An optimal design technique for multivariable SISO controllers

Abstract

R 0 . C In the past decades there has been considerable interest in developing control strategies for multivariable processes because of genuine industrial needs. Currently available techniques range from simple combination of feedback loops to fullscale multivariable controllers. However, industrial applications of multivariable control schemes have been rather limited due to design and implementation complexities. Most chemical processes are still being operated with standard PI or PID controllers. Success of this approach in a multivariable environment depends heavily on proper variable pairing and loop tuning. Parameters of the single-input/single-output (SISO) controllers must be specified to provide overall system integrity and satisfactory performance in the face of setpoint change and load disturbance. In addition, optimal controller design is critical not just for pairing the input/output variables but also in analysis and evaluation of the effectiveness of more complex control configurations.A number of techniques have been proposed to facilitate the design of multivariable feedback controllers. Niederlinski ( I 97 1) was the first to recommend the use of maximum gain and critical frequency obtained from continuous cyclic behavior of the system in calculating the settings. The lack of completeness of this method resulted in poor acceptance. The framework of Direct Nyquist Array (DNA) (Rosenbrock, 1974) and related methods such as Inverse Nyquist Array (INA) and Characteristic Loci can also be used in this context. Yet, additional tuning is still required to improve control quality since only the proportional gain based stability region is specified (Waller et al., 1984;Economou and Morari, 1986). Extension of the singleloop Nyquist method to multivariable systems was proposed by Luyben (1986). By setting the biggest log modulus empirically, a detuning factor is calculated and used to relax the diagonal transfer functions-based Ziegler-Nichols settings. Subsequent modifications to the original simple BLT method by adding derivative control action or using a weighted detuning factor for each loop or both were also reported (Monica et al., 1988). Extension of the internal model control (IMC) principles to multiloop systems by treating interactions as perturbations on a SISO structure can also lead to the design of robustly stable controllers (Economou and Morari, 1986;Huang et al., 1987). In this approach, the IMC filters can be used to determine the parameters of the feedback controllers. Yet, none of these methods guarantees system performance since design of the feedback controllers is largely based on the diagonal elements of the transfer function matrix. They are best suited for obtaining a set of initial parameters, and further adjustments have to be carried out to improve control quality. This fine-tuning procedure can be quite tedious when manipulated variable constraints and stability robustness are to be considered. And it may even become impossible as the system dimensions increase.A different a...