Department of thechnology


Lecture plan

SCE4106 Model Predictive Control


 
Week nr. Date Subject Tehme Topic
34 24.8. Introduction, notations, cost function, constraints, prediction model.

Ch. 2.1

35 31.8 Prediction Model (PM) from state space models. Rewriting the cost function in order to remove the summation. Explicit unconstrained solution of the MPC problem. Ch. 2, Ch. 3
36 7.9 MPC in terms of control rate of change variables. Prediction models by using rate of change variables, Ch. 2.3.2. Prediction models using models with non-zero mean values, Ch. 2.3.4.
37 14.9 How to handle process constraints, ch. 9 and 10.. More general criterion, ch. 6. Solving QP problems using MATLAB software, etc.. Ch. 3. Optimization.
38 21.9 Constraints (e.g. output) in the MPC problem. Model Predictive Control with integral action (item 2 in Syllabus list) or Ch. 10 in Lecture notes. Prediction models using models with non-zero mean values, Ch. 2.3.4.
39  28.9 Model Predictive Control with integral action. How to handle time delay.

More on optimization of non-linear functions and QP problems. Overview of numerical optimization. Serach methods. Newton method. Stepest descernt method. Line search parameter. Newton method for quadratic problems.

LQ control with integral action: mic-journal

40 5.10 Model Predictive Control with integral action. Exercise with integrator and time delay. exercise_integrator_mpc.pdf Implementation. Models used in MPC.

New method for PI controllertuning of integrating pluss time delay systems.

41 12.10.  No lecture. Work with exercise project.

42

19.10

MPC overview. 1) System model, 2) Control objective, 3) Prediction model, 4) Optimization method, 5) State observer.

LQ optimal control with integral action mic-journal

Discrete LQ optimal control. Presenting Exercise 6. Syllabus

State observers: Note

Syllabus: Exercises 1-5. Lecture notes. Ch. 1, Ch. 2. (skip Ch. 2.3.5. skip example 2.6). Ch. 3. Ch. 4. Ch. 5 (overview). Ch. 8 and 9.

43 26.10 Discrete LQ optimal control. Presenting Exercise 6. Syllabus

Main Topic: MPC vs. Optimal Control

44 2.11 LQG control, state estimation, relations to MPC. Section 2.5 in Note Mention shortly. The separation principle. Check for robustness separatly

1. How to incorporate integral action in MPC. Discussion.

2. State estimation on observers, paper. Matlab m-files in paper: lpe2.m, lpe.m, ss2ocf.m

45 9.11 No Lecture: Work with as described below:

1) Exercises and the 5 exercise project.

2) Read paper about historical overview of MPC (Qin 2000 paper) and methods as DMC, MAC.

3) Lecture notes Ch. 2.3.5, Ex. 2.6. Generalized Predictive Control (GPC). CARIMA and ARIMAX models. Diophantine quation. Software: poly2gpcpm.m, demo_gpcpm.m, demo_gpcpm2.m m-files used: ss2essm.m htilde2.m

4) LQ and MPC of a inverted pendulum. Some continuous LQ optimal control theory and similarities with MPC control. In connection with Example 5.7 in the lecture notes. Software main_empc_pendel.m ss2h.m

46  16.11 1. More on MPC with integral action. Exercise 6 and simulation results. Control horizon, Ch. 4. MATLAB m-file implementation  main_exercise6_mpc.m  of Exercise 6 (MPC of non-linear chemical rector).

2. Discrete LQ optimal control with integral action and connection to standard PID controller (Paper) and  (MIC-paper) Software for computing the LQ controller: dlqdu_pi  Example m-files: Example 5.1  dlq_ex4_du.m Example 5.2: dlq_ex3_du.m 

3. MPC using local PID/PI controllers. Robustness of standard feedback systems.

47 23.11 1) Computing present state, x_k. Kalman filter. In terms of past inputs and outputs. Lecture notes, Ch. 2.

2) Estimating present state, x_k. Extended Kalman Filter (EKF). Kalman filter on prediction form, and apriori aposteriori form.

3) Uncented Kalman Filter (UKF). UKF note

48 30.11 Summing up lecture. Exam tasks.
49 7.12.  
 

 

Faglærer: Dr. ing., 1. amanuensis David Di Ruscio                             


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Oppdatert 19.08.2002 av david.di.ruscio@hit.no