Model based multivariable control scheme in a reset configuration for stable multivariable systems

Abstract

The multivariable control scheme is a widely used advanced process control methodology to control key process variables in chemical engineering processes. However, successful implementation of multivariable control requires a simplified control structure, a lower number of tuning parameters, and an appropriate tuning method. In this work, a model based multivariable control scheme is realized in reset configuration for the control of stable multi‐input and multi‐output systems. This control scheme utilizes the process transfer function matrix and the inverse of the steady state gain matrix for its implementation. The control scheme has a single tuning parameter and also inherently takes into account the interaction that exists between process inputs and outputs. This scheme is easy to implement and apply in multivariable systems with multiple delays, high‐dimensional systems, non‐square systems, and systems with RHP zeros. Simulation examples from process system engineering such as industrial scale polymerization reactor system, quadruple‐tank system, temperature control for the four room process, and shell control problem are presented to show the efficacy of the proposed multivariable control scheme.

Sequential synthesis of PID controllers based on LQR method

“…However, when processes have multipleinput/multiple-output (MIMO) dynamics with complex interactions among variables, such as most chemical processes (Pathiran and Jagadeesan, 2018), the design of PI/PID controllers simultaneously achieving a correct control system operation (adequate set-point tracking, disturbance rejection and insensibility to model uncertainty) is not an easy task (Liu et al, 2010;Maghade and Patre, 2012;Ram and Chidambaram, 2015;Besta et al, 2018); moreover, the application of tuning methods developed for singleinput/single-output (SISO) plants to individual control loops may compromise performance and stability (Vu and Lee, 2010;Nandong and Zang, 2014).…”

“…Thus, the PID control design for a 2 × 2 MIMO system involves the tuning of 12 parameters, but the number of involved variables increases up to 27 and 48 for 3 × 3 and 4 × 4 MIMO processes, respectively. It is clear that the optimization problem of finding the control parameters set achieving process stability as well as some other performance measures quickly escalates in size and complexity (Pathiran and Jagadeesan, 2018), specially when considering that no previous information about the feasible solution space is known. This problem can be simplified by considering a multiloop control whenever the process allows for it or existing control hardware does not have the capacity to implement the centralized structure.…”