Carlos E. García

Model predictive control: theory and practice—a survey

Abstract We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and have been studied by academia. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. In this paper the issues of importance that any control system should address are stated. MPC techniques are then reviewed in the light of these issues in order to point out their advantages in design and implementation. A number of design techniques emanating from MPC, namely Dynamic Matrix Control, Model Algorithmic Control, Inferential Control and Internal Model Control, are put in perspective with respect to each other and the relation to more traditional methods like Linear Quadratic Control is examined. The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed. The application of MPC to non-linear systems is examined and it is shown that its main attractions carry over. Finally, it is explained that though MPC is not inherently more or less robust than classical feedback, it can be adjusted more easily for robustness.

QUADRATIC PROGRAMMING SOLUTION OF DYNAMIC MATRIX CONTROL (QDMC)

QDMC is an improved version of Shells Dynamic Matrix Control (DMC) multivariable algorithm which provides a direct and efficient method for handling process constraints. The algorithm utilizes a quadratic program to compute moves on process manipulated variables which keep controlled variables close to their targets while preventing violations of process constraints. Several on-line applications have demonstrated its excellent constraint handling properties, transparent tuning and robustness, while requiring minimal on-line computational load.

State-space interpretation of model predictive control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC).

Model predictive control: Theory and practice

Abstract We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and have been studied by academia. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. In this paper the issues of importance that any control system should address are stated. MPC techniques are then reviewed in the light of these issues in order to point out their advantages in design and implementation. A number of design techniques emanating from MPC, namely Dynamic Matrix Control, Model Algorithmic Control, Inferential Control and Internal Model Control, are put in perspective with respect to each other and the relation to more traditional methods like Linear Quadratic Control is examined. The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1–, 2–, and ∞ system norm formulations of the performance objective are discussed. The application of MPC to nonlinear systems is not covered for brevity. Finally, it is explained that though MPC is not inherently more or less robust than classical feedback, it can be adjusted more easily for robustness.

Design Methodology Based On the Fundamental Control Problem Formulation

After more than ten years of advanced process control developments at Shell, we have come to the realization that a Unified Approach to control design is needed. Two main reasons for this need exist. On the one hand, the costs associated with treating each control problem as a separate and unique case study are becoming increasingly higher. On the other hand, with the increase in the number of control applications, it is becoming prohibitively costly to have expert manpower maintaining loops. Our own experience dictates that a unification of approach is only possible after there is a complete understanding of the Fundamental Control Problem. This involves a recognition that every control system attempts to meet certain Performance Criteria given a Process Representation. Therefore, a design methodology that recognizes all elements of this Fundamental Control Problem up front and allows for intelligent introduction of necessary assumptions and compromises by the designer should provide the desired unification. In this paper we outline a design methodology based on this Fundamental Control Problem definition indicating the future research efforts needed in order to realize it.

Design of Robust Process Controllers

Abstract The task of designing a robust process controller consists of determining the control algorithm that meets the system performance requirements across a broad range of operating conditions while recognizing the compromises demanded by the available implementation vehicles. This design task generally involves an iterative procedure wherein the compromises forced on the designer and the performance demanded represent an infeasible set that must be negotiated upon until a resolution is achieved. In the chemical and refining industries this task is particularly challenging for two reasons. On the one hand, there is little freedom to change the basic process design in order to achieve feasibility. On the other hand, large levels of research and/or engineering effort to mathematically represent the process is normally not justifiable because of the fact that the number of processes of a given genre is small and so the cost is not distributed across a large number. The needs of our industry have forced a unified approach to control theory wherein the economy is incorporated in the fact that a single design procedure is utilized. In this paper we describe our work in developing such a unified approach to process control. Because of its generality, it is proposed as a potential solution to many of the current control problems encountered not only in our industry but across a broad class of industrial needs. In addition, we outline our current research efforts which will lead to the development of highly versatile and robust controllers whose structure changes to meet the performance requirements on-line in real time.

State-Estimation-Based Model Predictive Control with On-Line Robustness Tuning Parameters

We show that unconstrained Model Predictive Control (MPC) based on step response models is identical to linear quadratic optimal output feedback under a particular disturbance and measurement noise assumption. More specifically, MPC in its unconstrained form is equivalent to the optimal state observer (Kalman filter) designed for step disturbances at the output and in the absence of measurement noise, plus linear quadratic state feedback. Analytical results on the state estimation based on step response models allow us to generalize the conventional MPC (which is widely applied in industry) to processes with integrators and to cases with white measurement noise without introducing any additional complexity. For the case of an integrated white noise disturbance entering at the output through general first order dynamics (including integrator) and white measurement noise, the optimal state estimator is conveniently parametrized in terms of a real parameter vector whose dimension is equal to the number of outputs. This parametrization is independent of model complexity and eliminates the need for solving a Riccati equation of potentially very large order. It also provides natural on-line tuning parameters for closed-loop robustness and noise-filtering. Our analysis shows that the new state-estimation-based MPC is a direct extension of conventional MPC techniques such as Dynamic Matrix Control (DMC) and Internal Model Control (IMC).

Review and application of quantitative tools for industrial control system design

Abstract Given process models, commissioning a control system involves the selection of a control structure, algorithms and tuning parameters. In making these selections, the engineer’s goal is to obtain a control system that provides good performance in the presence of uncertainty and disturbances but requires low maintenance. Several approaches, of varying sophistication, have been suggested to solve this problem. These approaches necessarily compromise between their rigor and the effort required to obtain a solution. The purpose of this paper is to present the approach adopted by Shell, illustrate its use through an industrial example and pose challenges to the academic community.