Computation of multiloop controllers having desired closed-loop responses

Abstract

For n-by-n multivariable processes, multiloop controllers have n degrees of freedom and hence the n diagonal elements of closed-loop transfer functions can be designed to have desired closed-loop responses. Multiloop controllers having desired closed-loop responses can be considered as an extension of the single-input single-output internal model control and they can be used as reference controllers. However, computations of such multiloop controllers have not been well developed. The Newton-Raphson method and the iterative sequential loop closing method can be used, but they can suffer from a divergence problem for some processes. Here, the continuation method is applied to obtain multiloop control systems with desired closed-loop responses for a robust computation. The multiloop controllers with desired closed-loop responses can be used to obtain dynamic interaction measures and design multiloop PID controllers.