2. Introduction to Feedback Systems / © 1999 Önder YÜKSEL

3. 14.02.19991.1 - Introduction 2 CONTENTS çIntroduction çTransfer Functions çMathematical Models, Transfer fns. and block diagrams, Block Diagram Simplification çState Equations çState equations from transfer fns., Canonical forms, Controllability and Observability çTime Domain Analysis çTransient response & Steady state error

4. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 3 CONTENTS (cont’d) çStability çRouth-Hurwitz test, Root locus çState Feedback çPole placement, Observer design çNyquist Stability Criterion çNyquist criterion & Relative Stability çDesign in Frequency Domain ç Phase-lead & Phase-lag compensation

5. Introduction to Feedback Systems / © 1999 Önder YÜKSEL

6. 14.02.19991.1 - Introduction 5 input system = an interconnection of components that will provide a desired system response A control output

7. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 6 input output Process or Plant More generalMostly mechanical or electrical

8. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 7 OPEN-LOOP CONTROL SYSTEMS Controller Process output Desired output response

9. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 8 Desired output response Comparison CLOSED-LOOP (FEEDBACK) CONTROL SYSTEMS Measurement Controller Process output

10. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 9 Comparison is often a difference device Reference I/P I/Pelements Feedbackelements ControllerProcess O/P Command Reference input Actuating signal Manipulated variable Controlled variable Feedbacksignal Usually contain converters (tachometers, transducers etc.)

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23. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 22 BASIC FEEDBACK CONFIGURATION G H “reference” input“controlled”outputactuatingerror

24. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 23 TERMINOLOGY G H G: Forward path gain H: Feedback gain -GH: Loop gain

25. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 24 EFFECTS OF FEEDBACK: Overall transfer function G H C=G.E E=R-H.C C=G.R-G.H.C The return difference

26. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 25 EFFECTS OF FEEDBACK: Sensitivity G +G+GC+? Open-loop system ( H=0 ) C=G.RC+  C = (G+  G).R Thus  C =  G.R Relative change:

27. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 26 Sensitivity: Closed-loop system (H  0) Modified by S=1/return difference

28. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 27 EFFECTS OF FEEDBACK: Bandwidth G K Let (1+K)a -20log(1+K) K=1 K=2 K=0

29. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 28 Use of feedback modifies çthe denominator of the transfer fn îmodes (natural frequencies) îstability properties (absolute or relative) îbandwidth çsensitivity çdisturbance (noise) reduction properties

30. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 14.02.19991.1 - Introduction 29 End of Section General index Restart sectionNext section Next chapterRestart chapter End show The End i