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)
Exercise 3 in the Exercise note.
Contents: Definitions, impulse response matrices, realisation theory, etc..
Week 4. Exercise 1 in the note of exercises.
Contents: System identification of autonomeous 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
Contents: Identification of refiner data from former Union using the DSR Toolbox for MATLAB
Week 5-6. 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.
Week 7. The last part of exercise 11, i.e. the computation of B and E, or start with exercise 13.
Contents Week 6-7: 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 7-8-9. 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.
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
Contents: Subspace system identification of combined deterministic and stochastic systems.
Contents: Kalman filter and state estimation for linear dynamic systems.
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.)
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.
Exercise 14 and 15 in exercise booklet. Topic: Prediction Error Methods (PEM) for system identification.
See the following script as help support for solving Exercise 15, armax_demo.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 adavantage 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 higer order ARX model is identified. The second step is a model reduction step based on the Hankel matrix realization theory.
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.
Week 19. Preparation for the exam. Work with earlier exam tasks.