GMV control of nonlinear multivariable systems

A Generalized Minimum Variance control law is derived for the control of nonlinear, possibly time-varying multivariable systems. The solution for the control law is original and was obtained in the time-domain using a simple operator representation of the process. The quadratic cost index involves both error and control signal costing terms. The controller obtained is simple to implement and includes an internal model of the process. In one form might be considered a nonlinear version of the Smith Predictor. However, unlike the Smith Predictor a stabilizing control law can be obtained even for some open-loop unstable processe

Polynomial approach to nonlinear predictive generalized minimum variance control

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes

Predictive feedback control using a multiple model approach

A new method of designing predictive controllers for SISO systems is presented. The controller selects the model used in the design of the control law from a given set of models according to a switching rule based on output prediction errors. The goal is to design, at each sample instant, a feedback control law that ensures robust stability of the closed–loop system and gives better performance for the current operating point. The overall multiple model predictive control scheme quickly identifies the closest linear model to the dynamics of the current operating point, and carries out an automatic reconfiguration of the control system to achieve a better performance. The results are illustrated with simulations of a continuous stirred tank reactor

Controller performance design and assessment using nonlinear generalized minimum variance benchmark : scalar case

A nonlinear version of the Generalized Minimum Variance (GMV) multivariable control law has been recently derived for the control of nonlinear, possibly time-varying systems. This paper presents the results of the controller performance assessment against this Nonlinear GMV controller in the scalar case. The minimum variance of the generalized output is estimated from routine operating data given only the plant time delay and the technique is applied to a nonlinear reactor control example

Temperature control in transport delay systems

A control architecture is proposed for temperature control in manufacturing applications based on the internal model principle. It is applied to a problem where the material exit temperature is to be controlled by changing the transportation speed to influence the amount of heat loss. The internal model is used to achieve a fast response with minimal overshoot. The controller tuning is carried out using constraints on the sensitivity function to map out the controller parameter region to achieve this performance. The robustness of the controller to parametric uncertainty is also considered. Results are shown from the application of this controller to the temperature controller for a hot strip rolling mill

Non-linear predictive control for manufacturing and robotic applications

The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems

State dependent NGMV control of delayed piecewise affine systems

A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of delayed piecewise affine (PWA) systems which are an important subclass of hybrid systems. Under some conditions, discrete-time PWA systems can be transferred into their equivalent state dependent nonlinear systems form. The equivalent state dependent systems that include reference and disturbances models are very general. The process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [16] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems but has the advantage that it can stabilize open-loop unstable processes [17]

Design and real time implementation of nonlinear minimum variance filter

In this paper, the design and real time implementation of a Nonlinear Minimum Variance (NMV) estimator is presented using a laboratory based ball and beam system. The real time implementation employs a LabVIEW based tool. The novelty of this work lies in the design steps and the practical implementation of the NMV estimation technique which up till now only investigated using simulation studies. The paper also discusses the advantages and limitations of the NMV estimator based on the real time application results. These are compared with results obtained using an extended Kalman filter

Multi-variable LQG optimal control - restricted structure control for benchmarking and tuning

The paper introduces the benchmarking of multivarialbe systems using an offline optimal LQG approach

Benchmarking for process control with applications in the hot strip finishing steel mill

This paper describes how new benchmarking concepts can be applied to different aspects of process control performance assessment