A critical study of multivariable self‐tuning algorithms for distillation control

Abstract

A control algorithm which has been acclaimed as the best algorithm for a real system may not be the best algorithm for a different real system. Therefore, various self-tuning algorithms for real distillation columns have been evaluated, in order to compare their performances. A variable forgetting factor algorithm is modified using a filter which permits the employment of one instead of two covariance matrices for distillation control. A cautious self-tuning control of SISO system is extended to MIMO system of distillation control. Multivariable self-tuning regulator, multivariable self-tuning controller and multivariable cautious self-tuning controller are implemented with modified variable forgetting factor for linear transfer function model, Waller et al. column, and rigorous non-linear model, Wood and Berry column. For distillation control, a multivariable cautious self-tuning algorithm with modified variable forgetting factor is much simpler than earlier reported algorithms. This has produced better results and demonstrated its effectiveness, even in the presence of noise when other adaptive controllers give unsatisfactory performance.

Multirate Multivariable Self-Tuning Control of Distillation Columns Using Kalman Predictor

“…(1991b) have used different covariance matrices for each control loop. Recently, Radhakrishnan and Gangiah (1991) developed a multivariable self-tuning control strategy for distillation which uses a single covariance matrix retaining the multivariab1e structure of distillation process, and demonstrated its performance by application to two distillation columns of Wood and Berry (1973) and Waller et al (1988). Chien et al (1986) have extended multivariable STC of Koivo (1980) to systems with multiple time delays and control loops which have different sampling rates, and demonstrated its performance by simulation studies with two nonlinear distillation columns of benzene-toluene and methanol-ethanol separations.…”

“…Recently, a modification in variable forgetting factor of Ydstie et al (1985) is proposed by Radhakrishnan and Gangiah (1991), viz.,…”

“…It can be seen that the estimation is divided into p steps, and that the initial values of P(t) are assumed to be the same for these steps. The advantages of using one covariance matrix (Radhakrishnan and Gangiah, 1991) for the multivariable system over individual covariance matrix for each loop (Dahlquist, 1981) are to account for interaction parameters which are essential in MIMO interacting control of distillation column.…”

“…The concept of single covariance matrix developed by Radhakrishnan and Gangiah (1991) is employed. This Kalman predictor focuses attention on the use of past available measurements to predict the output variables when measurements are not available and corrects it whenever the output measurements are available.…”

Non-linear control of continuous bioreactors

“…In this paper the above nonlinear self-tuning control (NSTC) strategy is compared with Proportional Integral (PI) control. The linear ARMAX model is a subset of NARMAX model and self-tuning control using ARMAX model is discussed in Radhakrishnan and Gangiah [9].…”