Theoretical analysis of unconstrained nonlinear model predictive control

Abstract

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.

Feedback linearizing control of discrete-time nonlinear systems with input constraints

“…The linear state feedback (8) yields a linear subsystem with characteristic polynomial z r + a rz r-1 +´´´+ a 1 (Henson and Seborg 1993). Since this polynomial is stable by construction, it follows that limk® ¥ x (k) = 0 and limk® ¥ v(k) = 0.…”

Discrete-time nonlinear output feedback control for a class of nonlinear systems using finite difference approaches

“…INCE many nonlinear model-based control frameworks required full state information, in the past decades the observer-based controller designs have been addressed in continuous-time setting [1,2], and in discrete-time setting [3,4]. However, these nonlinear observers were open-loop state estimator in regard to consistent initialization.…”

Nonlinear model‐predictive control: Closed‐loop stability analysis

“…To avoid this problem, an implementable controller based on the approximate satisfaction of the terminal state constraint for continuous-time nonlinear systems is presented by Mayne and Michalska (1991). Henson and Seborg (1993) presented an analysis of unconstrained nonlinear predictive control of single-input, single-output (SISO) systems. They use an explicit discrete-time model obtained by forward difference approximation of the continuous-time model.…”

“…This type of discretization is not appropriate for control law generation as shown later. Also, Henson and Seborg (1993) assume that nonlinear transformations analogous to results in continuous-time differential geometry-based approaches are available to analyze the closed-loop properties. The only other approach to study the closed-loop properties of nonlinear model-based control algorithms is provided by de Oliveira and Biegler (1995).…”