PME320700 s Lecture 6 Instructor : Cheng-Hsien Liu 劉承賢 liuch@pme.nthu.edu.tw http://mx.nthu.edu.tw/~chhsliu Lecture 6 1 http://mx.nthu.edu.tw/~chhsliu/control/ta_hours.pdf Lecture 6 2 1
Chapter 1: An Overview and Brief History of Feedback Control Chapter 2: Dynamic Models Chapter 3: Dynamic Response Chapter 4: A First Analysis of Feedback Chapter 5: The Root-locus Design Method Chapter 6: The Frequency-response Design Method Chapter 7: State-space Design Chapter 8: Digital Control Chapter 10: Control Systems Design: Principles and Case Studies Appendix A: Laplace Transforms Appendix B: Solutions to the Review Questions Appendix C: MATLAB Commands Appendix WA: A Review of Complex Variables Appendix WB: Summary of Matrix Theory Appendix WC: Controllability and Observability Appendix WD: Ackermann's Formula for Pole Placement Chapter 9: Nonlinear Systems Appendix W2.1.4: Complex Mechanical Systems Lecture 6 3 error control r e u y K P desired output Controller Plant actual output /reference input Lecture 6 4 2
Y R T ol Lecture 6 5 p. 7 p. 9 p. 8 Lecture 6 6 3
Lecture 6 7 Lecture 6 8 4
Lecture 6 9 E Lecture 6 10 5
desired output error r e K u Controller ybar Terms control r(t): reference input or command signal y(t): sensed/actual outpt e(t)= r(t) - ybar(t) u(t): control input Plant P ybar: estimate of y Purpose: find compensator/controller - error is small - stability is good d i sensor P Plant disturbances n d o sensor noise y Lecture 3 Lecture 6 If r(t) is a constant -> regulator problem If r(t) =function of time -> servo or tracking problem 11 Lecture 6 12 6
What does Feedback Control do? 1. Static response (steady-state) 2. Dynamic response (transient) 3. Disturbance rejection Lecture 6 13 Laplace transform for functions f Lecture 3 Lecture 6 14 7
error control r e u y K P desired output Controller Plant actual output /reference input Lecture 6 15 Page 10 X E cl = E E cl =E Lecture 6 16 8
Recap Lecture 6 17 Recap Lecture 6 18 9
Page 10 X E cl = E E cl =E Lecture 6 19 E(s) E cl =R-Y E cl =R-Y=E Lecture 6 20 10
System Type System type: a figure of merit for a control system with respect to tracking command/rejecting disturbance R(s) E(s) Gs () Y(s) 1 Test Signals Y G() s R() s Es () R Y R 1 G( s) 1 Gs ( ) E cl 2 t r( t) 0 r( t) t u(t) r( t) t u(t) 2 u(t) Step Input Ramp Input Parabolic Input Lecture 6 21 1 r( t) t 0 R(s) E(s) Gs () Y(s) R() s Es () R Y 1 Gs ( ) Lecture 6 22 11
1 R(s) E(s) Gs () Y(s) 1 type N system (type 1 system / type 2 system ) Lecture 6 23 r( t) t R(s) E(s) Gs () Y(s) R() s Es () R Y 1 Gs ( ) Lecture 6 24 12
R(s) E(s) Gs () Y(s) Lecture 6 25 R(s) E(s) Gs () Y(s) R() s Es () R Y 1 Gs ( ) Lecture 6 26 13
R(s) E(s) Gs () Y(s) type 0 system & type 1 system type 2 system type 3 system / type 4 system Lecture 6 27 Test Signals 1 0 r( t) t u(t) r( t) t u(t) 2 t r( t) 2 u(t) Lecture 6 28 14
(1) 有興趣自己看懂! Page 209~210 你們不用問我! 我們不用此解釋! (2) GD cl has n poles at the origin Lecture 6 29? Lecture 6 30 15
X Page 19 Homework! Lecture 6 =? 31 Lecture 6 32 16
Practice by your own 不需跟著課本解法 搞懂上課筆記教的 看是否解得出課本的最後答案 Lecture 6 33 Page 212 Page 215 Lecture 6 34 17