2. Introduction to Feedback Systems / © 1999 Önder YÜKSEL EXAMPLE

3. 25.02.1999EE 302 - Block Diagrams - O. Yuksel 2 Return to example combine cascaded blocks TMTM + - MM MOTOR G1G1

4. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 3 valve MM KvKv MM q0q0

5. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 4 Double tank + - q0q0 q1q1 h1h1 - h2h2 + q1q1 + - q2q2 h2h2

6. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 5 turbine-generator KGKG iFiF vLvL h2h2 GG N TGTG B G +sJ G N q2q2 K G (R F +sL F )N(B G +sJ G )

7. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 6 No more cascaded blocks No parallel blocks 1 feedback configuration comparatormotorvalvedouble tankturbine-generator K + - VRVR VLVL VMVM KvKv q0q0 + - h1h1 - + q1q1 + - h2h2 q2q2 N TGTG VLVL + - MM

8. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 7 Double tank q0q0 h1h1 - h2h2 + q1q1 + - q2q2 h2h2 q1q1 + -

9. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 8 Double tank feedback + q1q1 + - q2q2 q0q0 + - - h2h2

10. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 9 Double tank - + + q1q1 - h2h2 - q2q2 + q0q0 +

11. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 10 Double tank cascaded q1q1 + - q2q2 q0q0 - h2h2 +

12. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 11 Double tank q1q1 + - q2q2 q0q0 - + cascaded

13. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 12 Double tank feedback + + q0q0 - - q2q2

14. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 13 Double tank - q2q2 q0q0 +

15. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 14 + - MM G1G1 ebeb KbKb K + - VRVR VLVL VMVM h2h2 N TGTG VLVL N(B G +sJ G )K G (R F +sL F ) - q2q2 q0q0 + K v /s cascade G3G3 feedback G2G2

16. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 15 feedback + - VRVR VLVL TGTG VLVL K G (R F +sL F ) VMVM q0q0 K K v /s G2G2 + - q2q2 G3G3 N

17. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 16 TGTG K G (R F +sL F ) VMVM q0q0 K K v /s G2G2 VLVL + - VRVR VLVL cascade G4G4

18. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 17 VLVL VLVL + VRVR G4G4

19. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 18 Parameter values Motor êR a =1 êL a =1 êK m =1 êK b =1 êJ M =1 êB M =1 Turbine êN=1 Generator êJ G =1 êB G =1 êL F =1 êR F =1 êK G =1 Valve êK v =1 êB v = 1 Double tank êA 1 =1 êA 2 =1 êR 1 =1 Comparator gain K is the control parameter

20. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 19

21. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 20

22. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 21

23. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 22 t=0:.1:20; for K=5:21; n=K*[1,1,1];d=[1,5,9,K+6,K,K]; step(n,d,t), text(21,0,strcat('K=',num2str(K))), pause,figure(1), end MATLAB simulation

24. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 23

25. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 24 Time (sec.) Amplitude Step Response 0246810 0 50 100 150 200 250 300 350 K=1 K=40 K=10

26. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 25 End of Chapter General index Restart section Next chapterRestart chapter End show The End i