Nonlinear Controller Design for Input-Constrained, Multivariable Processes

Abstract

Nonlinear control laws are presented for input-constrained, multiple-input, multiple-output processes, whether their delay-free part is minimum or nonminimum phase. This study addresses the nonlinear control of input-constrained processes by exploiting the connections between modelpredictive control and input-output linearization. The continuous-time control laws involve the solution of constrained optimization problems online. They minimize the error between controlled outputs and their reference trajectories, subject to the input constraints. Their application and performance are illustrated using numerical simulation of two chemical reactors that exhibit nonminimum-phase behavior.

Real‐time, nonlinear control of a constrained, nonminimum‐phase process

“…While the error-feedback control law presented Ž . by Kanter et al 2002 is used to design both controllers, the second uses auxiliary outputs, constructed using the method Ž . of Niemiec and Kravaris 1998 .…”

“…Devasia, 1999;Isidori, 1995 . Recently, a differential-geomet-Ž . ric control law was developed by Kanter et al 2002 for stable, nonlinear processes with input constraints and deadtimes, whether the delay-free part of the process is nonminimum-or minimum-phase. This control law minimizes the error between the delay-free controlled outputs and their reference trajectories.…”

“…This article presents a real-time implementation of the Ž . control law in Kanter et al 2002 on a pilot-scale, multivari-able, liquid-level process in the Process Control Laboratory at the Dept. of Chemical Engineering of the University of Ž .…”

Shortest-prediction-horizon non-linear model-predictive control with guaranteed asymptotic stability

“…A widely used differential geometric control method is input-output linearization, which cannot be used to operate a plant at a NMP steady state. Efforts to make input-output linearization applicable to plants with a NMP steady state include the use of equivalent output(s) in the controller design (Wright and , coordinated control (McLain et al 1996), controller design by inverting the minimum-phase part of the plant model Daoutidis 1990, Doyle et al 1996), approximate input-output linearization (Kanter et al 2002), and approximate input-state linearization (Panjapornpon et al 2006). The output feedback of Isidori (2000) is another method of controlling a class of NMP nonlinear systems.…”

Control of non-minimum-phase nonlinear systems through constrained input-output linearization

“…A widely used differential geometric control method is input-output linearization, which cannot be used to operate a process at a NMP steady state. Efforts to make input-output linearization applicable to processes with a NMP steady state include the use of equivalent output(s) for the controller design [4], coordinated control [5], controller design by inverting the minimum-phase part [6,7], and approximate input-output linearization [8,9]. This study was supported by the National Science Foundation Grant CTS-0101133.…”