Chapter 20 Model Predictive Control (MPC) from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 1 rev. 2.1 of May 4, 2016

Detailed Process Understanding Intelligent Use of Modern Control Systems Improved Profitability $ Introduction on MPC Introduction to Process ControlRomagnoli & Palazoglu Scope The combination of detailed process understanding with the intelligent use of modern control systems (hardware, software and technology) to achieve improved profitability.

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 3 Introduction on MPC  Introduced since 1980  It works in discrete time framework  It partly overcomes the need of a feedback architecture  It integrates dynamic modeling and optimization  It is inherently multi-variable  It does more than set point tracking and disturbance rejection …

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 4 Side Objectives of Model Predictive Control 1.Prevent violations of input and output constraints. 2.Prevent excessive movement of the input (manipulated) variables. 3.Drive some output (controlled) variables to their optimal set points, while maintaining other outputs within specified ranges. 4.If a sensor or actuator becomes not available anymore, still control as much of the process as possible.

Chapter 20 from ControlWiki 5 Model Predictive Control: Conceptual schematics

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 6 Model Predictive Control: Basic Concepts 1.Future values of output variables are predicted using a dynamic model of the process and current measurements at the k-th sampling instant : ŷ(k+1)=f [ŷ(k), u(k)] Unlike time delay compensation methods, the predictions are made for more than one time delay ahead. 2.The control calculations are based on both current measurements and future predictions. 3.The manipulated variables, u(k), at the k-th sampling instant are calculated so that they minimize an objective function J, e.g.: The reference trajectory y*(k) is based on set points calculated using Real Time Optimization (RTO).Real Time Optimization (RTO) 4.Inequality & equality constraints, and measured disturbances are included in the control calculations.

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 7 Figure 20.2 Basic concept for Model Predictive Control Manipulated variable y*    y* reference trajectory MPC time trajectories

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 8 Model Predictive Control: Calculations 1.At the k-th sampling instant, the values of the manipulated variables, u, at the next M sampling instants, {u(k), u(k+1), …, u(k+M -1)} are calculated. This set of M “control moves” is calculated so as to minimize the predicted deviations from the reference trajectory over the next P sampling instants while satisfying the constraints. Typically, an LP or QP problem is solved at each sampling instant. Terminology: M = control horizon, P = prediction horizon 2.Then the first “control move”, u(k), is implemented. 3.At the next sampling instant, k+1, the M-step control policy is re-calculated for the next M sampling instants, k+1 to k+M, and implement the first control move, u(k+1). 4.Then Steps 1 and 2 are repeated for subsequent sampling instants. Note: This approach is an example of a receding horizon approach.

Chapter 20 9 Model Predictive Control MPC is like … … playing chess and planning moves ahead

Chapter 20 The on-line calculation of optimal set-points, also called real- time optimization (RTO), allows the profits from the process to be maximized while satisfying operating constrains. In real-time optimization (RTO), the optimum values of the set points are re-calculated on a regular basis (e.g., every hour or every day). These repetitive calculations involve solving a constrained, economic optimization problem, based on: 1.A steady-state model of the process, traditionally a linear one 2.Economic information (e.g., prices, costs) 3.A performance Index to be maximized (e.g., profit) or minimized (e.g., cost). Note: Items # 2 and 3 are sometimes referred to as an economic model. Chapter 19 Real-Time Optimization (RTO)

Chapter 20 Model Predictive Control: Conceptual schematics  from Romagnoli & Palazoglu (2005), “Introduction to Process Control” 11

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 12 When Should Predictive Control be Used? 1.Processes are difficult to control with standard PID algorithm (e.g., large time constants, substantial time delays, inverse response, etc.) 2.There is significant process interactions between u and y. i.e., more than one manipulated variable has a significant effect on an important process variable. 3.Constraints (limits) on process variables and manipulated variables are important for normal control.

Chapter 20 MPC displays its main strength when applied to problems with  a large number of manipulated and controlled variables  constraints imposed on both the manipulated and the controlled variables.  time delays  interaction between variables  multiple disturbances; if can be measured, exploits the built-in feedforward capabilities of MPC Introduction to Process ControlRomagnoli & Palazoglu Model Predictive Control

Chapter 20 from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 14 Figure 20.9 Flow chart for MPC calculations. Terminology: y ↔ CV u ↔ MV d ↔ DV y*(k+1) … y*(k+M) u(k+1) … u(k+M) u(k+1)