An Overview of Nonlinear Model Predictive Con- trol ...

An Overview of Nonlinear Model Predictive Control Applications S. Joe Qin and Thomas A. Badgwell Abstract. This paper provides an overview of nonlinear model predictive control (NMPC) applications in industry, focusing primarily on recent applications reported by NMPC vendors. A brief summary of NMPC theory is presented to highlight issues pertinent to NMPC applications. Five industrial NMPC implementations are then discussed with reference to modeling, control, optimization, and implementation issues. Results from several industrial applications are presented to illustrate the bene ts possible with NMPC technology. A discussion of future needs in NMPC theory and practice is provided to conclude the paper.

1. Introduction

The term Model Predictive Control (MPC) describes a class of computer control algorithms that control the future behavior of a plant through the use of an explicit process model. At each control interval the MPC algorithm computes an open-loop sequence of manipulated variable adjustments in order to optimize future plant behavior. The rst input in the optimal sequence is injected into the plant, and the entire optimization is repeated at subsequent control intervals. MPC technology was originally developed for power plant and petroleum re nery applications, but can now be found in a wide variety of manufacturing environments including chemicals, food processing, automotive, aerospace, metallurgy, and pulp and paper. Theoretical and practical issues associated with MPC technology are summarized in several recent review articles. Qin and Badgwell (1997) present a brief history of MPC technology and a survey of industrial applications in [25]. Meadows and Rawlings summarize theoretical properties of MPC algorithms in [16]. Morari and Lee discuss the past, present, and future of MPC technology in [18]. The success of MPC technology as a process control paradigm can be attributed to three important factors. First and foremost is the incorporation of an explicit process model into the control calculation. This allows the controller, in principle, to deal directly with all signi cant features of the process dynamics. Secondly the MPC algorithm considers plant behavior over a future horizon in time. This means that the eects of feedforward and feedback disturbances can be

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anticipated and removed, allowing the controller to drive the plant more closely along a desired future trajectory. Finally the MPC controller considers process input, state and output constraints directly in the control calculation. This means that constraint violations are far less likely, resulting in tighter control at the optimal constrained steady-state for the process. It is the inclusion of constraints that most clearly distinguishes MPC from other process control paradigms. Though manufacturing processes are inherently nonlinear, the vast majority of MPC applications to date are based on linear dynamic models, the most common being step and impulse response models derived from the convolution integral. There are several potential reasons for this. Linear empirical models can be identi ed in a straightforward manner from process test data. In addition, most applications to date have been in re nery processing [25], where the goal is largely to maintain the process at a desired steady-state (regulator problem), rather than moving rapidly from one operating point to another (servo problem). A carefully identi ed linear model is suciently accurate in the neighborhood of a single operating point for such applications, especially if high quality feedback measurements are available. Finally, by using a linear model and a quadratic objective, the nominal MPC algorithm takes the form of a highly structured convex Quadratic Program (QP), for which reliable solution algorithms and software can easily be found [31]. This is important because the solution algorithm must converge reliably to the optimum in no more than a few tens of seconds to be useful in manufacturing applications. For these reasons, in many cases a linear model will provide the majority of the bene ts possible with MPC technology. Nevertheless, there are cases where nonlinear eects are signi cant enough to justify the use of NMPC technology. These include at least two broad categories of applications:  Regulator control problems where the process is highly nonlinear and subject to large frequent disturbances (pH control, etc.)  Servo control problems where the operating points change frequently and span a suciently wide range of nonlinear process dynamics (polymer manufacturing, ammonia synthesis, etc.). It is interesting to note that some of the very rst MPC papers describe ways to address nonlinear process behavior while still retaining a linear dynamic model in the control algorithm. Richalet et al. [28], for example, describe how nonlinear behavior due to load changes in a steam power plant application was handled by executing their Identi cation and Command (IDCOM) algorithm at a variable frequency. Prett and Gillette [24] describe applying a Dynamic Matrix Control (DMC) algorithm to control a uid catalytic cracking unit. Model gains were obtained at each control iteration by perturbing a detailed nonlinear steadystate model. While theoretical aspects of NMPC algorithms have been discussed quite effectively in several recent publications (see, for example, [14] and [16]), descriptions of industrial NMPC applications are much more dicult to nd. A rare exception

An Overview of Nonlinear Model Predictive Control Applications MPC not yet applied

MPC applied Number of MPC applications

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Refinery Petrochemical Chemicals Polymers Gas plants Pulp & paper Process nonlinearity

Distribution of MPC applications versus the degree of process nonlinearity. Figure 1.

can be found in the paper by Ogunnaike and Wright presented at the CPC-V conference [20]. This is probably due to the fact that industrial activity in NMPC applications has only begun to take o in the last few years. In a previous survey of MPC technology [25], over 2200 commercial applications were discovered. However, almost all of these were implemented with linear models and were clustered in re nery and petrochemical processes. In preparing this paper the authors found a sizable number of NMPC applications in areas where MPC has not traditionally been applied. Figure 1 shows a rough distribution of the number of MPC applications versus the degree of process nonlinearity. MPC technology has not yet penetrated deeply into areas where process nonlinearities are strong and market demands require frequent changes in operating conditions. It is these areas that provide the greatest opportunity for NMPC applications. The primary purpose of this paper is to provide a snapshot of the current state-of-the-art in NMPC applications. A brief summary of NMPC theory is presented to highlight what is known about closed-loop properties and to emphasize issues pertinent to NMPC applications. Then several industrial NMPC implementations are discussed in terms of modeling, control, optimization, and implementation issues. A few illustrative industrial applications are then discussed in detail. The paper concludes with a discussion of future needs and trends in NMPC theory and applications.

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2. Theoretical Foundations of NMPC For the sake of discussion we rst de ne a simpli ed NMPC algorithm. The calculations necessary for an implementable MPC algorithm are described in detail in [25]. For a more thorough discussion of theoretical issues pertaining to NMPC the reader is referred to [14]. Assume that the plant to be controlled can be described by the following discrete-time, nonlinear, state-space model: xk+1 = f (xk ; uk ; vk ; wk ) (1) yk = g (xk ) + k (2) where uk 2