Skip to main content

2017 | Book

Economic Model Predictive Control

Theory, Formulations and Chemical Process Applications


About this book

This book presents general methods for the design of economic model predictive control (EMPC) systems for broad classes of nonlinear systems that address key theoretical and practical considerations including recursive feasibility, closed-loop stability, closed-loop performance, and computational efficiency. Specifically, the book proposes:

Lyapunov-based EMPC methods for nonlinear systems; two-tier EMPC architectures that are highly computationally efficient; and EMPC schemes handling explicitly uncertainty, time-varying cost functions, time-delays and multiple-time-scale dynamics.

The proposed methods employ a variety of tools ranging from nonlinear systems analysis, through Lyapunov-based control techniques to nonlinear dynamic optimization. The applicability and performance of the proposed methods are demonstrated through a number of chemical process examples.

The book presents state-of-the-art methods for the design of economic model predictive control systems for chemical processes.In addition to being mathematically rigorous, these methods accommodate key practical issues, for example, direct optimization of process economics, time-varying economic cost functions and computational efficiency. Numerous comments and remarks providing fundamental understanding of the merging of process economics and feedback control into a single framework are included. A control engineer can easily tailor the many detailed examples of industrial relevance given within the text to a specific application.

The authors present a rich collection of new research topics and references to significant recent work making Economic Model Predictive Control an important source of information and inspiration for academics and graduate students researching the area and for process engineers interested in applying its ideas.

Table of Contents

Chapter 1. Introduction
The traditional approach for optimization and control of chemical processes is to employ a hierarchical approach. While this approach has been successfully deployed in industrial process control practice, a more integrated solution to optimization and control is needed for next-generation process operations. Economic model predictive control (EMPC) is a control technology that merges economic process optimization and control. A brief overview of the traditional hierarchical approach to optimization and control, key motivating factors for an integrated approach to optimization and control, and a high level discussion of the main difference between EMPC and more standard, i.e., tracking, model predictive control are provided in this chapter. Next, a few chemical process applications are presented. These applications are used in the subsequent chapters to study and analyze the various EMPC methods presented in this book. Finally, the objectives and the organization of this book are given.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 2. Background on Nonlinear Systems, Control, and Optimization
This chapter provides a brief review of several concepts that are used throughout this book. The first section presents the notation. In the second section, stability of nonlinear systems is discussed followed by a brief overview of stabilization (control) of nonlinear systems. In the last section, a review of nonlinear and dynamic optimization concepts is presented.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 3. Brief Overview of EMPC Methods and Some Preliminary Results
This chapter contains a brief background on economic model predictive control (EMPC) methods. The background on EMPC methods is meant to provide context to the EMPC design methodologies of the subsequent chapters. In particular, stability and performance under EMPC is discussed. The chapter concludes with a benchmark chemical process application where EMPC is applied to evaluate the closed-loop properties under EMPC.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 4. Lyapunov-Based EMPC: Closed-Loop Stability, Robustness, and Performance
In this chapter, various Lyapunov-based economic model predictive control (LEMPC) designs are developed, which are capable of optimizing closed-loop performance with respect to general economic considerations for nonlinear systems. Numerous issues arising in the context of chemical process control are considered including closed-loop stability, robustness, closed-loop performance, asynchronous and delayed sampling, and explicitly time-varying economic cost functions. Closed-loop stability, in the sense of boundedness of the closed-loop state, under the LEMPC designs is analyzed. Additionally, when desirable, the LEMPC designs may be used to enforce convergence of the closed-loop state to steady-state. Under a specific terminal constraint design, the closed-loop system under the resulting LEMPC scheme is shown to achieve at least as good closed-loop performance as that achieved under an explicit stabilizing controller. The LEMPC approaches are demonstrated with chemical process examples.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 5. State Estimation and EMPC
In the previous chapters, full state feedback is assumed in the EMPC designs. This assumption is typically not satisfied in practical applications. In this chapter, two output feedback-based EMPC schemes with guaranteed closed-loop stability properties are presented. In the first scheme, a high-gain observer-based EMPC for the class of full-state feedback linearizable nonlinear systems is introduced. A high-gain observer is used to estimate the nonlinear system state using process output measurements. To achieve fast convergence of the state estimate to the actual system state as well as to improve the robustness of the estimator to measurement and process noise, a high-gain observer and a robust moving horizon estimation (RMHE) scheme are used to estimate the system states in the second output feedback-based EMPC. In particular, the high-gain observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value. Once the estimation error has converged to a small neighborhood of the origin, the RMHE is activated to provide more accurate and smoother state estimates. The two EMPC schemes are applied to a chemical process example to demonstrate the applicability and effectiveness of the schemes.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 6. Two-Layer EMPC Systems
In this chapter, several computationally-efficient two-layer frameworks for integrating dynamic economic optimization and control of nonlinear systems are presented. In the upper layer, economic model predictive control (EMPC) is employed to compute economically optimal time-varying operating trajectories. Explicit control-oriented constraints are employed in the upper layer EMPC. In the lower layer, a model predictive control scheme is used to force the system to track the optimal time-varying trajectory computed by the upper layer EMPC. The properties, i.e., stability, performance, and robustness, of closed-loop systems under the two-layer EMPC methods are rigorously analyzed. The two-layer EMPC methods are applied to chemical process examples to demonstrate the closed-loop properties.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Chapter 7. EMPC Systems: Computational Efficiency and Real-Time Implementation
In this chapter, three economic model predictive control (EMPC) schemes are presented that broadly address the issues of computational efficiency and real-time implementation. In the first section, a composite control structure featuring EMPC is presented for two-time-scale systems described by a class of nonlinear singularly perturbed systems. Owing to the fact that the dynamic models that describe such systems are inherently ill-conditioned, a composite control structure is well-conditioned which has computational advantages over the use of one centralized model-based controller formulated with the ill-conditioned model. The second section presents an application study of several distributed EMPC designs. For the chemical process example analyzed, similar closed-loop economic performance is achieved under distributed EMPC relative to that achieved under centralized EMPC. The last section presents a real-time implementation strategy for Lyapunov-based EMPC (LEMPC). The real-time LEMPC addresses potentially unknown and time-varying computational time for control action calculation. Closed-loop stability under this real-time LEMPC strategy is rigorously analyzed.
Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
Economic Model Predictive Control
Matthew Ellis
Jinfeng Liu
Panagiotis D. Christofides
Copyright Year
Electronic ISBN
Print ISBN