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Exercises in SCE4106 Model Predictive Control

Week 35         Exercise 1 (pdf-file)   Solutions:. See ex's 5.1-5.2 p 37-38

MATLAB m-files: Task 1:  main_ex1b.m , Task 2:  main_ex1_task2b.m

Week 35-36    Exercise 2 (ps-file)  Exercise 2 (pdf-file)   Solutions: main_ex2b.m

An alternative solution: main_exercise2.m

Week 36 -37   Exercise 3 (ps-file)  Exercise 3  (pdf-file)  Solutions: main_ex3.m

Solution proposal using scmat, q2qt and ss2h m-file functions: mpc_exercise3_task1.m

Week 37-38    Exercise 4 (ps-file)  Exercise 4 (pdf-file)  Solutions: losn_ov1_mpc.m   main_ex46.m

Simple active set implementation of a QP problem with inequality constraints: qpsol1.m Qpsol1 can be used as an alternative to quadprog in the MATLAB optimization toolbox.

Week 38-39    Exercise 5 (ps-file)  Exercise 5 (pdf-file)

Matlab solution m-files for Exercise 5, task 5: main_task5.m grad_ex5.m hess_ex5.m

Week 39-40  Work with the examples in MPC algorithm with integral action. Implement MPC algorithm.

Work with Exercise 5 and 5b below. Se also Exercises 1-4. Work with Lecture Notes.  Read Ch. 4 in the Lecture notes about "Reducing the number of unknown control variables in the MPC problem".

Exercise 5b Modify task 1 in exercise 2 in order to use the reduced MPC control strategy, i.e., unly the actual control, u_k, is computed. Solution in:  main_ex_ch4a.m

Week 40 MPC of systems with time delay. Simple integrator example with time delay and MPC compared with conventional PI control. exercise_integrator_mpc.pdf    Some preliminary m-file implementations: main_integrator_mpc.m Se also: ss4delay.m and ss2aug4delay.m Function to find LQ optimal controller for comparison purposes: dlqdu_pi.m

Week 41  Work with 5 exercise project.

Week 42-45  Exercise 6 (ps-file)  Exercise 6 (pdf-file)

Solution proposal: main_exercise6_mpc.m

Some useful MATLAB m-file functions: q2qt.m  eobsv.m  ss2h.m  scmat.m  prbs1.m

Week 45-46  Exercise 7 (pdf)  Exercise 7 (ps-file)     (MPC of a MIMO system).

Solution proposal: main_exercise7_mpc.m

Function to make binary reference signals: prbs1.m

Week 47

1. Work with MPC implementation of Example 1 and Example 3 in the paper "Model Predictive Control with Integral Action". Check different methods for estomating/computing the present state, x_k.

Function to compute the reversed  controllability matrix. rctrb2.m

Week 48  Exercise 8

Extend the MPC algorithm to control the chemical reactor in exercise 6 but where the output is delayed tau=4 samples.

The following m-file may be used as a starting point of solving Exercise 8: main_exercise8_mpc.m

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