Optimal proportional plus integral control for regulator and tracking problems

Abstract

SUMMARYTwo new design methods are proposed for optimal PI control which give fast recovery from load disturbances without producing large overshoots associated with set-point changes. Unlike existing methods, such as set-point filtering or any other scheme that essentially detunes the controller for set-point changes, the proposed methods do not increase the rise time significantly in order to reduce overshoot. The first method resets the integral term in the control law when the new set point is reached. The second method is a modified model-following approach that does not increase the overall dimension of the system. Two numerical examples demonstrate that the proposed methods are superior to alternatives such as set-point filtering and conventional model following.KLY WORDS Optimal proportional-integral control Model following Reset wind-up . INTRODUCTIONI t is usually desirable to include integral action in optimal control systems in order to eliminate offset due to unmeasured load disturbances or modelling error. Three basic approaches for incorporating integral control action have been reported in the literature. In the first method, a term involving the time derivative of the control vector is included in the performance index. '-' The resulting control law contains integrals of all of the state variables. However, this approach is valid only for systems where the number of control variables is at least equal to the number of state variables. Otherwise, it is not possible to eliminate offset in all of the state variables.4 A second way of incorporating integral action is to augment the state vector with integrals of selected state variables.4p5 The main advantage of this approach is that it allows the designer to choose the set of output variables for which integral control action is desired. The third approach for including integral control action is to use a disturbance model. This scheme has the advantage of allowing the designer to tailor the control system design to the specific type o f disturbances that are anticipated. However, the added complexity of requiring state estimation and a disturbance model is a significant disadvatage. Other approaches, such as the one suggested by Waller and Gustafson,' which includes the time derivative of both the output and the control vector in the performance index, are also reported in the literature.Although integral control action is essential for eliminating offsets, it creates a problem in designing the controller. In particular, the choice of the weighting matrices in a quadratic performance index usually involves a compromise between load and setpoint responses. The present paper proposed a remedy for this problem based on modifying the integral term in the PI control law.

Proportional plus integral MIMO controller for regulation and tracking with anti-wind-up features

“…Hence, overshoots that could be tolerated in regulation are not suitable for tracking. (b) Even though the regulation problem could be optimized looking for an overdamped behavior, integrators overload might cause important overshoots associated with set-point changes (Wong and Seborg, 1985).…”

“…In this paper, we propose a multivariable P+I control structure (MPI), particularly suited to MIMO systems. It is based on a standard optimal control structure with integral action (SOCI) (Kwakernaak and Sivan, 1972; W ong and Seborg, 1985), requiring knowledge of the system matrices (triplet S{AJi,C)). The MPI controller keeps SOCI optimal regulation properties, while yielding extra tracking-tuning parameters.…”

Designing Pid Controllers With a Minimum Iae Criterion by a Differential Evolution Algorithm

“…Recently, the design of PID controllers based on an optimization approach has received considerable attention (AstrGrn, 1983;Al-Assadi and Al-Chalabi, 1987;Imaeda et al, 1987;Vu, 1992;Wang and Kwok, 1994;Wong and Seborg, 1985;Yang et al, 1991). There are several reasons for this research interest.…”

A Practical Design for a Multivariable Proportional−Integral Controller in Industrial Applications

“…Compared to the multiloop controller, more design freedom for a multivariable controller can be used to adjust control performance and reduce interaction si-multaneously. In time-domain approaches, PI controller design methods that use the state feedback approach have been reported (Wong and Seborg, 1985;Pulleston and Mantz, 1993). However, direct state feedback may be impractical since states are not usually measurable.…”