange
The document describes an improved cascade control (ICC) structure that uses a Smith predictor in the outer loop of a cascade control system. This structure can provide better performance than conventional cascade control, single feedback control, or a Smith predictor alone. The ICC structure is applicable to temperature control problems where the inner loop process has little or no delay, while the outer loop process has a significant time delay. Two methods are proposed for tuning the controller parameters in the ICC structure: 1) Using optimization to minimize an integral performance criterion, and 2) An autotuning method that uses relay feedback to identify process models and apply tuning rules. Examples are provided showing the ICC structure can achieve improved disturbance rejection and setpoint tracking compared to alternative control configurations.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Self tuning adaptive control for an industrial weigh belt feederISA Interchange
This document summarizes a study on applying an adaptive control method called an indirect self-tuning regulator to control the feed rate of an industrial weigh belt feeder. The weigh belt feeder exhibits nonlinear behavior due to motor friction, saturation, and sensor noise. The self-tuning regulator uses a recursive least-squares method and pole placement design to adapt the controller parameters online to overcome the nonlinearities. Experimental results on the weigh belt feeder show the adaptive controller provides effective control for different reference inputs compared to a fixed PI controller, demonstrating the benefits of the adaptive approach.
Multivariable Control System Design for Quadruple Tank Process using Quantita...IDES Editor
This paper focus on design of multivariable
controller for Quadruple Tank Process, a two input two
output system with large plant uncertainty using QFT
methodology. In the present work, a new approach using
Quantitative Feedback Theory (QFT) is formulated for
design of a robust two degree of freedom controller for
Quadruple Tank Process. The design is done in frequency
domain. This paper presents a design method for a 2 x 2
multiple input multiple output system. The plant
uncertainties are transformed into equivalent external
disturbance sets, and the design problem becomes one of
the external disturbance attenuation. The objective is to
find compensator functions which guarantee that the
system performance bounds are satisfied over the range
of plant uncertainty. The methodology is successfully
applied to design a two degree of freedom compensator
Quadruple Tank Process.
Autotuning of a new PI-PD Smith predictor based on time domain specificationsISA Interchange
This document presents a new PI-PD Smith predictor controller configuration for processes with long time delays. The controller aims to improve set point tracking and disturbance rejection performance over existing Smith predictor designs. It does this by adding additional controllers - a PI controller (Gc1(s)) for set point tracking, a PD controller (Gc2(s)) to stabilize unstable processes, and a disturbance rejection controller (Gd(s)). Autotuning formulas are developed to identify plant models from relay feedback tests and design the PI-PD controller parameters based on specifications for damping ratio, natural frequency, and settling time. Examples are given to show the effectiveness of the proposed method.
The document describes optimizing an automatic generation control (AGC) scheme for a two-area power system using a particle swarm optimization (PSO) tuned fuzzy PID controller. A linearized model of the two-area power system is presented. A fuzzy PID controller is used to regulate the area control error of each area. The gains of the fuzzy PID controller are optimized using PSO to minimize time-domain performance metrics. Simulation results show the PSO tuned fuzzy PID controller provides better dynamic response than a conventional PSO PID controller, with lower error and faster settling time. Comparisons of tie-line power deviation also show improved performance with the PSO tuned fuzzy approach. The paper concludes the proposed method efficiently tunes fuzzy PID parameters
The document discusses the design of control system compensators using the root locus method (LGR) and frequency response (RF) methods. It covers introducing compensators to improve closed-loop response, different types of compensators (lead, lag, lead-lag), and the process for designing lead compensators using root locus graphs. An example is provided to illustrate how to design a lead compensator to place dominant closed-loop poles at a desired location on the s-plane to meet specifications like damping ratio and natural frequency.
Artificial Intelligent and meta-heuristic Control Based DFIG model Considered...IRJET Journal
This document summarizes a research paper that investigates different control methods for load frequency control in a multi-area power system incorporating wind energy from doubly fed induction generators. The control methods analyzed include PI control, PI control tuned with particle swarm optimization, and fuzzy logic control. MATLAB simulations are conducted on a 4-area power system consisting of both thermal and hydro power plants as well as DFIG-based wind power. Results show that all control methods are able to regulate tie line power and frequency to zero steady state values, but settling times differ between the methods.
Enhancement of Power System Performance by Optimal Placement of Distributed G...IRJET Journal
This document presents a comparative performance analysis of different control schemes for load frequency control in a multi-area power system incorporating wind energy conversion systems using doubly fed induction generators (DFIGs). The control schemes analyzed are PI control, PI control tuned using particle swarm optimization (PSO), and fuzzy logic control. MATLAB simulation results show the tie line power flow and frequency deviations for different control scenarios and cases. The scenarios consider different combinations of thermal, hydro, and DFIG systems across 4 areas. The results indicate that fuzzy logic control provides the fastest system response in the scenario with higher system complexity, while PSO-tuned PI control performs best in the scenario with lower complexity. The analysis focuses on minimizing the settling time as the primary
Optimal design & analysis of load frequency control for two interconnecte...ijctet
This document summarizes a research paper that proposes using Particle Swarm Optimization (PSO) to tune the parameters of PID controllers for Automatic Load Frequency Control (ALFC) in a system of two interconnected power generation areas. It describes modeling the two-area system and the objectives of ALFC to maintain frequency and distribute load. PSO is introduced as a technique to explore the search space to maximize objective functions by updating particle velocities and positions. The paper presents simulation results comparing the tuned PID controller performance to untuned controllers.
The document discusses synchronized phasor measurements in electric power systems and their applications. Precise synchronization of phasor measurements across substations separated by hundreds of miles enables a consistent description of the power system state. GPS provides an ideal synchronization source. Synchronized phasors can improve state estimation algorithms, provide dynamic state estimates, enhance control techniques, and improve protection concepts. The paper describes phasor measurement implementation and several uses including improved state estimation, control, detection of instability, and adaptive relaying.
1) Precise synchronization of phasor measurements across wide areas of the electric grid is important for monitoring system state, control, and protection. GPS provides an ideal synchronization source with accuracy of 1 microsecond or better.
2) Synchronized phasor measurements directly measure the system state vector and dynamic conditions, providing faster response than traditional state estimation. They can improve control schemes and adaptive relaying by providing real-time feedback across the entire system.
3) Detection of instability between two interconnected regions can be achieved using synchronized phasor measurements to predict angular stability based on the equal area criterion for a two-machine system.
1995 analysis of piezo actuators in translation constructionspmloscholte
1) A translation stage using piezo stacks as actuators was developed to generate displacements with nanometer accuracy over a dynamic range of 10 micrometers. Capacitive sensors were able to measure displacements with subnanometer resolution.
2) Using the high precision measurements from the capacitive sensors, the displacement properties of the piezo actuator in the translation stage could be characterized with great accuracy when different voltages were applied.
3) A model is presented to describe the general behavior of a piezo actuator in a translation stage, and the hysteresis behavior observed in the piezo actuator is found to have point symmetry properties and branches that can be described by third-order polynomials.
Gas chromatography in environmental analysis driscoll 2004 lDr. Jack Driscoll
The document provides an overview of gas chromatography (GC) theory and instrumentation for environmental analysis. Key points:
1) GC separates compounds based on their partitioning between a stationary and mobile phase. Retention time depends on a compound's vapor pressure and solubility in the stationary phase.
2) Column selection involves choosing a stationary phase that matches sample polarity. Capillary columns provide higher efficiency than packed columns.
3) Typical GC hardware includes an injector, column, carrier gas, oven, detector, and amplifier. The detector measures separated components and produces a chromatogram.
This document presents a comparative study of monotonic and non-monotonic phase linear time-invariant (LTI) systems using an improved analytical PID controller design. It discusses using gain crossover frequency and phase margin specifications to design controllers that ensure minimum phase margin inside the desired bandwidth. For the comparative study, it uses bode stability criterion, Nyquist stability criterion, and unit step response. It presents a case study comparing the design of controllers for a buck converter system, which exhibits a non-monotonic phase response, using both monotonic and non-monotonic design techniques. The results show that treating the non-monotonic system as monotonic leads to an overvalued proportional gain and undervalued derivative gain in the PID controller.
1. The document discusses numerical criteria for robust control of continuous systems when the system model is not precisely known.
2. It considers two classes of uncertain systems - systems with structured perturbations defined by state equations, and systems with unstructured disturbances involving unknown nonlinear functions.
3. For each class, sufficient conditions for asymptotic stability are established and illustrated with numerical examples, showing improvements over past works. The results provide guidance for robust controller synthesis.
This document provides an introduction to robust control concepts including Nyquist stability, gain and phase margins, loop transfer recovery, and H-infinity control. It discusses how the Nyquist stability criterion can be used to determine stability graphically and define gain and phase margins. Loop transfer recovery is introduced as a method to modify optimal LQG controllers to improve robustness. The H-infinity control problem is formulated to achieve robust performance and disturbance rejection. The Glover-Doyle algorithm provides a solution to the H-infinity problem by solving Riccati equations. Properties of H-infinity controllers include optimality, number of states, and pole-zero cancellation.
Non integer order controller based robust performance analysis of a conical t...Editor Jacotech
The design of robust controller for any non linear process is a
challenging task because of the presence of various types of
uncertainties. In this paper, various design methods of robust
PID controller for the level control of conical tank are
discussed. Uncertainties are of different types, among that
structured uncertainty of 30% is introduced to the nominal
plant for analysing the robustness. As a first step, the control
of level is done by using conventional integer order controller
for both nominal and uncertain system. Then, the control is
done by means of Fractional Order Proportional Integral
Derivative (FOPID) controller for achieving robustness. With
the help of time series parameters, a comparison is made
between conventional PID and FOPID with respect to the
simulated output using MATLAB and also analyzed the
robustness.
Similar to Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem (20)
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
This document presents an optimal general type-2 fuzzy controller (OGT2FC) for controlling traffic signal scheduling and phase succession to minimize wait times and average queue length. The OGT2FC uses a combination of general type-2 fuzzy logic sets and the Modified Backtracking Search Algorithm (MBSA) to optimize the membership function parameters. Simulation results show the OGT2FC performs better than conventional type-1 fuzzy controllers in regulating urban traffic flow.
Embedded intelligent adaptive PI controller for an electromechanical systemISA Interchange
In this study, an intelligent adaptive controller approach using the interval type-2 fuzzy neural network (IT2FNN) is presented. The proposed controller consists of a lower level proportional - integral (PI) controller, which is the main controller and an upper level IT2FNN which tuning on-line the parameters of a PI controller. The proposed adaptive PI controller based on IT2FNN (API-IT2FNN) is implemented practically using the Arduino DUE kit for controlling the speed of a nonlinear DC motor-generator system. The parameters of the IT2FNN are tuned on-line using back-propagation algorithm. The Lyapunov theorem is used to derive the stability and convergence of the IT2FNN. The obtained experimental results, which are compared with other controllers, demonstrate that the proposed API-IT2FNN is able to improve the system response over a wide range of system uncertainties.
State of charge estimation of lithium-ion batteries using fractional order sl...ISA Interchange
This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov’s stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estima- tion method is effective, and the designed observers have good performance.
Fractional order PID for tracking control of a parallel robotic manipulator t...ISA Interchange
This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB co-simulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.
Fuzzy logic for plant-wide control of biological wastewater treatment process...ISA Interchange
The application of control strategies is increasingly used in wastewater treatment plants with the aim of improving effluent quality and reducing operating costs. Due to concerns about the progressive growth of greenhouse gas emissions (GHG), these are also currently being evaluated in wastewater treatment plants. The present article proposes a fuzzy controller for plant-wide control of the biological wastewater treatment process. Its design is based on 14 inputs and 6 outputs in order to reduce GHG emissions, nutrient concentration in the effluent and operational costs. The article explains and shows the effect of each one of the inputs and outputs of the fuzzy controller, as well as the relationship between them. Benchmark Simulation Model no 2 Gas is used for testing the proposed control strategy. The results of simulation results show that the fuzzy controller is able to reduce GHG emissions while improving, at the same time, the common criteria of effluent quality and operational costs.
Design and implementation of a control structure for quality products in a cr...ISA Interchange
In recent years, interest for petrochemical processes has been increasing, especially in refinement area. However, the high variability in the dynamic characteristics present in the atmospheric distillation column poses a challenge to obtain quality products. To improve distillates quality in spite of the changes in the input crude oil composition, this paper details a new design of a control strategy in a conventional crude oil distillation plant defined using formal interaction analysis tools. The process dynamic and its control are simulated on Aspen HYSYS dynamic environment under real operating conditions. The simulation results are compared against a typical control strategy commonly used in crude oil atmospheric distillation columns.
Model based PI power system stabilizer design for damping low frequency oscil...ISA Interchange
This paper explores a two-level control strategy by blending a local controller with a centralized controller for the low frequency oscillations in a power system. The proposed control scheme provides stabilization of local modes using a local controller and minimizes the effect of inter-connection of sub-systems performance through a centralized control. For designing the local controllers in the form of proportional-integral power system stabilizer (PI-PSS), a simple and straight forward frequency domain direct synthesis method is considered that works on use of a suitable reference model which is based on the desired requirements. Several examples both on one machine infinite bus and multi-machine systems taken from the literature are illustrated to show the efficacy of the proposed PI-PSS. The effective damping of the systems is found to be increased remarkably which is reflected in the time-responses; even unstable operation has been stabilized with improved damping after applying the proposed controller. The proposed controllers give remarkable improvement in damping the oscillations in all the illustrations considered here and as for example, the value of damping factor has been increased from 0.0217 to 0.666 in Example 1. The simulation results obtained by the proposed control strategy are favorably compared with some controllers prevalent in the literature.
A comparison of a novel robust decentralized control strategy and MPC for ind...ISA Interchange
This document summarizes a research article that compares a novel decentralized control strategy based on override control to a model predictive controller (MPC) for controlling an industrial high purity methanol distillation column. Both controllers were able to maintain tight product purity and high recovery specifications under disturbances. The MPC provided tighter control of product purity but used more energy, while the proposed override control provided tighter recovery control and had lower costs. An economic analysis showed the optimal choice depends on factors like energy costs.
Fault detection of feed water treatment process using PCA-WD with parameter o...ISA Interchange
This research article proposes a new fault detection algorithm called PCA-WD that combines wavelet denoising (WD) with principal component analysis (PCA) to improve fault detection performance for feed water treatment processes (FWTP). The algorithm is applied to operational data from a FWTP sustaining two 1000 MW coal-fired power plants. Parameter selection for the PCA-WD algorithm is formulated as an optimization problem solved using particle swarm optimization to determine optimal parameters automatically rather than relying on individual experience. Results show that WD effectively reduces noise in PCA statistics, improving fault detection. The optimized PCA-WD algorithm outperforms classical PCA and a related method in detecting various faults in the FWTP data.
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...ISA Interchange
As higher requirements are proposed for the load regulation and efficiency enhancement, the control performance of boiler-turbine systems has become much more important. In this paper, a novel robust control approach is proposed to improve the coordinated control performance for subcritical boiler-turbine units. To capture the key features of the boiler-turbine system, a nonlinear control-oriented model is established and validated with the history operation data of a 300 MW unit. To achieve system linearization and decoupling, an adaptive feedback linearization strategy is proposed, which could asymptotically eliminate the linearization error caused by the model uncertainties. Based on the linearized boiler-turbine system, a second-order sliding mode controller is designed with the super-twisting algorithm. Moreover, the closed-loop system is proved robustly stable with respect to uncertainties and disturbances. Simulation results are presented to illustrate the effectiveness of the proposed control scheme, which achieves excellent tracking performance, strong robustness and chattering reduction.
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...ISA Interchange
Clock synchronization is an issue of vital importance in applications of wireless sensor networks (WSNs). This paper proposes a proportional integral estimator-based protocol (EBP) to achieve clock synchronization for wireless sensor networks. As each local clock skew gradually drifts, synchronization accuracy will decline over time. Compared with existing consensus-based approaches, the proposed synchronization protocol improves synchronization accuracy under time-varying clock skews. Moreover, by restricting synchronization error of clock skew into a relative small quantity, it could reduce periodic re-synchronization frequencies. At last, a pseudo-synchronous implementation for skew compensation is introduced as synchronous protocol is unrealistic in practice. Numerical simulations are shown to illustrate the performance of the proposed protocol.
An artificial intelligence based improved classification of two-phase flow patte...ISA Interchange
Flow pattern recognition is necessary to select design equations for finding operating details of the process and to perform computational simulations. Visual image processing can be used to automate the interpretation of patterns in two-phase flow. In this paper, an attempt has been made to improve the classification accuracy of the flow pattern of gas/ liquid two- phase flow using fuzzy logic and Support Vector Machine (SVM) with Principal Component Analysis (PCA). The videos of six different types of flow patterns namely, annular flow, bubble flow, churn flow, plug flow, slug flow and stratified flow are re- corded for a period and converted to 2D images for processing. The textural and shape features extracted using image processing are applied as inputs to various classification schemes namely fuzzy logic, SVM and SVM with PCA in order to identify the type of flow pattern. The results obtained are compared and it is observed that SVM with features reduced using PCA gives the better classification accuracy and computationally less intensive than other two existing schemes. This study results cover industrial application needs including oil and gas and any other gas-liquid two-phase flows.
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...ISA Interchange
In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.
Load estimator-based hybrid controller design for two-interleaved boost conve...ISA Interchange
This paper is devoted to the development of a hybrid controller for a two-interleaved boost converter dedicated to renewable energy and automotive applications. The control requirements, resumed in fast transient and low input current ripple, are formulated as a problem of fast stabilization of a predefined optimal limit cycle, and solved using hybrid automaton formalism. In addition, a real time estimation of the load is developed using an algebraic approach for online adjustment of the hybrid controller. Mathematical proofs are provided with simulations to illustrate the effectiveness and the robustness of the proposed controller despite different disturbances. Furthermore, a fuel cell system supplying a resistive load through a two-interleaved boost converter is also highlighted.
Effects of Wireless Packet Loss in Industrial Process Control SystemsISA Interchange
Timely and reliable sensing and actuation control are essential in networked control. This depends on not only the precision/quality of the sensors and actuators used but also on how well the communications links between the field instruments and the controller have been designed. Wireless networking offers simple deployment, reconfigurability, scalability, and reduced operational expenditure, and is easier to upgrade than wired solutions. However, the adoption of wireless networking has been slow in industrial process control due to the stochastic and less than 100% reliable nature of wireless communications and lack of a model to evaluate the effects of such communications imperfections on the overall control performance. In this paper, we study how control performance is affected by wireless link quality, which in turn is adversely affected by severe propagation loss in harsh industrial environments, co-channel interference, and unintended interference from other devices. We select the Tennessee Eastman Challenge Model (TE) for our study. A decentralized process control system, first proposed by N. Ricker, is adopted that employs 41 sensors and 12 actuators to manage the production process in the TE plant. We consider the scenario where wireless links are used to periodically transmit essential sensor measurement data, such as pressure, temperature and chemical composition to the controller as well as control commands to manipulate the actuators according to predetermined setpoints. We consider two models for packet loss in the wireless links, namely, an independent and identically distributed (IID) packet loss model and the two-state Gilbert-Elliot (GE) channel model. While the former is a random loss model, the latter can model bursty losses. With each channel model, the performance of the simulated decentralized controller using wireless links is compared with the one using wired links providing instant and 100% reliable communications. The sensitivity of the controller to the burstiness of packet loss is also characterized in different process stages. The performance results indicate that wireless links with redundant bandwidth reservation can meet the requirements of the TE process model under normal operational conditions. When disturbances are introduced in the TE plant model, wireless packet loss during transitions between process stages need further protection in severely impaired links. Techniques such as re-transmission scheduling, multi-path routing and enhanced physical layer design are discussed and the latest industrial wireless protocols are compared.
Fault Detection in the Distillation Column ProcessISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H1 framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.
A KPI-based process monitoring and fault detection framework for large-scale ...ISA Interchange
Large-scale processes, consisting of multiple interconnected sub-processes, are commonly encountered in industrial systems, whose performance needs to be determined. A common approach to this problem is to use a key performance indicator (KPI)-based approach. However, the different KPI-based approaches are not developed with a coherent and consistent framework. Thus, this paper proposes a framework for KPI-based process monitoring and fault detection (PM-FD) for large-scale industrial processes, which considers the static and dynamic relationships between process and KPI variables. For the static case, a least squares-based approach is developed that provides an explicit link with least-squares regression, which gives better performance than partial least squares. For the dynamic case, using the kernel re- presentation of each sub-process, an instrument variable is used to reduce the dynamic case to the static case. This framework is applied to the TE benchmark process and the hot strip mill rolling process. The results show that the proposed method can detect faults better than previous methods.
An adaptive PID like controller using mix locally recurrent neural network fo...ISA Interchange
Being complex, non-linear and coupled system, the robotic manipulator cannot be effectively controlled using classical proportional integral derivative (PID) controller. To enhance the effectiveness of the conventional PID controller for the nonlinear and uncertain systems, gains of the PID controller should be conservatively tuned and should adapt to the process parameter variations. In this work, a mix locally recurrent neural network (MLRNN) architecture is investigated to mimic a conventional PID controller which consists of at most three hidden nodes which act as proportional, integral and derivative node. The gains of the mix locally recurrent neural network based PID (MLRNNPID) controller scheme are initi- alized with a newly developed cuckoo search algorithm (CSA) based optimization method rather than assuming randomly. A sequential learning based least square algorithm is then investigated for the on- line adaptation of the gains of MLRNNPID controller. The performance of the proposed controller scheme is tested against the plant parameters uncertainties and external disturbances for both links of the two link robotic manipulator with variable payload (TL-RMWVP). The stability of the proposed controller is analyzed using Lyapunov stability criteria. A performance comparison is carried out among MLRNNPID controller, CSA optimized NNPID (OPTNNPID) controller and CSA optimized conventional PID (OPTPID) controller in order to establish the effectiveness of the MLRNNPID controller.
A method to remove chattering alarms using median filtersISA Interchange
Chattering alarms are the most found nuisance alarms that will probably reduce the usability and result in a confidence crisis of alarm systems for industrial plants. This paper addresses the chattering alarm reduction using median filters. Two rules are formulated to design the window size of median filters. If the alarm probability is estimated using process data, one rule is based on the probability of alarms to satisfy some requirements on the false alarm rate, or missed alarm rate. If there are only historical alarm data available, the other rule is based on percentage reduction of chattering alarms using alarm duration distribution. Experimental results for industrial cases testify that the proposed method is effective.
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Progress Report - Qualcomm AI Workshop - AI available - everywhereAI summit 1...Holger Mueller
Qualcomm invited analysts and media for an AI workshop, held at Qualcomm HQ in San Diego, June 26th. My key takeaways across the different offerings is that Qualcomm us using AI across its whole portfolio. Remarkable to other analyst summits was 50% of time being dedicated to demos / hands on exeriences.
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Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem
1. ISA Transactions 39 (2000) 419±431
www.elsevier.com/locate/isatrans
Robust PID tuning strategy for uncertain plants based on the
Kharitonov theorem
Ying J. Huang *, Yuan-Jay Wang
Institute of Electrical Engineering, Yuan Ze University, 135 Far-East RD., Chungli, 320 Taiwan
Abstract
In this paper, the Kharitonov theorem for interval plants is exploited for the purpose of synthesizing a stabilizing
controller. The aim here is to develop a controller to simultaneously stabilize the four Kharitonov-de®ned vortex
polynomials. Di€erent from the prevailing works, the controller is designed systematically and graphically through the
search of a non-conservative Kharitonov region in the controller coecient parameter plane. The region characterizes
all stabilizing PID controllers that stabilize an uncertain plant. Thus the relationship between the Kharitonov region
and the stabilizing controller parameters is manifest. Extensively, to further guarantee the system with certain robust
safety margins, a virtual gain phase margin tester compensator is added. Stability analysis is carried out. The control
system is proved to maintain robustness at least to the pre-speci®ed margins. The synthesized controller with coe-
cients selected from the obtained non-conservative Kharitonov region can stabilize the concerned uncertain plants and
ful®ll system speci®cations in terms of gain margins and phase margins. # 2000 Elsevier Science Ltd. All rights
reserved.
Keywords: Kharitonov theorem; Parameter plane; PID controller; Interval plants
1. Introduction theorem [3] and box theorem [4] then suggested
that the set of transfer functions generated by
In the past years, many important results in the changing its perturbed coecients in the pre-
area of robust control for uncertain plants have scribed ranges corresponds to a box in the para-
been based on the Kharitonov's celebrated theorem meter space and is referred to ``interval plants''.
[1±6]. The theorem investigates the stability char- Further, the Kharitonov theorem is generalized to
acteristics of the interval systems via four vortex obtain a ``Kharitonov region'' [5,6] in the complex
polynomials with real coecients varying in a plane for the robust stability of linear uncertain
bounded range. Kharitonov extended his results systems. In order to guarantee the uncertain sys-
into interval polynomials with complex coecients tems a stronger stability characteristic, a virtual
later. Based on the Kharitonov theorem, the edge compensator was introduced such that the closed
loop systems can maintain a suitable gain margin
(Gm) and phase margin (Pm) [7]. Recently, atten-
* Corresponding author. Tel.: +886-3-4638800 ext. 410; fax: tion has been given to the formulation of P, PI
+886-3-4633326. and PID controllers to stabilize an interval plant
E-mail address: eeyjh@saturn.yzu.edu.tw (Y.J. Huang). family [8].
0019-0578/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0019-0578(00)00026-4
2. 420 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
Despite the various results concerning the synthesizing ®xed and low order controllers, that
robust stability for uncertain plants, existing simultaneously stabilize a given interval plant
methods in the area of parametric robust control family in the parametric robust control area, is
are of analysis type which are passively concerned bene®cial. To achieve this goal, a systematic and
only if a family of Kharitonov polynomials are graphical robust controller design procedure is
Hurwitz or not. It turns out that a technique for established based on the Kharitonov-de®ned vortex
Fig. 1. Feedback control system with a gain phase margin tester.
Fig. 2. Stability boundary for GI …s†.
3. Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431 421
polynomials. A speci®c Kharitonov region can be also ful®lls several speci®cations simultaneously.
obtained in the parameter plane using the para- For every one of the four vortex polynomials, it
meters of the controller as the axes. Therefore, the suces to plot the constant gain margin and con-
stability characteristic for the uncertain system in stant phase margin boundaries in the parameter
question, with respect to the adjustment of the plane. The overlapped region of speci®cation-
controller parameters, is obvious. The aforemen- satis®ed area for each Kharitonov polynomial is
tioned region constitutes the whole admissible the useful parameter area for the selection of con-
stabilizing PID controllers. troller parameters, where the whole uncertain
Further, for the purpose of endowing the system, plant can be stabilized.
a robust performance in the case of parameter The advantage of the developed method is that
variation, it is of interest to insert speci®ed gain the procedure to design a robust stabilizing con-
margins and phase margins into the characteristic troller is systematic and straightforward. A trial
equations, such that the resulted system will and error process is unnecessary. All exploitable
maintain at least the pre-speci®ed robust margins. controller parameters can be obtained from the
The proposed method in this paper not only pro- non-conservative Kharitonov region. Controllers
vides a necessary and sucient condition for the selected from the region guarantee the uncertain
Hurwitz stability of an interval polynomial set but systems a pre-speci®ed safety margin. Moreover,
Fig. 3. Stability boundary for G1 …s† with di€erent value of KD .
4. 422 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
the intrinsic property of system stability corre- ``interval plants'' [4]. The controller C(s) is
sponding to the drift of the polynomial coecients designed to simultaneously stabilize the system
can be analyzed manifestly in the demonstrated and track the command signal. The gain phase
parameter planes. margin tester AeÀj is applied in the forward path,
where A and are subject to gain margin and
phase margin speci®cations, respectively. Let
2. Mathematical description
F…s† ˆ 1 ‡ AeÀj C…s†G…s† …P†
Consider the feedback control system as shown
in Fig. 1. The general expression of the plant G…s† is and
a0 ‡ a1 s ‡ a2 s2 ‡ Á Á Á ‡ am sm Fi …s† ˆ 1 ‡ AeÀj C…s†Gi …s†Y i ˆ 1Y Á Á Á Y 4Y …Q†
G…s† ˆ Y …I†
b0 ‡ b1 s ‡ b2 s 2 ‡ Á Á Á bn s n
where Gi …s† are the edge interval plants. If the
where am Tˆ 0, bn Tˆ 0, ai P ‰aÀ Y a‡ Š, bj P ‰bÀ Y b‡ Š,
i i j j controller C…s† can be designed with imposed spe-
and n5m. A set of transfer functions can be gen- ci®cations on gain margins and phase margins,
erated by changing the perturbed coecients in then it is of no doubt that the compensated system
the prescribed ranges, which correspond to boxes will maintain robust performance to some degree.
in the parameter plane. This is referred to as To show this, we present the following theorem.
Fig. 4. A speci®c Kharitonov region (hatched area) in the KP ÀKI plane.
5. Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431 423
Theorem 1. Consider the control system as shown in p1 …s† ˆ dÀ ‡ dÀ s ‡ d‡ s2 ‡ d‡ s3 ‡ dÀ s4 ‡ Á Á Á Y
0 1 2 3 4 …S†
Fig. 1, with the de®nitions (1) and (2), the entire
family G…s† is stabilizable by a controller C…s† if and
only if each interval plant Gi …s† is stabilizable by p2 …s† ˆ dÀ ‡ d‡ s ‡ d‡ s2 ‡ dÀ s3 ‡ dÀ s4 ‡ Á Á Á Y
0 1 2 3 4 …T†
that same controller C…s†.
p3 …s† ˆ d‡ ‡ dÀ s ‡ dÀ s2 ‡ d‡ s3 ‡ d‡ s4 ‡ Á Á Á Y
0 1 2 3 4 …U†
Proof. Consider the characteristic polynomial of
the closed-loop system shown in Fig. 1, i.e. the
numerator of F…s†, p4 …s† ˆ d‡ ‡ d‡ s ‡ dÀ s2 ‡ dÀ s3 ‡ d‡ s4 ‡ Á Á Á Y …V†
0 1 2 3 4
ˆ
n
p…s† ˆ di s i Y …R†
iˆ0 which are associated with Gi …s† in (3), respectively.
It follows that the entire family is Hurwitz stable
where di are the characteristic coecients, and if and only if the four vortex polynomials (4)±(7)
dÀ 4di 4d‡ . According to the Kharitonov theo-
i i are all Hurwitz stable. Hence one can determine
rem [1,4], every interval polynomial in the family all possible stabilizing controllers Ci …s† for each
is Hurwitz if and only if the following four Khar- vortex polynomial, and then take their intersection
„ „ „
itonov polynomials are Hurwitz, C…s† ˆ C1 …s† C2 …s† C3 …s† C4 …s† to obtain the
Fig. 5. Output responses for the PID controlled interval system.
6. 424 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
non-conservative robust parametric controller for The problem of characterizing all stabilizing PID
the uncertain plant G…s†. controllers for the entire family G…s† is to deter-
mine KP , KI and KD such that all the closed loop
In the following section, the controller sets, which characteristic polynomials are Hurwitz.
stabilize the uncertain plant, are demonstrated to lie Consider the same uncertain system in [9],
within a speci®c Kharitonov region in the parameter
plane. A strict Kharitonov region, which guarantees 5X2…s ‡ 2†
the system a robust margin, can be obtained. G…s† ˆ X …IH†
s… s3 ‡ b2 s2 ‡ b1 s ‡ b0 †
3. PID controller design for uncertain systems Assume that the coecients b0 Y b1 and b2 of the
denominator lie within the following bounds, where
For the uncertain plant (1), a PID controller 9X54b0 411X5Y 124b1 415, and 3X54b2 44X8. The
C…s† is developed with the exploitation of a gain desired speci®cations for the control system are sup-
phase margin tester in the forward loop. Let the posed to be 5db4Gm410dbY and 30 4Pm460 . By
controller C…s† be inserting a gain phase margin tester AeÀj in the
KD s2 ‡ KP s ‡ KI forward loop, it is found that the characteristic
C…s† ˆ X …W† polynomial is
s
Fig. 6. A speci®cation-oriented parameter area for G1 …s† with pre-speci®ed robust margins in gain and phase.
7. Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431 425
p…s† ˆ s5 ‡ b2 s4 ‡ b1 s3 ‡ b0 s2 p3 …s† ˆ s5 ‡ 3X5s4 ‡ 15s3 ‡ 11X5s2
 Â
‡ 5X2KD s3 ‡ …5X2KP ‡ 10X4KD †s2 ‡ 5X2KD s3 ‡ …5X2KP ‡ 10X4KD †s2
à Ã
‡ …5X2KI ‡ 10X4KP †s ‡ 10X4KI ‰A…™os À j sin †ŠX ‡ …5X2KI ‡ 10X4KP †s ‡ 10X4KI ‰A…™os À j sin †ŠY
…II† …IR†
From (11), in four Kharitonov polynomials result p4 …s† ˆ s5 ‡ 4X8s4 ‡ 15s3 ‡ 9X5s2
Â
p1 …s† ˆ s5 ‡ 4X8s4 ‡ 12s3 ‡ 9X5s2 ‡ 5X2KD s3 ‡ …5X2KP ‡ 10X4KD †s2
 Ã
‡ 5X2KD s3 ‡ …5X2KP ‡ 10X4KD †s2 ‡ …5X2KI ‡ 10X4KP †s ‡ 10X4KI ‰A…™os À j sin †ŠX
à …IS†
‡ …5X2KI ‡ 10X4KP †s ‡ 10X4KI ‰A…™os À j sin †ŠY
…IP†
The aim here is to ®nd that all possible sets of
p2 …s† ˆ s5 ‡ 3X5s4 ‡ 12s3 ‡ 11X5s2 KP , KI , and KD , which make the characteristic
 polynomials (12)±(15) to be Hurwitz stable. Take
‡ 5X2KD s3 ‡ …5X2KP ‡ 10X4KD †s2
à p1 …s† for instance, substituting s ˆ j3 and equating
‡ …5X2KI ‡ 10X4KP †s ‡ 10X4KI ‰A…™os À j sin †ŠY the real part and imaginary part of (12) to zero,
…IQ† respectively, one obtains
Fig. 7. A non-conservative Kharitonov region in the parameter plane with pre-speci®ed gain margin and phase margin speci®cations.
8. 426 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
C1 D2 À C2 D1 D2 ˆ sm…q1 …3Y KD ††Y …PQ†
KP ˆ Y …IT†
B1 C2 À B2 C1
and
D1 B2 À D2 B1
KI ˆ Y …IU†
B1 C2 À B2 C1 q1 …3Y KD † ˆ 4X834 À 5X2KD Asin33
À …11X5 ‡ 10X4KD A™os†32
where  Ã
j 35 À …12 ‡ 5X2KD A™os†33 ‡ 10X4KD Asin32 Y
B1 ˆ ‚e…q2 …3††A™os ‡ sm…q2 …3††AsinY …IV† …PR†
C1 ˆ ‚e…q3 …3††A™os ‡ sm…q3 …3††AsinY …IW† q2 …3† ˆ À5X232 ‡ j10X43Y …PS†
D1 ˆ ‚e…q1 …3Y KD ††Y …PH† q3 …3† ˆ 10X4 ‡ j5X23X …PT†
B2 ˆ sm…q2 …3††A™os À ‚e…q2 …3††AsinY …PI†
Referring to (16) and (17), JÁB1 C2 À B2 C1 is
C2 ˆ sm…q3 …3††A™os À ‚e…q3 …3††AsinY …PP† the Jacobian. Let KD ˆ 0X01Y A ˆ 1, and ˆ 0, a
Fig. 8. Bode diagrams for the PID controlled uncertain plants G1 …s† and G2 …s†.
9. Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431 427
stability boundary is plotted as shown in Fig. 2. pi …s†, i ˆ 2, 3, 4 are portrayed in Fig. 4, and Ji
The stability characteristics of the considered (i ˆ 1, 2, 3, 4) are the corresponding Jacobian of
polynomial are totally di€erent to the left and each vortex polynomial. We can, therefore, obtain
right of the boundary. Resorting to [10,11], it is a speci®c Kharitonov region in the plotted para-
concluded that if J b 0, then to the left of the sta- meter plane by ®nding the overlapped region, the
bility boundary facing the direction in which 3 hatched area, as shown in Fig. 4. The overlapped
increases is the stable area. Similarly, to the right area of the boundaries constitutes the entire fea-
of the stability boundary facing the direction in sible controller sets that can stabilize each parti-
which 3 increases is the stable region while J ` 0. cular selected edge polynomial. Within it, the KP ,
Then a graphical stability region in the controller KI , and KD of the PID controller can be arbitrarily
coecient parameter space as seen in Fig. 2 can be selected. To show that the obtained controller
obtained. For various KD , a family of stability parameter area can eciently compensate the
boundaries is portrayed in Fig. 3. It is realized that uncertain plant, a representative point P1 (KP ˆ 2,
with a larger KD , the stability region for the con- KI ˆ 1, KD ˆ 0X01) is picked for demonstration.
sidered plant would be larger. The resulting step responses are shown in Fig. 5. It
For example, choose KD ˆ 0X01. Following the is obvious that the designed controller stabilizes
same procedure, the other stability boundaries for all the four interval plants.
Fig. 9. Bode diagrams for the PID controlled uncertain plants G3 …s† and G4 …s†.
10. 428 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
Table 1 end, the constant gain margin boundaries and
Gain margins and phase margins for the family of uncertain constant phase margin boundaries are plotted in
polynomials with designed PID controller (KP ˆ 1X72, the KP ÀKI plane. It isolates speci®ed gain margin
KI ˆ 0X05, KD ˆ 0X01)
and phase margin regions in the parameter plane
b2 b1 b0 Gain margin (db) Phase margin (deg) to allow ¯exible choice of the controller para-
3.5 12 9.5 5.5293 42.1600
meters. For the edge polynomial p1 …s†, the hatched
11.5 5.1832 50.6060 area as shown in Fig. 6 is the suitable area for
selecting the stabilizing controller coecients.
15 9.5 9.0530 44.9010
11.5 8.7540 54.0440 Concurrently, system speci®cations can be
achieved.
4.8 12 9.5 6.0765 30.5700 A non-conservative Kharitonov region is
11.5 6.0978 38.0700 obtained, as seen in Fig. 7, by searching for the
15 9.5 10.0000 37.9260 intersectional region of the speci®cation-limited
11.5 9.9410 51.7380 areas from all edge polynomials pi …s†, i ˆ 1, 2, 3, 4.
This region constitutes all the possible stabilizing
PID controller sets for system with robust safety
margins. In other words, the KP , KI , and KD can
Successively, we provide the uncertain system be readily chosen from the non-conservative
with a robust performance through specifying the Kharitonov region. A representative point P2
gain margins and phase margins. Toward this (KP ˆ 1X72, KI ˆ 0X05, KD ˆ 0X01) is selected.
Fig. 10. The variation of gain margins subject to parameteric change of the control system with the selected PID controller
(KP ˆ 1X72, KI ˆ 0X05, KD ˆ 0X01).
11. Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431 429
Bode diagrams are plotted in Figs. 8 and 9. It is conservative Kharitonov region in the coecient
veri®ed that the designed controller can really sta- plane.
bilize the interval system with robust margins. Output responses are shown in Fig. 12. For a
Gain margins and phase margins for the con- standard second system, the speci®cations in terms
sidered uncertain plant with designed PID con- of gain margin and phase margin are de®ned
troller (KP ˆ 1X72, KI ˆ 0X05, KD ˆ 0X01) are exactly corresponding to time domain perfor-
tabulated in Table. 1. The resulting gain margins mance requirement. However, for the considered
and phase margins subject to the uncertain coe- system, to inherit the same design idea, it is of
cients b0 , b1 , and b2 with the selected controller are much interest to de®ne interval gain margin and
illustrated in Fig. 10 and Fig. 11, respectively. phase margin speci®cations such that the time
Obviously, the speci®cations 5db4Gm410dbY and domain performance can also be guaranteed to
30 4Pm460 are satis®ed. Note that for any some degree. From Fig. 12, it is seen that the rise
other KD , the whole exploitable PID coecients time is less than 2 s and the maximum overshoot is
can be obtained, similarly, by searching the non- less than 50%. Henceforth, the linkage of the time
Fig. 11. The variation of phase margins subject to parameteric change of the control system with the selected PID controller
(KP ˆ 1X72, KI ˆ 0X05, KD ˆ 0X01).
12. 430 Y.J. Huang, Y.-J. Wang / ISA Transactions 39 (2000) 419±431
Fig. 12. Output responses for the four interval plants with KP ˆ 1X72, KI ˆ 0X05, KD ˆ 0X01.
performance and the gain and phase margin spe- The relationship between the varying coecients
ci®cations can also be evinced. of the uncertain characteristic polynomial and its
corresponding stable area in the plotted parameter
plane is studied. Simulation results reveal the
4. Conclusions remarkable performance and the e€ectiveness of
the developed method. In future work, the devel-
The so-called interval plants are often used for oped method will be extended to uncertain systems
dealing with uncertain dynamical systems. A with adjustable parameters and time delay, and
robustness stability analysis is useful to provide systems with inherent nonlinearities.
some ®nite checking of the stability of the closed
loop system so that one can design the controller to
stabilize the whole uncertain plant. However, much
of the present success in the control of interval
systems is restricted to the analysis issue. In this References
paper, a parameter plane method based on the
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