1 Chapter 20 Model Predictive Control Model Predictive Control (MPC) – regulatory controls that use an explicit dynamic model of the response of process variables to changes in manipulated variables to calculate control “moves”. Control moves are intended to force the process variables to follow a pre-specified trajectory from the current operating point to the target. Base control action on current measurements and future predictions.

2 Figure: Two processes exhibiting unusual dynamic behavior. (a) change in base level due to a step change in feed rate to a distillation column. (b) steam temperature change due to switching on soot blower in a boiler.

3 DMC – dynamic matrix control became MPC – model predictive control Optimal controller is based on minimizing error from set point Basic version uses linear model, but there are many possible models Corrections for unmeasured disturbances, model errors are included Single step and multi-step versions Treats multivariable control, feedforward control

4 When Should Predictive Control be Used? 1.Processes are difficult to control with standard PID algorithm – long time constants, substantial time delays, inverse response, etc. 2.There is substantial dynamic interaction among controls, 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.

5 Model Predictive Control Originated in 1980s Techniques developed by industry: 1.Dynamic Matrix Control (DMC) -Shell Development Co., Cutler and Ramaker (1980), -Cutler later formed DMC, Inc. -DMC acquired by Aspentech in Model Algorithmic Control (MAC) ADERSA/GERBIOS, Richalet et al (1978) Over 4000 applications of MPC since 1980 (Qin and Badgwell, 1998 and 2003).

6 Model Predictive Control Based on Discrete-time Models Time-delay compensation techniques predict process output one time delay ahead. Here we are concerned with predictive control techniques that predict the process output over a longer time horizon. (e.g., open-loop response time).

7 Figure 20.2 Basic concept for Model Predictive Control

8 General Characteristics Targets (set points) selected by real-time optimization software based on current operating and economic conditions Minimize square of deviations between predicted future outputs and specific reference trajectory to new targets Discrete step response model Framework handles multiple input, multiple output (MIMO) control problems.

9 Can include equality and inequality constraints on controlled and manipulated variables Solves a quadratic programming problem at each sampling instant Disturbance is estimated by comparing the actual controlled variable with the model prediction Usually implements the first move out of M calculated moves

10 Discrete Step Response Models Consider a single input, single output process: Where u and y are deviation variables (i.e. deviations from nominal steady-state values).

11 Discrete Convolution Models (continued) Denote the sampled values as y 1, y 2, y 3, etc. and u 1, u 2, u 3, etc. The incremental change in u will be denoted as  u k = u k – u k-1 The response, y(t), to a unit step change in u at t = 0 (i.e.,  u 0 = 1 is shown in Figure 7.14.

12 Figure 7.14 Unit Step Response

13 In Fig. 7.14, Note:h i = S i – S i-1 y 1 = y 0 + S 1  u 0 y 2 = y 0 + S 2  u 0 (  u 0 = 1 for unit step.. change at t = 0).. y n = y 0 + S n  u 0

14 Alternatively, suppose that a step change of  u 1 occurred at t =  t. Then, y 2 = y 0 + S 1  u 1 y 3 = y 0 + S 2  u 1. y N = y 0 + S N-1  u 1 If step changes in u occur at both t = 0 (  u 0 ) and t =  t (  u 1 ).

15 From the Principle of Superposition for linear systems: y 1 = y 0 + S 1  u 0 y 2 = y 0 + S 2  u 0 + S 1  u 1 y 3 = y 0 + S 3  u 0 + S 2  u 1. y N = y 0 + S N  u 0 + S N-1  u 1 Can extend also to MIMO Systems

16 Figure Individual step-response models for a distillation column with three inputs and four outputs. Each model represents the step response for 120 minutes. Reference: Hokanson and Gerstle (1992).

17 Selection of Design Parameters Model predictive control techniques include a number of design parameters: N:model horizon  t:sampling period P:prediction horizon M:control horizon (number of control moves) Q:weighting matrix for predicted errors (Q > 0) R:weighting matrix for control moves (R > 0)

18 Selection of Design Parameters (continued) 1.N and  t These parameters should be selected so that N  t > open-loop settling time. Typical values of N: 30 < N < Prediction Horizon, P Increasing P results in less aggressive control action Set P = N + M 3.Control Horizon, M Increasing M makes the controller more aggressive and increases computational effort, typically 5 < M < 20 4.Weighting matrices Q and R Diagonal matrices with largest elements corresponding to most important variables