This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
Radial basis function neural network control for parallel spatial robotTELKOMNIKA JOURNAL
The derivation of motion equations of constrained spatial multibody system is an important problem of dynamics and control of parallel robots. The paper firstly presents an overview of the calculating the torque of the driving stages of the parallel robots using Kronecker product. The main content of this paper is to derive the inverse dynamics controllers based on the radial basis function (RBF) neural network control law for parallel robot manipulators. Finally, numerical simulation of the inverse dynamics controller for a 3-RRR delta robot manipulator is presented as an illustrative example.
The document is a lab report submitted by Mr. Yuvraj Singh for his Control System Lab course. It includes an index listing 8 experiments performed, along with the objectives, requirements, theory, programs, outputs, and results for Experiment 1 on introducing MATLAB software and Experiment 2 on obtaining a transfer function from zero-pole-gain parameters in MATLAB. The experiments involve modeling and analyzing first and second order control systems using MATLAB.
This document summarizes a research project on process identification using relay feedback tests. The project aims to identify low-order models like FOPDT and SOPDT from relay feedback data to enable performance assessment and controller tuning. A new identification method is proposed that uses neural networks to estimate the apparent deadtime from steady-state cycles. This deadtime and other parameters allow classification of the process model and parameter estimation for assessment and auto-tuning.
This document contains information about Kamalesh Karmakar, an assistant professor in the computer science department at Meghnad Saha Institute of Technology. It lists the algorithm topics he teaches, including algorithm analysis, design techniques, complexity theory, and more. It also provides references for algorithm textbooks and notes on time and space complexity analysis, asymptotic notation, and different algorithm design techniques like divide-and-conquer, dynamic programming, backtracking, and greedy methods.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Modern Control - Lec 03 - Feedback Control Systems Performance and Characteri...Amr E. Mohamed
The document summarizes key concepts about feedback control systems including:
- It defines the order of a system as the highest power of s in the denominator of the transfer function. First and second order systems are discussed.
- Standard test signals like impulse, step, ramp and parabolic are introduced to analyze the response of systems.
- The time response of systems has transient and steady-state components. Poles determine the transient response.
- For first order systems, the responses to unit impulse, step, and ramp inputs are derived. The step response reaches 63.2% of its final value after one time constant.
- For second order systems, the natural frequency, damping ratio, and poles are defined.
This document discusses discrete state space models. It begins with an introduction to state variable models and their generic structure. It then discusses various canonical forms for state space models including controllable, observable, and Jordan canonical forms. It also covers computing the characteristic equation, eigenvalues, state transition matrices using different techniques like inverse Laplace transform, similarity transformations, and Cayley-Hamilton theorem. Examples are provided to illustrate finding state space models from transfer functions and computing the state transition matrix.
This document provides definitions and explanations of key concepts in algorithm design and analysis including:
- Performance measurement is concerned with obtaining the space and time requirements of algorithms.
- An algorithm is a finite set of instructions that accomplishes a task given certain inputs and criteria.
- Time complexity refers to the amount of computer time needed for an algorithm to complete, while space complexity refers to the memory required.
- Common asymptotic notations like Big-O, Omega, and Theta are used to describe an algorithm's scalability.
- Divide-and-conquer and greedy algorithms are important design techniques that break problems into subproblems.
This document describes modeling and control of aircraft pitch dynamics. It presents:
1) The longitudinal equations of motion and state-space models of an aircraft's pitch.
2) Analysis of the open-loop system and design of an LQR controller for stable response.
3) Simulink modeling of the open-loop and closed-loop aircraft pitch systems.
Performance Assessment of Polyphase Sequences Using Cyclic Algorithmrahulmonikasharma
Polyphase Sequences (known as P1, P2, Px, Frank) exist for a square integer length with good auto correlation properties are helpful in the several applications. Unlike the Barker and Binary Sequences which exist for certain length and exhibits a maximum of two digit merit factor. The Integrated Sidelobe level (ISL) is often used to define excellence of the autocorrelation properties of given Polyphase sequence. In this paper, we present the application of Cyclic Algorithm named CA which minimizes the ISL (Integrated Sidelobe Level) related metric which in turn improve the Merit factor to a greater extent is main thing in applications like RADAR, SONAR and communications. To illustrate the performance of the P1, P2, Px, Frank sequences when cyclic Algorithm is applied. we presented a number of examples for integer lengths. CA(Px) sequence exhibits the good Merit Factor among all the Polyphase sequences that are considered.
This document summarizes a lab report on controlling a state-space system using multiple control methods. The lab explores controlling the pitch rate, speed change, and angle of attack outputs of a simulated aircraft system. Analyzing the system transfer functions showed the outputs have the same unstable eigenvalues. A state-space controller was designed using unrelated eigenvalues, failing to stabilize the system under impulse, step, and sine wave inputs. To stabilize the system, the original eigenvalues must be made negative.
Asymptotic features of Hessian Matrix in Receding Horizon Model Predictive Co...TELKOMNIKA JOURNAL
In this paper, Receding Horizon Model Predictive Control (RH-MPC) having a quadratic objective
function is studied through the Singular Value Decomposition (SVD) and Singular Vectors of its Hessian
Matrix. Contrary to the previous work, non-equal and medium sized control and prediction horizons are
considered and it is shown that the Singular Values converge to the open loop magnitude response of the
system and singular vectors contain the phase information. Earlier results focused on classical formulation
of Generalized Predictive Control (GPC), whereas, current work proves the applicability to modern
formulation. Although, method can easily be extended to MIMO systems, only SISO system examples
are presented.
1. A state variable representation uses state variables, inputs, and outputs to model dynamic systems. The state variables provide information about the internal state of the system.
2. The behavior of a system can be described by state equations that relate the time derivatives of the state variables to the inputs, state variables, and outputs.
3. Eigenvalues and eigenvectors, which are derived from state variable models, have many applications including vibration analysis, image recognition, and determining communication channel capacities.
This document discusses analyzing the time efficiency of recursive algorithms. It provides a general 5-step plan: 1) choose a parameter for input size, 2) identify the basic operation, 3) check if operation count varies, 4) set up a recurrence relation, 5) solve the relation to determine growth order. It then gives two examples - computing factorial recursively and solving the Tower of Hanoi puzzle recursively - to demonstrate applying the plan. The document also briefly discusses algorithm visualization using static or dynamic images to convey information about an algorithm's operations and performance.
This document provides an overview of time domain analysis techniques for control systems. It discusses common test inputs like impulse, step, and ramp functions used to characterize system performance. It describes how to determine a system's poles and zeros from its transfer function and use a pole-zero plot to understand system dynamics. Standard forms are presented for first and second order systems. Transient performance metrics like rise time, peak time, settling time, and overshoot are defined for characterizing step responses. The effects of poles and zeros on the system response are explained.
Here are the steps to solve for the transfer function G(s) = X2(s)/F(s) for the given system:
1. Draw the free body diagrams for both masses M1 and M2 showing all the forces acting on each mass.
2. Write the Newton's second law equation for M1:
(M1s2 + f1vs + k1)X1(s) - k2(X1(s) - X2(s)) = 0
3. Write the Newton's second law equation for M2:
-k2(X1(s) - X2(s)) + (M2s2 + f2vs + k
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
- The document details a state space solver approach for analog mixed-signal simulations using SystemC. It models analog circuits as sets of linear differential equations and solves them using the Runge-Kutta method of numerical integration.
- Two examples are provided: a digital voltage regulator simulation and a digital phase locked loop simulation. Both analog circuits are modeled in state space and simulated alongside a digital design to verify mixed-signal behavior.
- The state space approach allows modeling analog circuits without transistor-level details, improving simulation speed over traditional mixed-mode simulations while still capturing system-level behavior.
Low Power Adaptive FIR Filter Based on Distributed ArithmeticIJERA Editor
This paper aims at implementation of a low power adaptive FIR filter based on distributed arithmetic (DA) with
low power, high throughput, and low area. Least Mean Square (LMS) Algorithm is used to update the weight
and decrease the mean square error between the current filter output and the desired response. The pipelined
Distributed Arithmetic table reduces switching activity and hence it reduces power. The power consumption is
reduced by keeping bit-clock used in carry-save accumulation much faster than clock of rest of the operations.
We have implemented it in Quartus II and found that there is a reduction in the total power and the core dynamic
power by 31.31% and 100.24% respectively when compared with the architecture without DA table
Consider the following nonlinear system:
dx/dt = f(x) + g(x)u
Where x is an n-dimensional vector and f and g are sufficiently smooth vector fields.
The goal is to design a feedback control law u = α(x) that renders the origin globally asymptotically stable (GAS).
Backstepping provides a systematic approach to solve this problem by considering the system as a cascade of "pseudo" linear systems with intermediate virtual controls.
The procedure recursively constructs stabilizing functions and control laws to backstep through this cascade until the actual control input is determined.
This approach systematically cancels out the nonlinearities in f while preserving the desirable properties introduced by g
Control of non linear system using backsteppingeSAT Journals
Abstract The defining attribute of a servomechanism is that the controlled output of a mechanism is automatically compared with the controlling input. The difference between the settings or positions of the output and the input is called the error signal, which acts to bring the output to its desired value.The paper work shows the application of backstepping technique to stabilize a nonlinear dynamical system. Any nonlinear dynamical system can be stabilized only by means of Lyapunov function approach. In this approach backstepping technique is invariably adopted. In case of normal backstepping technique stabilizing function is designed at every step of dynamics starting from the output towards input. The Backstepping approach provides a recursive method for stabilizing the origin of a system in strict-feedback form. The controller contains the terms of system state variables, reference input & its derivatives, and error. The basic aim of the controller is to settle down error and its derivatives to zero. The controller is designed through Lyapunov based function so as to render strong closed loop stability.In the theory of control systems, Lyapunov functions are scalar functions that may be used to prove the stability of equilibrium of a control system. Keywords: Lyapunov function, backstepping, nonlinear system, stability, derivative
Adaptive predictive functional control of a class of nonlinear systemsISA Interchange
This document summarizes an adaptive predictive functional control algorithm for nonlinear systems.
1) It uses a concept called pseudo-partial derivative (PPD) to dynamically linearize the nonlinear system model based on input-output data.
2) It predicts future outputs using an internal model based on the estimated PPD.
3) Predictive functional control (PFC) is used to design the control algorithm, where only two coincidence points are used to calculate the manipulated variable.
4) The proposed algorithm provides bounded inputs/outputs and setpoint tracking without steady-state error using a simple structure that is easy to tune for real-time control of nonlinear systems.
Adaptive backstepping sliding mode control with fuzzy monitoring strategy for...ISA Interchange
This paper proposes an adaptive backstepping sliding mode control (ABSMC) law with a fuzzy monitoring strategy for tracking control of a class of nonlinear mechanical systems. The ABSMC scheme combines sliding mode control and backstepping techniques to ensure finite-time convergence of the tracking error to equilibrium. An adaptive control law is used to compensate for lumped perturbations. A fuzzy monitoring strategy improves adaptive capacity and softens the control signal. Numerical simulations demonstrate the effectiveness of the proposed control scheme.
Design of Nonlinear State Feedback Control Law for Inertia Wheel Pendulum Sys...Shubhobrata Rudra
This document describes a block backstepping control approach for stabilizing an inertia wheel pendulum system with 2 degrees of freedom and 1 control input. It presents the system model, defines new control variables using block backstepping, derives the control law, and shows simulation results demonstrating stabilization. The control law relies on invertibility of the system and asymptotically stabilizes the equilibrium. The approach can be extended to other underactuated systems and generalized to higher-order systems.
Design of Nonlinear State Feedback Control Law for Rotating Pendulum System: ...Shubhobrata Rudra
This document presents a block backstepping control approach for stabilizing a rotating pendulum system. It begins with an overview of the rotating pendulum dynamics and standard state space model. It then introduces the block backstepping control method, defining new control variables and their dynamics. This allows designing stabilizing functions and deriving the required control input to realize the desired closed loop dynamics. Simulation results demonstrate the control law stabilizes both the shaft position and pendulum position. The approach can be extended to other underactuated mechanical systems and generalized for higher degree of freedom systems.
Определение параметров средств отделения створок головного обтекателя ракеты-носителя. Презентация к лекции курса "Основы синтеза механических систем".
Материалы лекции курса "Динамика твёрдого тела и систем твёрдых тел". Построение уравнений движения систем со сферическими, универсальными и цилиндрическими шарнирами. Метод Й. Виттенбурга.
The document discusses models and experiments to analyze the tip-off rate dynamics of CubeSats during separation from deployers. A simplified model and complex ADAMS model were developed to simulate the effects of parameters like center of mass position, spring stroke, and gap between guide rails on tip-off rate. Ground experiments using laser sensors to measure angular velocities of a 3U CubeSat mock-up showed results that agreed satisfactorily with simulations. The models and experiments allow estimating tip-off rates to help design CubeSat deployers that minimize initial angular velocities.
The document presents a sliding mode control algorithm and adaptive nonlinear observer for regulating wheel slip in anti-lock braking systems for commercial vehicles. Simulation results using an ADAMS vehicle model show the new control approach can achieve a stopping distance of 54 meters from 60 mph, satisfying new regulations requiring shorter stopping distances. The algorithm holds tire slip near its peak to maximize braking force, and the observer estimates brake forces using a LuGre tire friction model.
Презентация к лекции "Движение твёрдого тела в случае Эйлера" курса Динамика твёрдого тела и систем тел. Рассматриваются следующие вопросы и понятия: эллипсоид энергии и эллипсоид инерции, полодии, перманентное вращение, неустойчивость вращения вокруг оси со средним моментом инерции, определение угловых скоростей и углов Эйлера, регулярная прецессия.
The document discusses active debris removal in space using tethered towing. The authors have developed a mathematical model of the attitude motion of a debris-tether-tug system. The model accounts for factors such as flexible appendages on the debris, fuel residuals, tether properties, and environmental forces. The authors aim to further study the capture dynamics of debris and stabilization after capture, and create a comprehensive model covering all stages from initial capture to atmospheric reentry.
This document provides a wiring diagram for an anti-lock braking system (ABS) with vehicle stability control for a vehicle made by TMC. It includes a list of components, their connections and pinouts. Key components include ECUs, sensors for wheel speed, steering angle, yaw rate and other variables. The diagram shows the interconnections between these components and their related power and ground connections.
A comparative study of controllers for stabilizing a rotary inverted pendulumijccmsjournal
The document describes a comparative study of various controllers - PID, LQR, fuzzy logic, and H-infinity - for stabilizing a rotary inverted pendulum (RIP) system. The controllers are modeled and tested in MATLAB Simulink. Key findings:
- PID control stabilizes the pendulum angle to zero within 1 second.
- LQR control stabilizes the pendulum angle to zero within 1.5 seconds.
- Fuzzy logic control stabilizes the pendulum angle within 0.5 seconds.
- H-infinity control provides robust stabilization of the RIP system.
A Comparative study of controllers for stabilizing a Rotary Inverted Pendulumijccmsjournal
This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
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.
Comparison of backstepping, sliding mode and PID regulators for a voltage inv...IJECEIAES
In the present paper, an efficient and performant nonlinear regulator is designed for the control of the pulse width modulation (PWM) voltage inverter that can be used in a standalone photovoltaic microgrid. The main objective of our control is to produce a sinusoidal voltage output signal with amplitude and frequency that are fixed by the reference signal for different loads including linear or nonlinear types. A comparative performance study of controllers based on linear and non-linear techniques such as backstepping, sliding mode, and proportional integral derivative (PID) is developed to ensure the best choice among these three types of controllers. The performance of the system is investigated and compared under various operating conditions by simulations in the MATLAB/Simulink environment to demonstrate the effectiveness of the control methods. Our investigation shows that the backstepping controller can give better performance than the sliding mode and PID controllers. The accuracy and efficiency of the proposed backstepping controller are verified experimentally in terms of tracking objectives.
Global stabilization of a class of nonlinear system based on reduced order st...ijcisjournal
The problem of global stabilization for a class of nonlinear system is considered in this paper.The sufficient
condition of the global stabilization of this class of system is obtained by deducing thestabilization of itself
from the stabilization of its subsystems. This paper will come up with a designmethod of state feedback
control law to make this class of nonlinear system stable, and indicate the efficiency of the conclusion of
this paper via a series of examples and simulations at the end. Theresults presented in this paper improve
and generalize the corresponding results of recent works.
SLIDING CONTROLLER DESIGN FOR THE GLOBAL CHAOS SYNCHRONIZATION OF IDENTICAL H...ijait
This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very useful in secure
communication devices and data encryption. Using sliding mode control theory and Lyapunov stability theory, a general result has been obtained for the global chaos synchronization of identical chaotic nonlinear systems. As an application of this general result, this paper designs a sliding controller for the
global chaos synchronization of hyperchaotic Yujun systems. Numerical results and simulations are shown to validate the proposed sliding controller design and demonstrate its effectiveness in achieving global chaos synchronization of hyperchaotic Yujun systems.
Stability and stabilization of discrete-time systems with time-delay via Lyap...IJERA Editor
The stability and stabilization problems for discrete systems with time-delay are discussed .The stability and
stabilization criterion are expressed in the form of linear matrix inequalities (LMI). An effective method
allowing us transforming a bilinear matrix Inequality (BMI) to a linear matrix Inequality (LMI) is developed.
Based on these conditions, a state feedback controller with gain is designed. An illustrative numerical example
is provided to show the effectiveness of the proposed method and the reliability of the results.
COMPARATIVE ANALYSIS OF CONVENTIONAL PID CONTROLLER AND FUZZY CONTROLLER WIT...IJITCA Journal
All the real systems exhibits non-linear nature,conventional controllers are not always able to provide good and accurate results. Fuzzy Logic Control is used to obtain better response. A model for simulation is designed and all the assumptions are made before the development of the model. An attempt has been made to analyze the efficiency of a fuzzy controller over a conventional PID controller for a three tank level control system using fuzzification & defuzzification methods and their responses are compared. Analysis is done through computer simulation using Matlab/Simulink toolbox. This study shows that the application of Fuzzy Logic Controller (FLC) gives the best response with triangular membership function and centroid defuzzification method.
This paper deals with a comparative study of circle criterion based nonlinear observer and H∞ observer for induction motor (IM) drive. The advantage of the circle criterion approach for nonlinear observer design is that it directly handles the nonlinearities of the system with less restriction conditions in contrast of the other methods which attempt to eliminate them. However the H∞ observer guaranteed the stability taking into account disturbance and noise attenuation. Linear matrix inequality (LMI) optimization approach is used to compute the gains matrices for the two observers. The simulation results show the superiority of H∞ observer in the sense that it can achieve convergence to the true state, despite the nonlinearity of model and the presence of disturbance.
This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
Philippe Guicheteau (1998) - Bifurcation theory: a tool for nonlinear flight ...Project KRIT
Philippe Guicheteau "Bifurcation theory: a tool for nonlinear flight dynamics", Phil.Trans.R.Soc.Lond.A (1998) 356, 2181-2201
This paper presents a survey of some applications of bifurcation theory in flight dynamics at ONERA (France). After describing basic nonlinear phenomena due to aerodynamics and gyroscopic torque, the theory is applied to a real combat aircraft, and its validation in flight tests is shown. Then, nonlinear problems connected with the introduction of control laws to stabilize unstable dynamic systems and transient motions are addressed.
Test Generation for Analog and Mixed-Signal Circuits Using Hybrid System Mode...VLSICS Design
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
TEST GENERATION FOR ANALOG AND MIXED-SIGNAL CIRCUITS USING HYBRID SYSTEM MODELSVLSICS Design
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
This document describes a fuzzy logic controller for maintaining liquid level in a tank. It presents the concepts of fuzzy logic and fuzzy sets, and explains how a fuzzy controller was developed for a single-input, single-output system to control liquid level. The controller takes the error in liquid height as input and outputs the flow rate to adjust. Membership functions were created for the input and output, and a rule base of five linguistic rules was developed to relate input error to output flow rate. The fuzzy controller was able to maintain a constant liquid level despite variations in input flow, demonstrating the effectiveness of the approach.
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.
Output feedback trajectory stabilization of the uncertainty DC servomechanism...ISA Interchange
This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...Wireilla
ABSTRACT
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO, it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...ijfls
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of
Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized
Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the
system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in
nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO,
it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
Similar to FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKS (20)
THE PRESSURE SIGNAL CALIBRATION TECHNOLOGY OF THE COMPREHENSIVE TEST SYSTEMieijjournal
The pressure signal calibration technology of the comprehensive test system which involved pressure
sensors was studied in this paper. The melioration of pressure signal calibration methods was elaborated.
Compared with the calibration methods in the lab and after analyzing the relevant problems,the
calibration technology online was achieved. The test datum and reasons of measuring error analyzed,the
uncertainty evaluation was given and then this calibration method was proved to be feasible and accurate.
8 th International Conference on Education (EDU 2023)ieijjournal
8th International Conference on Education (EDU 2023) will provide an excellent
international forum for sharing knowledge and results in theory, methodology and
applications impacts and challenges of education. The conference documents practical and
theoretical results which make a fundamental contribution for the development of
Educational research. The goal of this conference is to bring together researchers and
practitioners from academia and industry to focus on Educational advancements and
establishing new collaborations in these areas. Original research papers, state-of-the-art
reviews are invited for publication in all areas of Education
Informatics Engineering, an International Journal (IEIJ)ieijjournal
The document is a call for papers for the Informatics Engineering, an International Journal. It discusses that informatics is a rapidly developing field involving human-computer interaction and interface design. It aims to bring together researchers from academia and industry working in areas of computing, communication, multimedia, and human-computer interaction. Topics of interest include computational complexity, artificial intelligence, database mining, health informatics and more. Authors are invited to submit original papers by May 27, 2023.
Big data is a prominent term which characterizes the improvement and availability of data in all three
formats like structure, unstructured and semi formats. Structure data is located in a fixed field of a record
or file and it is present in the relational data bases and spreadsheets whereas an unstructured data file
includes text and multimedia contents. The primary objective of this big data concept is to describe the
extreme volume of data sets i.e. both structured and unstructured. It is further defined with three “V”
dimensions namely Volume, Velocity and Variety, and two more “V” also added i.e. Value and Veracity.
Volume denotes the size of data, Velocity depends upon the speed of the data processing, Variety is
described with the types of the data, Value which derives the business value and Veracity describes about
the quality of the data and data understandability. Nowadays, big data has become unique and preferred
research areas in the field of computer science. Many open research problems are available in big data
and good solutions also been proposed by the researchers even though there is a need for development of
many new techniques and algorithms for big data analysis in order to get optimal solutions. In this paper,
a detailed study about big data, its basic concepts, history, applications, technique, research issues and
tools are discussed.
LOW POWER SI CLASS E POWER AMPLIFIER AND RF SWITCH FOR HEALTH CAREieijjournal
This research was to design a 2.4 GHz class E Power Amplifier (PA) for health care, with 0.18um
Semiconductor Manufacturing International Corporation CMOS technology by using Cadence software.
And also RF switch was designed at cadence software with power Jazz 180nm SOI process. The ultimate
goal for such application is to reach high performance and low cost, and between high performance and
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FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKS
1. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
DOI : 10.5121/ieij.2015.3401 1
FEEDBACK LINEARIZATION AND BACKSTEPPING
CONTROLLERS FOR COUPLED TANKS
Bachir Nail1,3
, Belkacem Bekhiti2
, Ahmed Hafaifa1,3
, Abdellah Kouzou1,3
and
Nadji Hadroug1,3
1
Science and Technology Department, University of ZianeAchour, Moudjbara Street BP
3117 Djelfa, Algeria .
2
Electronics and Electrotechnics Institute, University of Boumerdes, Boumerdes 35000,
Algeria.
3
The Applied Automation and Industrial Diagnostics Laboratory LAADI, University of
DJELFA, Algeria.
ABSTRACT
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder
to control a nonlinear Coupled Tanks System. The first control procedure is called the
Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global
exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand
with a negligible norm of the error. The second control procedure is the approaches of
Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov
functionwith the design of feedback control, from simulation results it shown that this method preserves
tracking, robust control and it can often solve stabilization problems with less restrictive conditions may
beencountered in other methods. Finally both of the proposed control schemes guarantee the
asymptoticstability of the closed loop system meeting trajectory tracking objectives.
KEYWORDS
Feedback linearization, Backstepping, Lyapunov candidate function, Coupled tanks system,
Nonlinearcontrol.
1. INTRODUCTION
The modeling and the control of industrial process , present a big challenge, hence the reservoirs
andhydraulic systems are considered an important part in them, so the selection of the coupled
tanks isnot accidental for several reasons, first the coupled tanks are very useful in industry, in the
researchlaboratories in petroleum reservoir engineering and in nuclear reactor, the second reason
is related bythe behavior of this systems in general, we see the dynamic model of the coupled
tanks is nonlinearand contains a square root in mathematical differential equations that considered
a good example fortesting the stability and the robustness of any control.
There are several works and researches and scientific articles have preceded us to work on this
systemand they are applied too many controllers (linear and nonlinear). Among these works,
2. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
2
Sliding ModeControl And Optimal GPC Algorithm for Coupled Tanks [1], Modelling and
Control of Coupled Tank Liquid Level System using Backstepping Method [2], Model and
Control for Coupled Tanks using Labview [3], A Neuro-fuzzy sliding Mode Controller Using
Nonlinear Sliding Surface Applied to theCoupled Tanks System [4], and Nonlinear constrained
predictive control [5].In this paper we haveused efficient feedback linearization control without
transformation, and the we have ameliorate the quality of the signal control and the statical error
in the two controllers, compared to the previous works [1-5].
The paper is organized as follows. The first section contains the system model, in the form of
nonlineardifferential equations, and the structure of coupled tanks. The second section, gives
somepreliminary of feedback linearization approach [6],[7], and how do we apply these control
on this system, explaining that in scheme block diagram, and simulation results with some
comments on them. The third section, We dealt also about the backstepping approach [8],[9] and
its theory in second order system, then the application of this control on coupled tanks ,
explaining that in scheme block diagram, and simulation results with some comments on them.
Finally, the fourth section is a conclusion, containing a comparison between the two approaches,
and highlights the pros and cons of each in their application the coupled tanks.
2. WATER TANK MODEL
The schematic drawing in (Figure.1) represents the model of a two degree of freedom (DOF)
statecoupled,water tank system [10]:
Figure 1: Coupled Tanks System.
3. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
3
The coupled tank system is defined by the following nonlinear differential equations:
With
where h1,2are liquid levels in the tanks 1,2 respectively, g is the gravitational constant, s1,2channel
sectionalarea,kp,ksarepumpandsensorgains,andqirepresenttheflowrate.
By Letting x1 = h2, x2= h1, and the output y = ksh2, the dynamic representation of our system will
beinthenonlinearstatespaceformasshown[9]:
Where f, g and h are sufficiently smooth in a domain D ⊂ Rn.The mappings f: D→ Rn and
g :D→ Rn are called vector fields on D.
With
And
4. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
4
Where
3. FEEDBACK LINEARIZATION APPROACH
Feedback linearization is an approach to nonlinear control design that has attracted lots of
research in recent years. The central idea is to algebraically transform nonlinear systems
dynamics into (fully or partly) linear ones, so that linear control techniques can be applied.
This differs entirely from conventional (Jacobian) linearization, because feedback linearization is
achieved by exact state transformation and feedback, rather than by linear approximations of the
dynamics.
3.1 LIE DERIVATIVES
Given a scalar function h(x) and a vector field f (x), we define a new scalar function Lf h(x),
called the Lie derivative (or simply, the derivative) of h with respect to f .
Definition 1: f is called smooth if f∈ Rn. That f is continuous and all derivatives of all order are
continuous [10].
Definition 2: Let h : Rn → R be smooth scalar function, and f : Rn → Rn be a smooth vector
field on Rn, then the Lie derivative of h with respect to f is scalar function defined by [10]:
Let we choose the level of the second tank h2 as the controlled output rather than the position
control The derivative y˙ is given by:
5. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
5
Where
Lfh : is called the Lie Derivative of h with respect to f .
If Lgh(x)=0 , then y˙=Lf h(x) , independent of u . If we continue to calculate the second
derivative of y , denoted by y(2), we obtain:
Then u does not appear in the equations of y, y˙and appears in the equation of y(2) With a nonzero
coefficient:
The forgoing equation shows clearly that the system is input-output linearizable, since the state
feedback control.
Reduces the input-output map to
Which is a chain of ρ = 2 integrators. In this case, the integer ρ is called the relative degree of the
system.
After some algebraic manipulations and calculations the control input u is given by :
6. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
6
Where
andυ is an auxiliary control input to be designed. Typically, υ is chosenas
This yield to the error equation
Equation (17) shows that the error dynamics are governed by a linear second order system.
Furthermore, if the gains are chosen to be diagonal, then the system will be perfectly decoupled.
By suitable choosing the matrices Kp and Kv , the tracking error will converge asymptotically to
zero. To illustrate this, we can write the error equation (17) in state space representation, i.e. we
define the state variable z=(y˜,y¨˜) , and we can write
In order to investigate the stability of the equilibrium point, z=0 , we choose the Lyapunov
function candidate
WhereP=PT>0isthesolutiontoLyapunovequation
7. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
7
Which is negative definite function, from which and according [11] global uniform exponential
stability of the equilibrium point follows. (Figure.2) shows the implementation of this feedback
linearization
Figure 2: Schematic block diagram of feedback linearization with auxiliary controller
3.2 SIMULATION RESULTS OF FEEDBACK LINEARIZATION CONTROL
Simulations results of the feedback linearized tank system as in (Figure.3) demonstrates both
trackingand good regulation objectives are achieved, no excess is recorded in both transient and
steady state which are well shown by the level error, moreover the chosen Lyapunov candidate
function show that the global uniform exponential stability of the equilibrium point (guaranteed
stability), and from the level error (Figure.4) we see that the system is also nearly robust to the
rejected noise.
8. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
8
Figure 3: The level tracking for feedback linearization control
Figure 4: The level error for feedback linearization control
9. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
9
Figure 5: The control signal of feedback linearization control
4. BACKSTEPPING APPROACH
The backstepping was developed by Kanellakopoulos [12], and inspired by the work of Feurre&
Morse [13] on the one hand and Tisinias and Kokotovic&Sussmann [14]. The basic idea of this
method is to leave some states of the system act as virtual inputs. The backstepping uses a form
of the system chain of integrators, after a coordinate transformation of a triangular system and
based on the direct method of Lyapunov. The method is to split the system into a set of subsystem
nested descending order. From there, it is possible to design systematically and recursively
controllers and corresponding Lyapunov functions.
4.1 THE SYNTHESIS OF BACKSTEPPING CONTROL
The backstepping is a control law for nonlinear systems, based on Thelyapunov theory. It applies
to systems of form triangular cascade. Each state of the system, control the previous state and
called Virtual Control until the last state that is controlled by the actual control. The objective of
this technique is to compute multistage a control law that provides the overall stability of the
system [15],[16].
This control law takes the form of a recursive algorithm, the calculation steps are as follows:
The tracking errors are written in the form below
10. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
10
We consider the case of the the second order nonlinear systems of the form :
Suppose that the system (23) after a transformation can be put under the chained form as follows:
We desired to follow the output y = x1 the trajectory yr. This trajectory is assumed known and
uniformly bounded and since the system is a second order the design is done in two steps:
First iteration
First consider the equation (24), where x2 the state variable is treated as a virtual control, and we
Defined like the first desired value.
The first error variable is defined by:
With equation (28), the equation system (22) is written:
For such a system, it was shown that the candidate function is a good choice of the Lyapunov
function:
11. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
11
Its derivative is given by:
A judicious choice of x2 would render negative V˙1(e1) and ensures the stability of the origin of
the subsystem described by equation (24).
Take for value x2, the function t1, suchas:
Where k1 > 0 is a design parameter.
Equation (32) implies that the condition:
This implies that the error given by equation (27) tends to zero which ensures the convergence
of thesubsystem (24) and its asymptotic stability.
From Equation (32) we obtained:
Second iteration
We consider the subsystem equation (25) and the new error variable is defined:
Thisequationrepresentsthegapbetweenthestatevariablex2anditsdesiredvaluet1,theerrore2is
notinstantlynull.Theobjectiveofthisstepisthentoforceittocancel.
Theequationsofthesystemtobecontrolledinspace(e1,e2),arewritten:
12. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
12
Lyapunov function is chosen as:
its derivative
Toensurestabilityitisnecessarythattheequationisequalto−k2e2withK2>0
The control is:
With this choice of control u we obtained:
So finally, we guarantee the asymptotic stability of the system.
13. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
13
Shows the implementation of this Backstepping in (Figure.6)
14. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
14
Figure 6: Schematic block diagram of Backstepping control
4.2 SIMULATION RESULTS OF BACKSTEPPING CONTROL
After seeing these results, we can conclude that :
The Backstepping is a control technque that ensures the stability within the Lyapunov sense.
Thetechnique provides a flexible handling, we see the level coincides with its reference ( best
tracking), (Figure.7) no overshooting, no statistical error, no excess is recorded in both
transient and at steady state, which are well shown by the error (Figure.8).
Figure 7: The level tracking for backsteppingn control
15. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
15
Figure 8: The level error for backstepping control
Figure 9: The control signal of backstepping control
16. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
16
5. CONCLUSION
In this paper two types of nonlinear control schemes has been presented in detailed manner and
applied to coupled tanks system. Concerning the feedback linearization controller, it can be said
from the results has been done satisfactory and the simulations demonstrate a good performance
of regulation and tracking. The total coupled tanks system is globally asymptotic stable and
maintained nearly robust against perturbations. For the second controller approximately the same
obtained results only the difference in the robustness which is preserved by the later scheme with
less restrictive conditions.
The choice of the coefficients (controller gains) can be very tricky and difficult in the two
approaches(FLC,BC) although these are selected positive but may induce instability problem,
even in the chosen that ensure system stability, they can make signal very energetic order .
Finally in order of the work completion there are several points in this paper which may be
naturalpoints of departure for further studies, the investigation of other methods rather than the
used ones provides future works. If we consider the parametric variation in certain interval the
hyper-stability adaptive control will be more efficient from the identifiability and the stability
point of view.
Table 1: Parameters and variables of the coupled tanks, and the controllers (FLC,BC)
17. Informatics Engineering, an International Journal (IEIJ), Vol.3, No.4, December 2015
17
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