Computer Science prof. Jerzy Świątek System Analysis and Decision Support in Computer Sciences

Transcription

1 Computer Science prof. Jerzy Świątek System Analysis and Decision Support in Computer Sciences modeleisystemy.pl/dla studenta L.1. Model in the systems research. Introduction basic concept

2 Contact hours room 120, building C-3 Monday: and Tuesday (first and last in month): Tuesday: Wednesday: Saturday: and

3 Exam

4 SUBJECT OBJECTIVES C1 Acquisition of skills to create mathematical models of technical and nontechnical processes. C2 Learn how to formulate typical decision making problems and how to solve them. C3 Acquisition of skills to apply computer methods for decision making support.

5 SUBJECT EDUCATIONAL EFFECTS related to knowledge: PEK_W01 Knowledge of modern techniques of modelling and analysis of dynamical processes. PEK_W02 Knowledge of generic decision making problems in computer science. related to skills: PEK_U01 Knows how to apply rules of using class room and laboratory. PEK_U02 Knows how to apply system analysis in scientific and engineering problems. PEK_U02 Knows how to use MATLAB and SIMULINK for engineering computations, in particular for modelling and optimization. related to social competences: PEK_K01 Knows how to present results of its works in clear way. PEK_K02 Knows modern methods of dynamical processes analysis, comprehends the need for new solutions and his/her knowledge improvement

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

7 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

8 Complex systems description benzene solution 1st stage of crystallisation and filtration benzene raw acetylsalicylic acid 1st batch mother liquid dissolution, 2nd stage of crystallisation and filtration drying raw acetylsalicylic acid - 2nd batch acetic acid, benzene, pollutants aspirin Complex system of chemical nature

9 Complex systems description 1 x 2 x 1 u y 1 u 3 O O u 3 1 u 2 2 u 2 2 y 1 O 2 2 y 2 1 y 2 1 y 3 1 v 2 v 3 v Example of complex system

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

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

12 Physical models Laboratory scale of the investigated process Aerodynamic channel

13 Analog models Physical analogue 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

14 Analog models

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

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

17 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.

18 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

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

20 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

21 Identification Task Input Identification plant Output Identifier MODEL

22 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

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

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

25 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

26 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 yn y n u u n

27 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,.

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

29 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

30 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

31 Identifiers realization Identification algorithm Computer program Hardware realization

32 Lecture program 1. Model in systems research. Introduction basic concept. 2. Model building task based on experiment identification problem. 3. Identification of static plant. Deterministic problem determination of the plant parameters. 4. Identification of static plant. Deterministic problem choice of the best model. 5. Noised measurements of the physical values. 6. Estimation of plant parameters with noisy measurements. 7. Choice of the best model probabilistic case. Regression functions. 8. Determination of the regression functions based on the experimental data. 9. Model based decision making (optimal decision, satisfactory decision, acceptable decision). 10. Numerical optimization method 11. Decision under uncertainty 12. Polioptimization

33 Lecture program 13. Identification of dynamic systems. 14. Recursive identification algorithms. 15. Selected problems of complex systems modeling. 16. Modeling of complex of operation systems.

34 Classes and laboratory 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.

35 Seminar 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.

36 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.

37 . 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., Chong E.K.P., Żak S.H., An Introduction to Optimization, Wiley-Interscience, Ogata K., Modern Control Engineering, Prentice Hall, 2009.

38 Thank you for attention