Model Predictive Control

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Presentation transcript:

Model Predictive Control

Review

Miall, R. C., Weir, D. J., Wolpert, D. M., and Stein, J. F., (1993), "Is the Cerebellum a Smith Predictor ?", Journal of Motor Behavior, 25, 203-216.

Miall et al

Smith Predictor qd b Plant G(s) q Controller Gc(s) Gm(s) - G*(s)

Model Predictive Control

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 1997. 2. Model Algorithmic Control (MAC) • ADERSA/GERBIOS, Richalet et al. (1978) in France. • Over 5000 applications of MPC since 1980

MPC Features Receding (Finite) Horizon Control Using Time (Impulse/Step) Response Based on Optimal Control with Constraints Suitable for MIMO system

Model Predictive Control Basis

Model Predictive Control b q qd Controller Plant Td Optimizer qm Plant & Disturbance Model

Prediction for SISO Models: Example: Step response model Si = the i-th step response coefficient N = an integer (the model horizon) y0 = initial value at k=0 Unit Step Response

Smith Predictor & MPC Comparison

Comparison of MPC & Smith Predictor Case Plant Plant Model Plant Model Delay Delay I 1/[s(s+wc)] 1/[s(s+wc)] 150 150 II 1/[s(s+wc)] 1/[s(s+wc)] 150 250 III 1/[s(s+wc)] 1/[s(s+wm)] 150 150 IV 1/[s(s+wc)] 1/[s(s+wm)] 150 250 V (s-0.5)/[s(s+wc)] (s-0.5)/[s(s+wc)] 150 150 wc = 2*pi*(0.9), wm = 2*pi*(0.54), Gc=20, time delay is in ms.

Smith Predictor and MPC Outputs for Perfect Model Time (s) Smith Predictor and MPC Outputs for Perfect Model

Smith Predictor and MPC Outputs for Time Delay Mismatch Time (s) Smith Predictor and MPC Outputs for Time Delay Mismatch

Smith Predictor and MPC Outputs for Non-Minimum Phase System Time (s) Smith Predictor and MPC Outputs for Non-Minimum Phase System

Comparison of MPC & Smith Predictor ( Cont. ) Error Case I Case II Case III Case IV Case V SPC 0.2664 0.3096 0.3271 0.3830 0.2485 MPC 0.0519 0.1363 0.1428 0.2525 0.0303 SPC = Smith Predcitor Controller, MPC = Model Predictive Controller, Error is root mean square errors (rad).