A MIMO cautious self‐tuning controller

Abstract

IntroductionAdaptive controllers are generally based on linear models. Most chemical processes, however, are inherently nonlinear. In addition, extra nonlinearities are introduced by nonlinear sensors and control valves. The existing linear-model-based, adaptive algorithms face serious problems when applied to highly nonlinear systems. One might observe large sustained oscillations, failure of the algorithm to drive the system to the setpoint, and even instability. Such incidents have been reported by Song et al. (1984), Gustafsson (1984). for the minimum variance self-tuning regulator (STR).Self-tuning controllers (Clarke and Gawthrop, 1975) involving input penalization have been proved to be more robust than the STR (Gawthrop and Lim, 1982) and are perhaps the most industrially accepted adaptive controllers (Dumont, 1986). The major drawback these controllers face is the requirement to know, apriori, weights that result in a closed-loop stable system. For open-loop stable systems, stability and robustness can be achieved with heavy penalization of the control variable, but this results in sluggish performance. Pole/zero placement adaptive controllers with fixed poles and fast performance specifications are faced with similar problems (Papadoulis, 1987). Another alternative is the approach taken by generalized predictive control (GPC) algorithms (e.g., Ydstie and Liu, 1984; Ydstie et al., 1985; Clarke et al., 1987a, 198713). Robustness is enhanced by aiming to reach the set points (or achieve another performance measure) at a time (horizon) greater than the minimum dictated by time delays and zeroes outside the unit circle. With constant horizons, this approach has the disadvantage that large horizons might be necessary to ensure robustness, thus leading to sluggish performance. To circumvent these problems, algorithms involving input penalization with time-varying weights automatically adjusted on-line, have been presented. Allidina and Hughs (1 980) calculate the weights on-line as the solution to pole placement related, Diophantine equations. Latawiec and Chyra (1 983) utilize online stability criteria to adjust the weights. Toivonen (1983) interprets the input weight as the Langrange multiplier of a control variance constrained optimal control problem. These algorithms (all developed for SISO systems) require a large amount of on-line computations which may become prohibitive in the multivariable case.A different approach for some nonlinear systems is the use of nonlinear adaptive controllers. Promising algorithms have been proposed by Gustafsson (1984), Golden and Ydstie (1985), and Agarwal and Seborg (1987). But these controllers require that the nonlinearities be known apriori and that they be static, conditions seldom fulfilled in practice.An alternative method for SISO systems that maintains the essential simplicity and small computational requirements of the STR has been presented by Papadoulis et al. (1987). Namely, the CSTC is a simple STC whose weight is tuned on-line, based on a measure of the ...