Theory and application of an extended horizon self‐tuning controller

Abstract

A robust version of the self-tuning regulator is developed. The regulator, which requires relatively little knowledge of system characteristics (estimated order of transfer function polynomials and an upper bound for transportation delays), has been shown to yield stable control and convergence for linear, time-invariant systems. Simulations and practical tests on a large pilot-scale process have shown that the inclusion of a variable forgetting factor and an "extended horizon" control criterion provides the regulator with a sufficient degree of robustness and flexibility to perform well in a nonlinear time-varying environment. The regulator makes use of intuitively easy-to-understand concepts and leaves few degrees of freedom for the potential user. Furthermore, extensive experiments and simulation studies have shown it to be insensitive to choice of initial conditions and dynamic characteristics set by the user. SCOPEThe idea of the self-tuning regulator was developed (ktrom and Wittenmark, 1973) to cope with the problem of controlling linear, time-invariant systems with unknown or uncertain models, and which were subject to stochastic disturbances-a situation which is not common in the chemical industry. There have been subsequent attempts to modify the basic concepts to obtain algorithms which can deal with the more typical chemical engineering problem-the control of processes with nonlinear, uncertain, nonconstant dynamics and with long and variable transportation delays.In order to deal with this more complex problem it is necessary to incorporate some adaptive mechanism into the part of the algorithm which estimates a model for the process being controlled. It is also necessary to "detune" the control action in an appropriate way to prevent severe overshoot and potential instability of the real nonlinear process. Finally, it is important to reduce the sensitivity of the algorithm to any remaining parameters which must be specified a priori by the operator or control engineer.Only if all the above are achieved is the resulting control algorithm likely to be robust enough to be generally useful in the control of process plants. CONCLUSIONS AND SIGNIFICANCEIt is likely that some form of self-tuning controller will find significant application in the control of time-dependent nonlinear processes within the chemical industry. These controllers have the advantages of simplicity, flexibility, and cornpatability with microcomputer technology, as well as an intuitively satisfying basis.The results of this study have shown that the basic self-tuning algorithm can be modified to produce a version far more robust than the early formulations. The algorithm has been shown to Correspondence concerning this paper should be addressed to L. S. Kershenbaum. B. E. Y&e is presently at Chemical Engineering Department, University of Marsachuset6Amherst. MA 01003.be stable and convergent for linear, time-invariant systems, and requires only a few parameters to be supplied by the operator. Moreover, for a wide range of simulati...

Mean-square performance of a convex combination of two adaptive filters

“…In this paper we shall study the mean-square performance of the above combination procedure (1)- (5), as well as the behavior of the following modified version: (6) where (7) with being a small positive constant. In other words, the adaptation of will continue to be given by (5) in terms of , and we shall instead set to zero or one whenever is close to the endpoints rather than limit to the values or as before.…”

“…More generally, on-line adaptation of certain filter parameters or even cost functions has been attempted to influence filter performance, such as adjusting the forgetting factor of recursive least squares (RLS) algorithms [6], [7] or minimizing adjustable cost functions [8]- [11]. Recently, there has been an interest in combination schemes, where the outputs of several filters are mixed together to get an overall output of improved quality [12]- [15], with some of these approaches sacrificing performance in lieu of analytical tractability.…”

Adaptive Torque Control of a Diesel Engine for Transient Test Cycles

“…This means that all the data in the step-response test is weighted equally in the parameter estimation algorithm. However, during the continuous update of parameters, a variable forgetting factor due to Ydstie et al [54] was the use of the variable forgetting factor helps to avoid the estimator windup, it does not guarantee that P stays bounded. Therefore, as a precaution, updating of the parameters and the covariance matrix are stopped whenever the process excitation is low or the estimation error is sufficiently small.…”

“…It was found that the variable forgetting factor of Ydstin et al [54] gave better parameter convergence, and it was used in the results presented in Table 6.12.…”

“…Both a constant forgetting factor with values of 0.975, 0.99, and 0.999 and a variable forgetting factor due to Ydstin et al [54], as discussed in Section 5.6, were used in the parameter estimation algorithm. It was found that the variable forgetting factor of Ydstin et al [54] gave better parameter convergence, and it was used in the results presented in Table 6.12.…”