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EE 302 Introduction to Feedback Systems

EE 302 Introduction to Feedback Systems. CONTENTS. Introduction Transfer Functions Mathematical Models, Transfer fns. and block diagrams, Block Diagram Simplification State Equations State equations from transfer fns., Canonical forms, Controllability and Observability

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EE 302 Introduction to Feedback Systems

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  1. EE 302 Introduction to Feedback Systems

  2. CONTENTS • Introduction • Transfer Functions • Mathematical Models, Transfer fns. and block diagrams, Block Diagram Simplification • State Equations • State equations from transfer fns., Canonical forms, Controllability and Observability • Time Domain Analysis • Transient response & Steady state error 1.1 - Introduction

  3. CONTENTS (cont’d) • Stability • Routh-Hurwitz test, Root locus • State Feedback • Pole placement, Observer design • Nyquist Stability Criterion • Nyquist criterion & Relative Stability • Design in Frequency Domain • Phase-lead & Phase-lag compensation 1.1 - Introduction

  4. Introduction: Basic concepts

  5. input output A control system = an interconnection of components that will provide a desired system response 1.1 - Introduction

  6. Process or Plant input More general Mostly mechanical or electrical output 1.1 - Introduction

  7. Process output OPEN-LOOP CONTROL SYSTEMS Controller Desired output response 1.1 - Introduction

  8. Controller Process Desired output response output CLOSED-LOOP (FEEDBACK) CONTROL SYSTEMS Comparison Measurement 1.1 - Introduction

  9. + Reference I/P elements Controller Process O/P - Feedback elements Comparison is often a difference device Command Reference input Actuating signal Manipulated variable Controlled variable Feedback signal Usually contain converters (tachometers, transducers etc.) 1.1 - Introduction

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  22. E R C + G - H BASIC FEEDBACK CONFIGURATION “reference” input actuating error “controlled” output 1.1 - Introduction

  23. E R C + G - H TERMINOLOGY G: Forward path gain H: Feedback gain -GH: Loop gain 1.1 - Introduction

  24. E R C + G - H The return difference EFFECTS OF FEEDBACK:Overall transfer function C=G.E E=R-H.C C=G.R-G.H.C 1.1 - Introduction

  25. EFFECTS OF FEEDBACK:Sensitivity +G C +? G Open-loop system ( H=0 ) C=G.R C+C = (G+G).R ThusC = G.R S=1 Relative change: 1.1 - Introduction

  26. Sensitivity:Closed-loop system (H0) Modified byS=1/return difference 1.1 - Introduction

  27. R C + G -20log(1+K) - K=0 K K=1 K=2 (1+K)a EFFECTS OF FEEDBACK:Bandwidth Let 1.1 - Introduction

  28. Use of feedback modifies • the denominator of the transfer fn • modes (natural frequencies) • stability properties (absolute or relative) • bandwidth • sensitivity • disturbance (noise) reduction properties 1.1 - Introduction

  29. End of Section Next section Restart section Next chapter Restart chapter i The End General index End show 1.1 - Introduction

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