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## Model Predictive Control (MPC)

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**Model Predictive Control (MPC)**rev. 2.8 of May 25, 2018 by M. Miccio from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Introduction on MPC**• Introduced since 1980 • It works in discrete time framework • It partly overcomes the need of a feedback architecture • It better handles complicate dynamics (large dead time, inverse response, etc.) present in a wide system • It integrates dynamic modeling and optimization • It is inherently multi-variable • It may integrate feedforward control • It does more thanset pointtrackingand disturbancerejection … from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Side Objectives of Model Predictive Control**• Prevent violations of constraints on input (manipulated) and output (controlled) variables. • Prevent excessive movement of the input (manipulated) variables. • Drive some output (controlled) variables to their optimal set points, while maintaining other outputs within specified ranges. • If a sensor or actuator becomes not available anymore, still control as much of the process as possible. from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Model Predictive Control: Conceptual schematics**from ControlWiki**Model Predictive Control: schematics of time evolution**y* y* reference trajectory Manipulated variable Figure 20.2 Basic concept for Model Predictive Control from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Model Predictive Control: Calculations modules**• The reference trajectory y*(k) is obtained, based on set points calculated using Real Time Optimization (RTO). • Future values of state/output variables ŷ(•) are predicted using a dynamic model of the process and current measurements at the k-th sampling instant, for a given sequence of future control inputs u(k). ŷ(k+1)=f [ŷ(k), u(k)] • Unlike time delay compensation methods, the predictions are made for more than one time delay ahead until the prediction horizon P ( N) • Inequality & equality constraints, and measured disturbances are included in the model calculations. • The manipulated variablesu(•) are calculated at the k-th sampling instant for a future time length set as M ( N), i.e., the control horizon,so that they minimize a given objective function J. For example: • Typically, an LP or QP problem is solved from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Model Predictive Control: Calculation sequence**• At the k-th sampling instant • The set of M“control moves”, i.e.,the values of the manipulated variablesu at the next M sampling instants, {u(k), u(k+1), …, u(k+M -1)} are calculated so as to minimize the predicted deviations from the reference trajectory over the next P sampling instants while satisfying the constraints. • Terminology: M = control horizon, P = prediction horizon • Then, the first “control move”u(k) is implemented in plant control until the next sampling instant k+1 • 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 the first control move u(k+1) is implemented. • Then, steps are repeated for subsequent sampling instants. This is an example of a receding horizon approach. Although a sequence of M control moves is calculated at each sampling instant, only the first move is actually implemented from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed**Model Predictive Control**MPC is like … … playing chess and planning moves ahead**Real-Time Optimization (RTO)**• 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 imposed on some relevant process variables. • 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: • A steady-state model of the process, traditionally a linear one • Economic information (e.g., prices, costs) • 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**When Should Predictive Control be Used?**MPC displays its main strength when applied to problems with • Processes are difficult to control with standard PID algorithm (e.g., large time constants, substantial dead times, inverse response, etc.) • There is a large number of manipulated (u) and controlled variables (y) • 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. • Constraints (limits) on process variables and manipulated variables are important for normal control • There are multiple disturbances; if they can be measured, this exploits the built-in feedforward capabilities of MPC from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed