     # IIA2217 System Identification and Optimal Estimation

There will be one new exercise approximately every week. The exercises are related to the weekly exercises which follows the lecture plan. Some of the exercises are taken from a note of exercises which can be down loaded from this page:  Note with exercises Data files: Task/exercise 9 (yov5.dat uov5.dat)

Introduction: Week 6. Mandatory Exercise1  Partial Solution proposal Mandatory

Week 3. Exercise 1.        Solution 1.      Matlab script for solution of the numerical part of exercise 1.

Exercise 3 in the  Exercise note.

Contents: Definitions, impulse response matrices, realization theory, etc..

Week 4. Exercise 1 in the note of exercises. Solution: m-file

Contents: System identification of autonomous systems.

Week 4-5. Exercise 8, using OLS, PCA og PCR. Alternatively Exercise 7 about using the DSR method.

m-file mypcr.m in Exercise 7: mypcr.m

Refiner time series data for Exercise 6 and 7: utmp2.dat, ytmp2.dat  (create folder and save the files, open with MATLAB using the load command)

1. Solution tmp_demo1.m Using utmp.dat, ytmp.dat

2. Solution  (tmp_demo2.m) Using time series data:  r1sd1710.txt

Contents: Identification of refiner data from former Union using the DSR Toolbox for MATLAB

Week 6. Mandatory Exercise1  for spring 2023

Extra task: SID of deterministic systems. Exercises 11 and 12 in the exercise booklet. For the sake of simplicity you can start with exercise 12 which is smaller than exercise 11.

Data files: u.dat   y1.dat  y2.dat

Start working with Task/Exercise13 in note: m-file  proposals:  main_oppg13.m,    mydsr.m

Week 7-8. The last part of Exercise 11, i.e. the computation of B and E, or start with exercise 13.

Contents: Subspace system identification of deterministic systems, and combined deterministic and stochastic systems. Tasks 11, 12 and 13 in Note with exercises

Week 8. Task 13 in exercise booklet. Or work with Tasks 11 and 12 in exercise booklet.

Help function to be used to make the data Hankel matrices to be used in exercise 13, mat4oppg13.m

Week 9. Tasks 1 and 2 in the partial test from 2008: ex08_partial

Week 7-8-9. Exercise 13 in the exercise booklet. It is suggested that you generate test data by simulating a system. Se a proposal in the solution proposal file, main_oppg13.m.

Partial solution proposal:  main_oppg13.m,    mydsr.m    main_task13.m

Help function which can be used to make the data Hankel matrices to be used in exercise 13, mat4oppg13.m

Function used in order to make binary test excitation signals (is used in main_oppg13.m): prbs1.m

An example using the shift invariance technique in Exercise 13: main_idsys.m  sys_sim.m  idsys.m

Contents: Subspace system identification of combined deterministic and stochastic systems.

Week 9-10. Exercise 6 (pdf-file).  Solution proposal solution (pdf) of some parts.

Some help and solution proposals:   main_ov6_1.m   main_ov6_2
main_ex_march6.m

Contents: Kalman filter and state estimation for linear dynamic systems.

Week 11-12.

1) Quadruple tank process. System identification and Extended Kalman filter. Exercise. Data files: Y_4tank.dat and U_4tank.dat

File for simulation of 4tank: main_sim_4tank.m
EKF in paralell with model: main_kalman_4tank.m

2) System Identification example for data from the quadruple tank process. Input and output data in files: Y.dat and U.dat  Example using DSR and PEM for model identification main_quad_14c.m

Week 12-13. Exercise 7 (pdf-file) with MATLAB-scripts.

prbs1.m        (Matlab-script used to generate binary signals. useful  in order to generate input experiments.)

Solution proposal:  main_reak_kf.m, main_reak_ol.m, main_reak_cl.m, main_real_kfd.m

Contents: Extended Kalman filter for non linear systems. Augmented Kalman-filter for combined state and parameter estimation. System identification by use of DSR for non-linear system in both open and closed loop.

Week 12-14-15

Exercise 14 and 15 in exercise booklet. Topic: Prediction Error Methods (PEM) for system identification.

Data set uov8.dat, yov8.dat      Some solutions: losn_oppg12.m

Data set uov9.dat, yov9.dat      Some solutions: losn_oppg13.m

ROLS method: Check out Ex. 7.2 Lecture notes and m-file main_rols_ex.m

R-DSR Toolbox for MATLAB

Week 16.

Exercises 15 (Data set uov9.dat, yov9.dat ) and 16 in exercise booklet. Data set uov10.dat, yov10.dat

See the following script as help support for solving Exercise 15, armax_demo.m

Matlab script solution to Exercise 15 (sol_exercise15.m, utype.m)

Matlab script to simulate system in Exercise 15 (ex15_model_sim.m). Simulation of this file gives the same data as on the files yov9.m and uov9.m.

Week 17. Exercise 16 in the exercise booklet and the ss-pem Toolbox for MATLAB.

A simple and direct optimization based implementation of the prediction error method is presented in the SS-PEM Toolbox for MATLAB. Se the lecture notes (MPC and optimization notes) Ch. 12.5. Investigate how the ss-pem.m function can be used for system identification.

Work with Exercise 16 in the exercise booklet. You can with advantage use the ss-pem function in order to solve this exercise.

modsim.m function to generate data matrices Y and U by simulating the known 2 x 2 system MIMO model

Contents: Prediction error methods and use of the System Identification Toolbox for MATLAB.

Week 18. Exercise 18 in the exercise booklet

Contents: An implementation of a subspace alike method for system identification which is based on two steps. In the first step an higher order ARX model is identified. The second step is a model reduction step based on the Hankel matrix realization theory.

Hence, first estimate a higher order ARX model followed by model reduction in order to construct an n-th order state space model.  Software implementation in the functions: harxmr.m, hank_m.m

Closed loop data matrices Y and U which can bu used in the exercise obtained by running: main_clop_dat.m This file simulate a 2nd order SISO system controlled by a PI controller. The reference is perturbed by a Binary Signal in order to exite/perturb the system sufficiently.

Script for comparing DSR_e and harxmr.m functions: main_dsr_harxmr_chk.m and fun_clop_data.m

Week 19. Preparation for the exam. Work with earlier exam tasks.

 Oppdatert 3.1.2018 av david.di.ruscio@usn.no