Computer Science Jerzy Świątek Systems Modelling and Analysis. L.1. Model in the systems research. Introduction basic concept

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1 Computer Science Jerzy Świątek Systems Modelling and Analysis L.1. Model in the systems research. Introduction basic concept

2 Model in the systems research. Introduction basic concept Model in the systems research Identification task Model based decision Lecture review References

3 Model in the systems research Hypothesis Methods, algorithms: - Projects - Management - Control - Diagnosis Review Identification plant Effect: - New knowledge, - New plant, - Management rolls, - New controllers, -Measurement and diagnostic devices. Experiment Data Goal: - investigation, - project, - management, - control, - diagnosis, Investigator Model Adaptation Comparison

4 Model in the systems research Conceptual models Physical models Analog models Mathematical models Computer models

5 Conceptual models How process is organized? Process elements Connections Elementary functions Example Two stage management system Upper level Element 1 Element 2 Element M

6 Physical models Laboratory scale of the investigated process Aerodynamic channel

7 Analog models Phisical analogs U2 I R ΔU U1 P2 ip ΔP P1 T2 ic ΔT T1 U 2 -U 1 = R I P 2 -P 1 = i p R p T 2 -T 1 = i c R c electrical object hydraulical object termal object

8 Analog models

9 Mathematical models I = C du dt I = U we - U R U we - U du = C R dt to du dt = U we - U RC t U = U we (1-e RC )

10 Example 1 Example 2 d dt d dt x 1 (t)=- x 1 (t)+ y(t)= x 2 (t) R 1 c 1 R 1 c 2 1 c 1 R 2 c 2 u(t) x 2 (t)= x 1 (t) - x 2 (t) x n+1 = x n +u n modulo 2 y n = x n u n {0,1} x 1 (t) y(t)=x 2 (t) u c R c 2 R 2

11 Computer models Analog Digital program ADA; var i,klucz :integer; Napis : string; Napis_sz : array[1..100] of char; Procedure czytaj; begin Write('Podaj klucz: '); readln(klucz); If klucz <=0 then writeln('błędne dane') else readln; end.

12 Model in the systems research Hypothesis Methods, algorithms: - Projects - Management - Control - Diagnosis Review Identification plant Effect: - New knowledge, - New plant, - Management rolls, - New controllers, -Measurement and diagnostic devices. Experiment Data Goal: - investigation, - project, - management, - control, - diagnosis, Investigator Model Adaptation Comparison

13 Mathematical model in the plant investigation K(s) =? = 0,2Hz y(t) output u(t) input

14 Model in the systems research Hypothesis Methods, algorithms: - Projects - Management - Control - Diagnosis Review Identification plant Effect: - New knowledge, - New plant, - Management rolls, - New controllers, -Measurement and diagnostic devices. Experiment Data Goal: - investigation, - project, - management, - control, - diagnosis, Investigator Model Adaptation Comparison

15 Identification Task Input Identification plant Output Identifier MODEL

16 Identification task 1. Determination of the identification plant 2. Determination of the class model 3. Experiment organization 4. Determination of the identification algorithms 5. Identifiers realization

17 Ad.1. Determination of the identification plant z u Identification plant y u input y output measured disturbances unmeasured disturbances

18 Ad.2. Determination of the class of model Process analysis Data analysis y ut y n yt t Arbitrary model Expert model u n t

19 Ad.2. Determination of the class of model Plant in the class of model y u n Identification Plant y n Plant characteristic y n u u n

20 Ad.2. Determination of the class of model Choice of the best model y u n Identification Plant y n Plant characteristic Difference Model y n Model y n y n u u n

21 Ad.3. Experiment organization Static plant U N u u u Y y y y, 1 2 N N 1 2 N Dynamic plant T u t) T tt, YT y( t t t UT ) 0 0 (, Discrete type observations t, t,, Dynamic, discrete type plant t N t n t T, n 1,2,, 0 1 2, N N N u tn ) N n N n1, Y y( t ) n. U ( 1 N u N n n YN yn n U N 1 1,.

22 Ad.3. Experiment organization Passive experiment: Active experiment: U N is measured U N is designed

23 Ad.4. Identification algorithm Input Identification plant Output Identifier N U, Y N MODEL N U N Y N N measurements of input signals measurements of output signals identification algorithm

24 Ad.4. Identification algorithm a U, Y N N Q( a) N n1 ( y n au n 2 ) a * n N y n n n1 2 un u

25 Identifiers realization Identification algorithm Computer program Hardware realization

26 Lecture program 1. Model in systems research. Introduction basic concept. 2. Physical signal characteristics. 3. Continuous signal, Laplace a transforms. 4. Discrete signal, Z transforms. 5. Typical plant models relation between descriptions. 6. Model building task based on experiment identification problem. 7. Identification of static plant. Deterministic problem determination of the plant parameters. 8. Identification of static plant. Deterministic problem choice of the best model.

27 Lecture program 9. Noised measurements of the physical values. 10. Estimation of plant parameters with noisy measurements. 11. Choice of the best model probabilistic case. Regression functions. 12. Determination of the regression functions based on the experimental data. 13. Identification of dynamic systems. 14. Recursive identification algorithms. 15. Selected problems of complex systems modeling. 16. Modeling of complex of operation systems. 17. Model based decision making (optimal decision, satisfactory decision, acceptable decision).

28 Classes Illustration of problems presented during the lecture, and in particular: presentation of the models of chosen computerized plant, exercises connected with the description and analysis of physical signals, a synthesis of chosen identification algorithms, formulation o decision problems based on process model.

29 Seminars Review of typical plant model: conceptual models, mathematical models, examples of difference plant models and decision problems: technical (continuous, discrete type), production process (complex of operations), queuing system modeling, economical process, biomedical plants.

30 Conditions of the course acceptance/credit Classes Students get credit provided they passed tests. Seminars Students get credit provided they realized planned seminars and their reports were positively marked. The lecture ends with the exam. Students are allowed to take the exam provided they got credit from classes and laboratory. To pass the written exam at least 50% of the total points must be obtained. Written exam result may be changed as the result of the oral exam.

31 References Basic literature: Bubnicki Z., Identyfication of control plants, PWN, Warszawa, Bubnicki Z. Modern Control Theory, Springer, Berlin-Heidelberg-New York, Ikonen E., Najim K., Advanced identification and control, CRC Press LLC, Coughanowr D.R., Process Systems Analysisand Control, McGraw Hill International Editions. Hayek S.I., Advanced mathematical methods in science and Engineering, Marcel Dekker, Inc Additional literature: Bazaraa M. S., Sherali H.D., Shett C. M., Nonlinear Programming Theory and Algorithms, John Wiley and Sons, Inc., 2006.

32 Thank you for attention