
Exercises:IIA2217 System Identification and Optimal Estimation 

There will be one new exrecise approximately every week.
The exercises are related to the weakely exercises which
follows the lecture plan. Some of the exercises are taken
from a note of exeercises which can be down loaded from
this page: Note with
exercises Date files: Task/exercise 9 (yov5.dat uov5.dat) Introduction Week 2. Mandatory
Exercise1 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, realisation theory, etc.. Week 4. Exercise 1 in the note of exercises.
Solution: mfile
Contents: System identification of autonomeous systems. Week 45. Exercise 8, using OLS, PCA og PCR. Alternatively Exercise 7 about using the DSR method. mfile 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 56. SID of deterministic systems. Exercises 11 and 12 in yhe 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 Week 7. The last part of exercise 11, i.e. the computation of B and E, or start with exercise 13. Contents Week 67: Subspace system identification of deterministic systems, and combined deterministic and stochastic systems. 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 789. Exercise 13 in the exercise booklet. It is suggested that you generate test data by simulationg a system. Se a proposal in the solution proposal file, main_oppg13.m. Partial solution proposal: main_oppg13.m, mydsr.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 eample 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 910. Exercise 6 (pdffile).
Solution proposal solution
(pdf) of some
parts.
Some help and solution proposals: main_ov6_1.m
main_ov6_2
Contents: Kalman filter and state estimation for linear dynamic systems. Week 1112. 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
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 1213. Exercise 7 (pdffile) with MATLABscripts. prbs1.m (Matlabscript 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 Kalmanfilter for combined state and parameter estimation. System identification by use of DSR for nonlinear system in both open and closed loop. Week 121415 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 mfile main_rols_ex.m 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 sspem Toolbox for MATLAB. A simple and direct optimization based implementation of the prediction error method is presented in the SSPEM Toolbox for MATLAB. Se the lecture notes (MPC and optimization notes) Ch. 12.5. Investigate how the sspem.m function can be used for system identification. Work with Exercise 16 in the exercise booklet. You can with adavantage use the sspem 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 higer order ARX model is identified. The second step is a model reduction step based on the Hankel matrix realization theory. Hence, first estimate a higer order ARX model followed by model reduction in order to construct an nth 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 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. 

