Alex Zheng

Anti-windup design for internal model control

This paper considers linear control design for systems with input magnitude saturation. A general anti-windup scheme which optimizes nonlinear performance, applicable to MIMO systems, is developed. Several examples, including an ill-conditioned plant, show that the scheme provides graceful degradation of performance. The attractive features of this scheme are its simplicity and effectiveness.

Robust stability analysis of constrained model predictive control

Abstract In this paper, we show that a constrained Model Predictive Controller, based on one plant model, stabilizes another plant if and only if some corresponding constrained Model Predictive Controller, based on the plant, stabilizes the plant. Thus strong nominal stability results can be used to analyze robust stability properties of some existing Model Predictive Control algorithms, without introducing any additional on-line computations and without modifying any of their attractive features. How the results may be used to synthesize robust controllers is also discussed. Examples are shown to illustrate the key ideas behind the approach.

Robust control of linear time-varying systems with constraints

Despite a rich and complete theory developed for robust control of linear systems, little work has been done for robust control of linear systems with constraints. In this paper, a synthesis method to design a model predictive controller which optimizes robust performance is proposed for a stable linear time-varying discrete-time system represented by a finite impulse response model. In the absence of constraints, we show that with this method robust bounded-input-bounded-output stability of the resulting closed-loop system is guaranteed. Both necessary and sufficient conditions for robust global asymptotic stability, i.e. offset free tracking for all plants in the set, are stated. Furthermore, robust global asymptotic stability is preserved for a class of asymptotically constant disturbances entering at the plant output. These results hold for any uncertainty description expressed in the time-domain. However, there is a trade-off between the generality of the uncertainty description and the computational complexity of the resulting optimization problem. For a broad class of uncertainty descriptions, we show that the optimization problem can be cast as a linear program of moderate size.

Global stabilization of linear discrete-time systems with bounded controls-a model predictive control approach

A linear discrete-time system is globally stabilizable with bounded controls if and only if the system is stabilizable and all its poles are in the closed unit disk. In this paper, the authors propose an implementable model predictive control algorithm to globally stabilize such systems. The authors show that with this scheme a linear discrete-time system with n poles on the unit disk (with any multiplicity) can be globally stabilized if the number of control moves is at least n+1. For pure integrating systems, this condition is also necessary. Moreover the authors show that global asymptotic stability is preserved for any asymptotically constant disturbance entering at the plant input.

Reducing on-line computational demands in model predictive control by approximating QP constraints

Abstract In this paper, we propose two Model Predictive Control algorithms, whose on-line computational demands are significantly smaller than that for conventional Model Predictive Control algorithms, for control of large-scale constrained linear systems. We show that closed-loop stability can be guaranteed under some conditions. We also propose an optimal anti-windup scheme for approximating Model Predictive Control (thus eliminating the need for solving an on-line optimization problem) and derive a quantitative condition under which Model Predictive Control can be approximated effectively. These results make Model Predictive Control a very attractive candidate to be applied to systems with small sampling times and/or with a large number of inputs, and address achievable constrained performance by any anti-windup design.

Control of linear unstable systems with constraints

We analyze and determine the domain of attraction for a linear unstable discrete-time system with bounded controls. An algorithm is proposed to construct the domain of attraction. A class of control laws is developed to stabilize all initial conditions in the domain of attraction.

Stability of model predictive control with time-varying weights

In this paper, we show that the stability of constrained Model Predictive Control (MPC) systems can be guaranteed by using time-varying weights. It unifies two popular MPC algorithms with guaranteed stability - Infinite Horizon MPC and MPC with End Constraint. Use of time-varying weights may also be useful in analyzing stability properties of MPC for linear time-varying systems as well as uncertain linear systems.

The stability of a reactive flash

In this paper, we study the steady state behavior of an isobaric, adiabatic reactive flash for a binary mixture. The presence of vapor–liquid equilibrium can remove or create multiple steady states. For example, a system that does not have multiple steady states in a one-phase CSTR can display multiple steady states as a two-phase reactive flash unit. Both steady state input multiplicity (i.e., multiple values of input resulting in one value of output) and output multiplicity (i.e., one value of input resulting in multiple values of output) are possible. The existence of multiple steady states and their stability properties are related to a dimensionless quantity, Λ, that depends on the heats of reaction and vaporization as well as the compositions in the system. The results are illustrated in several examples.

Some Practical Issues and Possible Solutions for Nonlinear Model Predictive Control

Several practical issues (e.g., excessive on-line computational time) associated with a conventional Nonlinear Model Predictive Control algorithm are illustrated through simulation studies on two chemical processes — a binary distillation column and the Tennessee Eastman Challenge Process. We show why it is generally not a good idea to use a small control horizon to reduce the on-line computational time. The effectiveness of the Nonlinear Model Predictive Control algorithm recently proposed by Zheng in resolving these issues is illustrated.

Control system design for recycle systems

Abstract This paper considers the control system design for recycle systems. We derive a condition which quantifies the effect of recycling on closed-loop performance. The condition is independent of control/controller structure. With insight from this condition, we develop a set of heuristics for properly designing a controller without detailed knowledge of recycle dynamics for the important special case where the system is represented by a first-order-plus-time-delay model and where the IMC tuning rules are used. The heuristics require only a minimal amount of information on the recycle dynamics. Their effectiveness is illustrated on a reactor/feed-effluent heat exchanger/furnace process under various conditions.