Generalized Minimum Variance Control Law Research Articles

Design of a Data-Oriented Performance Driven Control System Based on the Generalized Minimum Variance Control Law

In process industries, it is necessary to maintain the user-specified control performance in order to achieve desired productivity. This paper describes a design scheme for control performance eval...

Recursive Gauss–Seidel algorithm for direct self‐tuning control

SUMMARYA recursive algorithm based on the use of Gauss–Seidel iterations is introduced to adjust the parameters of a self‐tuning controller for minimum phase and a class of nonminimum phase discrete‐time systems. The proposed algorithm is called the Recursive Gauss–Seidel (RGS) algorithm and is used to update the controller parameters directly. The use of the RGS algorithm with a generalized minimum variance control law is also given for nonminimum phase systems, and a forgetting factor is used to track the time‐varying parameters. Furthermore, the overall stability of the closed‐loop system is proven by using the Lyapunov stability theory. Using computer simulations, the performance of the RGS algorithm is examined and compared with the widely used recursive least squares algorithm.Copyright © 2011 John Wiley & Sons, Ltd.

GMV control of non-linear continuous-time systems including common delays and state-space models

A non-linear generalized minimum variance control law is proposed for the control of non-linear continuous-time multivariable systems with common delays on input and output channels. The quadratic cost index involves both error and control signal costing terms. The solution for the control law is obtained using a non-linear operator representation of the plant and a linear state-equation model for the disturbance and reference models. The reference and disturbance models are represented by linear subsystems. However, the plant model can be in a very general non-linear operator form, which could involve state-space, transfer operators or non-linear function look up tables. The structure of the system and criterion is chosen so that a simple controller structure and solution is obtained. The controller obtained is simple to implement, particularly in one form, which might be considered to be a state-space version of a non-linear Smith predictor. The results are related to those for discrete-time systems but the presence of the transport delay terms complicates the solution rather more in the continuous-time case.

Nonlinear decoupling PID control using neural networks and multiple models

For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential (PID) controller is proposed, which consists of a traditional PID controller, a decoupling compensator and a feedforward compensator for the unmodeled dynamics. The parameters of such controller is selected based on the generalized minimum variance control law. The unmodeled dynamics is estimated and compensated by neural networks, a switching mechanism is introduced to improve tracking performance, then a nonlinear decoupling PID control algorithm is proposed. All signals in such switching system are globally bounded and the tracking error is convergent. Simulations show effectiveness of the algorithm.

NONLINEAR GENERALIZED MINIMUM VARIANCE CONTROL UNDER ACTUATOR SATURATION

A new Generalized Minimum Variance control law has been derived recently for the control of nonlinear multivariable systems. In this paper we restrict our interest to single-input, single-output plants with input nonlinearities in the form of hard actuator limits. Since in real systems saturation always exists in some form, e.g. as a result of valve opening limits or finite power supply, this is a natural case to consider. One of the well-known problems associated with input saturation is the integral windup phenomenon, which occurs whenever the controller includes integral action. In this paper, we show that the classical form of the “anti-windup” mechanism can be obtained within the Nonlinear GMV controller framework by a suitable selection of the design parameters. The advantage of the approach is that the anti-windup mechanism is obtained naturally from the optimization problem. There is also the possibility that the technique can be extended for other specialized nonlinear compensation problems.

Self-Tuning PID Controllers Based on the Strongly Stable Generalized Minimum Variance Control Law

Abstract This paper proposes a new design scheme for a self-tuning PID controller. Expressions to calculate PID parameters from the identified plant coefficients are given. These expressions are derived by approximating the PID controller to the generalized minimum variance control (GMVC) law. To obtain a better approximation, the PID controller has a time-varying proportional gain. The PID control law approximates the strongly stable GMVC resulting in a stable closed-loop system and a stable control law. Using a numerical example, the control performance of the proposed method is compared with those of PID controllers designed by other schemes.

Design and Implementation of a Self-Tuning PID Controller

PID control schemes based on the classical control theory, have been widely applied to real control systems, and there have been a lot of works on the tuning of PID parameters, as they affect control performance. Several self-tuning and auto-tuning PID techniques have been reported for systems with unknown or slowly time-varing parameters. None, however, is applicable to discrete-time system with unknown dead time. In this paper, a self-tuning PID control algorithm is proposed based on the relationship between the PID control law and the generalized minimum variance control law which is one of self-tuning control strategies. The proposed control scheme is practically evaluated on a temperature control system of a poly butene reactor.

A Design of Generalized Minimum Variance Controllers for Nonlinear Systems

The generalized minimum variance control (GMVC) method was proposed by Clarke, and it was developed by Allidina taking into account of the closed-loop properties. However, these methods could not be applied to nonlinear systems. In this paper, a new design method of GMVC for nonlinear systems is proposed. This method is a kind of the hybrid controllers by using linear controllers and neural networks (NN). The GMVC law is derived for the known linear model of the controlled object, and the NN learns to compensate the modeling error. Finally, a numerical simulation example is illustrated in order to show the effectiveness of the proposed method.

A Design of Self-Tuning PID Controllers Based on the Generalized Minimum Variance Control Law

Self-tuning control schemes need many control parameters corresponding to the order and the time-delay of the controlled object. Using such many control parameters yields the inferiority in the transient property. Therefore, in order to design practical self-tuning controllers, it is seemed that it is desirable to construct control systems with as few parameters as possible.In this paper, we propose a method how to tune PID parameters adaptively, that is, a self-tuning PID control scheme, based on the relationship between a generalized minimum variance control (GMVC) law and a PID control law. Furthermore, we consider a design scheme of user-specified parameters included in the cost function of the GMVC. Finally, we apply the proposed scheme to an air pressure control system in order to investigate the effectiveness.

Self-Tuning PID Control of a Polybutene Process

Abstract PID control schemes based on classical control theory, have been widely applied to real control systems, since the control parameters can be considered as PID gains of proportional, integral and differential actions. Furthermore, there has been a lot of research on the tuning of PID gains, as they affect control performance. Several self-tuning and auto-tuning techniques have been reported for PID control systems with unknown parameters. None, however, is applicable to discrete-time system with an unknown dead time. A self-tuning PID control algorithm is proposed based on the relationship between the PID control law and the generalized minimum variance control law, which is a self-tuning control strategy. Furthermore, the proposed control scheme is applied to the temperature control system of a polybutene reactor, and the results are discussed.

A real-time 3-D acoustic noise attenuation system

An implicit self-tuning controller derived from Generalized Minimum Variance control law is proposed for active noise attenuation ANA system. Unlike the concurrent ANA controllers, it has the ability to estimate the main acoustic, feedback and error path dynamics simultaneously. It is also interesting to point out that existing available ANA controllers are found to be the special cases of this controller, but only associated with different weighting functions. In this paper, both parameter estimation and controller algorithms are outlined. To justify its effectiveness in noise control, experimental results obtained from a real-time 3-D configuration are included.

Global Convergent Inferential Self-Tuning Control Algorithm

A new inferential self-tuning control algorithm presented in this paper can deal with the systems with unmeasured controlled output. This control algorithm uses the generalized minimum variance control law and inferential strategy adopting double measurements as auxiliary outputs. The analysis of global convergence of this controller is also given.

Adaptive PID Control - A Pole Placement Algorithm with a Single Controller Tuning Parameter

Two approaches to the design of self-tuning PI and PID control strategies are considered. These are based upon a generalized minimumvariance control law and a pole-placement control law.The two designs are analysed, using Root Locus techniques, with respect to their stability and transient performance. The control performance of the pole placement design is studied in the presence of model-plant mismatch. Simulation studies using both transfer functionrepresentations and a detailed mechanistic model of a binary distillation column demonstrate the capabilities of the pole-placement based design.