Multivariable Control

Two approaches for constructing control charts to monitor multivariate attribute processes when data is presented in linguistic form are suggested. Two monitoring statistics T \(^{\rm 2}_{f}\) and W 2 are developed based on fuzzy and probability theories. The first is similar to the Hotteling’s T 2 statistic and is based on representative values of fuzzy sets. The W 2 statistic, being a linear combination of dependent chi-square variables, its distribution is derived by Satterthwaite’s approximation. Resulting multivariate control charts are compared based on the average run length (ARL). A numerical example is given to illustrate the application of the proposed multivariate control charts and the interpretation of out-of-control signals.

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the traditional approach using Euler angles (yaw, pitch and roll). A transfer matrix general form of the ROV attitude control system was obtained. It was shown that with the increase of inclination angles the transfer matrix of the system becomes multivariable. Algorithms of disturbances compensation and a methodology for parameters selection for decomposition algorithm were proposed. The obtained results were verified during the in situ tests of the ROV “Iznos”, developed in Bauman Moscow State Technical University (BMSTU). The proposed decomposition algorithms allow to expand the ranges of working angles and to improve the quality of the control system performance without significant re-engineering of its structure.

Abstract: a Linear Quadratic Gaussian Controller (LQG) is designed for a tail controlled surface-to-air missile model in order to meet design specifications. The mathematical model of the flexible missile is subject to uncertainties that may arise from unmodelled dynamics, parameter variation or linearization of nonlinear elements. Since these uncertainties are not taken into account in the LQG controller, microns Analysis is applied to the design in order to evaluate the Robust Performance, Robust Stability, and Nominal Performance of the system. Finally, a Linear Quadratic Gaussian controller is designed using Loop Transfer Recovery (LQGLTR) in order to improve the Robust Stability of the system. It is found that the Robust Stability of the design is improved, but as a consequence of losing nominal performance. The microns Analysis and Synthesis Toolbox and the Control Toolbox of MATLAB were used for the design, assembly, analysis and simulation of the missile flight control system. Robust multivariable control, Linear optimal estimation, Missile autopilot.

"Keywords: Pemodelan Sistem, Stabilitas dan Analisis Sistem, Sistem Ruang Status, Keterkendalian dan Keteramatan,  Rancangan Kendali Klasik, Regulator Balikan Status Penuh ( Full State Feedback Regulator), Kendali LQR ( LQR Control ), Estimator, Estimator Berorde Penuh (Full Order Estimator), Estimator Orde Tereduksi (Reduced Order Estimator), Perbandingan Berdasarkan Strategi Pengendalian"
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A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

Two formulations of a nonlinear model predictive control scheme based on the second-order Volterra series model are presented. The first formulation determines the control action using successive substitution, and the second method directly solves a fourth-order nonlinear ...

This paper aims to present a model predictive controller based on discrete state-space modeling, where the future control trajectory is approximated by a set of discrete-time Laguerre functions instead of shift forward operators. The benefit of using these orthonormal Laguerre functions is that they have fewer parameters to adjust in the optimization problem and the computation load is significantly lower than the standard predictive control. The effectiveness of this controller is illustrated through the quadruple tank process, which is a highly interacted, multivariable and constrained system.

The paper deals with the issue of developing an attitude control system for a remotely operated vehicle (ROV) for large inclination angles (pitch, roll). The construction of the orientation control system is considered based on the traditional approach using Euler angles (yaw, pitch and roll). A transfer matrix general form of the ROV attitude control system was obtained. It was shown that with the increase of inclination angles the transfer matrix of the system becomes multivariable. Algorithms of disturbances compensation and a methodology for parameters selection for decomposition algorithm were proposed. The obtained results were verified during the in situ tests of the ROV “Iznos”, developed in Bauman Moscow State Technical University (BMSTU). The proposed decomposition algorithms allow to expand the ranges of working angles and to improve the quality of the control system performance without significant re-engineering of its structure.

Interpretation of the out-of-control signal poses a persistent problem in multivariate control chart owing to the limitations of available general methods like Hotelling T2. Many research papers address these problems and present alternative approaches to diagnose faults in out-of-control conditions and to help identify aberrant variables. This work reviews the different methods and attempts to make a comparative study of some of these methods viz. Mason, Tracy and Young method (Journal of Quality Technology 27:99–108, 1995), Murphy method (The Statistician 36:571–583, 1987), Hawkins method (Technometrics 33:61–75, 1991) and Doganaksoy, Faltin and Tucker method (Communications in Statistics — Theory and Methods 20:2775–2790, 1991). A simulation approach was taken to generate data on various out of control situation and to compare the powers of different targeted methods. In control sate was characterised by a multi-variate normal with standardised mean and variance assuming intra-class correlation structure. Data were generated for different values of correlation and various out of control situation with respect to the shift of mean in one, two or more variables. Due to the limitations of using average run length as a performance criterion especially in case of skewed distribution of run length it was decided to use power as a measure of comparison. Situations in which the particular method works satisfactorily were identified with respect to correlation structure and pattern of shift of mean.

Different traditional and advanced control strategies have been tested and the performance investigated, revealing their incentives. The investigated control approaches are: conventional decentralized PID control, MPC control based on analytical model, MPC based on Artificial Neural Networks (ANN) model and Fuzzy Logic Control (FLC). Comparative control results are shown for the multivariable control structures, aimed to control the main variables

The paper describes the design of an optimal controller, based on output feedback, to provide integrated control of the exciter and prime mover of a micro^synchronous-generator. Modelling of the control input-output measurement dynamics of the power system by an output prediction equation using least-squares analysis, is followed by multivariable control-system design based on discrete dynamic programming to minimise a quadratic performance index. This approach avoids any reference to the system state vector, which may contain states which are difficult to measure, and thus any need for state estimation techniques or the omission of unmeasurable states from the state feedback control law. The paper evaluates the effectiveness of this controller over a wide range of operating conditions, including dynamic and transient stability boundaries and 3-phase faults, with and without permanent line outage.

As die feature sizes continue to decrease, advanced process control has become essential for controlling profile and CD uniformity across the wafer. Gate CD variation must be suppressed by process optimization of lithography, photoresist trim, and gate etch in order to achieve the demanding CD control tolerances. Currently, APC is used in the lithography and etch processes for within wafer (WiW) and wafer-to-wafer (W2W) CD control. APC can make improvements in process results, but there is still variation that needs to be further reduced. Analysis of the current lithography edge CD showed that the variation trend transferred to the post-etch edge CD measurement. Additionally, the etch process created variation in the edge CD independently of the lithography process. It can be challenging to compensate for the variations in the etch process and such compensations degrade through pitch OPC. Multivariable control of the etch process can reduce the need for compensations and, consequently, through pitch variation. A DOE was designed and run using the production etch process as a center reference for the creation of a WiW etch control model. This control model was then tested with a MATLAB based simulation program that simulates the etch production process sequence and the ability to target the edge CD. This demonstration shows that through rigorous methodology a multivariate model can be created for targeting both center CD (W2W) and edge CD (WiW) control, providing an opportunity at etch to reduce compensation for the etch variations at litho, and to provide the capability at etch to compensate for both litho and etch uniformity changes by wafer.

This paper describes a proposed framework for multivariate process control chart recognition. The proposed methodology uses the Artificial Neural Networks (ANNs) to recognize set of subclasses of multivariate abnormal patterns, identify the responsible variable(s) on the occurrence of abnormal pattern and classify the abnormal pattern parameters. The performance of the proposed approach has been evaluated using a real case study. The numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart multivariate pattern recognition. In addition, accurately identifies and classifies the parameters of the errant variable(s).

For the design of most multivariate control charts, it is assumed that the observations follow a multivariate normal distribution. In practice, this assumption is rarely satisfied. In this work, a distribution-free EWMA control chart for multivariate processes is proposed. This chart is based on equential rank of data depth measures.

Frequency-domain methods have provided an established approach to the analysis and design of single-loop feedback control systems in many application areas for many years. Individual Channel Analysis and Design (ICAD) is a more recent development that allows neo-classical frequency-domain analysis and design methods to be applied to multi-input multi-output control problems.