Model Predictive Controller Emad Ali Chemical Engineering Department King Saud University

Review Major Control Elements: Instrumentation Instrumentation Control algorithm Control algorithm Process model Process model

Review Control Algorithms: Classical: Classical: PID, cascade, override, ratio, split range, inferential PID, cascade, override, ratio, split range, inferential Advanced: Advanced: Adaptive control Adaptive control Fuzzy logic control Fuzzy logic control Internal model control Internal model control Optimal control Optimal control Neural network control Neural network control Globally linearizing control Globally linearizing control Model predictive control Model predictive control

Benefits of MPC

Industrial MPC Technology  IDCOM (Identification and Command) Model type: Impulse response Model type: Impulse response Optimization is solved by QP approach Optimization is solved by QP approach  DMC (Dynamic Matrix Control) Model type: Step response Model type: Step response Optimization is solved by LP approach Optimization is solved by LP approach  OPC (Optimum Predictive Control) Use step response, solves LP problem Use step response, solves LP problem Model building, controller design and simulation Model building, controller design and simulation tasks are carried out on PCs tasks are carried out on PCs  PCT (Predictive Control Technology) Combines the aspects of IDCOM and DMC Combines the aspects of IDCOM and DMC  HMPC (Horizon Multivariable Predictive Control) For proprietary reasons, information is unavailable For proprietary reasons, information is unavailable

Multivariable vs. Multi-loops

General Application Concept

Receding Horizon Concept (Prediction)

Process Model Model: Y(k/k) = [y(k/k) y(k+1/k) … y(k+n-1/k)] Y(k-1/k) = [y(k-1/k) y(k/k) … y(k+n-2/k)] Prediction: Y(k+1/k) = [y(k/k) y(k+1/k) … y(k+P-1/k)]  U(k/k) = [  u(k/k)  u(k+1/k) …  u(k+M-1/k)] Y(k/k) = M Y(k-1/k) + S  u(k-1/k) Y(k+1/k ) = M P Y(k/k) + S P  U(k/k)

Process Model Correction Output Feedback: Output Feedback: Y(k+1/k ) = Y(k+1/k) + N  y p (k)-y m (k)]

Methods of Solution 1. Algebraic Equation: 2. Linear Programming (LP) R(k+1)=Y(k+1) = M P Y(k) + S P  U(k) |R(k+1)-Y(k+1)| = |R(k+1)-[M P Y(k) + S P  U(k)]| = 0

3. Quadratic Programming Methods of solution 4. Constrained QP min [R(k+1)-Y(k+1)] T  [R(k+1)-Y(k+1)] +  U T (k)   U(k)  U(k) min [R(k+1)-Y(k+1)] T  [R(k+1)-Y(k+1)] +  U T (k)   U(k)  U(k) U l ≤ U ≤ U u  U l ≤  U ≤  U u

Methods of solution Constrained QP QPLPAlgebraic LargerLargemediumSmalldifficulty better YesNooptimization YesNo constraints

Tuning Parameters Output weights: Input weights: Prediction horizon: Control horizon:

Tuning Guidelines function Tuning parameter Gives more weight to a specific output  Slower response, stabilizing effect  More stable and robust response P Faster (even unstable) response M

Generating Step Response Model 1. Step testing

Generating Step Response Model 2. PBRS Testing

Step Vs. PBRS Requires long testing time Simple and straightforward Step Requires less testing time Requires knowledge about identification theory PBRS

Implementation requirement DCS system DCS system Personal Computer Personal Computer Step response model Step response model Tuning Tuning

Special Features of MPC Feed-forward capability Feed-forward capability Inferential control Inferential control Output Constraints Output Constraints Y(k+1/k) = M Y(k/k) + S  U(k/k) + W d(k/k) Y(k+1/k) = M Y(k/k) + S  U(k/k) Z(k+1/k) = CY(k+1/k) Y l (k+1) ≤ Y (k+1) ≤ Y u (k+1)

Special Features of MPC Variable set point Variable set point or constraints

Simulation Example

F200/C2, P100/P2

P100/C2, F200/P2

Thank You Questions ?