Chapter 4 Ho PID Controllers for Stable Plants 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 1/71
Chapter 4 H∞ PID Controllers for Stable Plants Zhang, W.D., CRC Press, 2011 Version 1.0 1/71
Ho PID Controllers for Stable Plants 14.1 Traditional Design Methods 24.2 H PID Controllers for the First-Order Plant 34.3 Hoo PID controller and the Smith Predictor 4.4 Quantitative Performance and Robustness 54.5 H PID Controllers for the Second-Order Plant 64.6 All Stabilizing PID Controllers for Stable Plants 4口，4@，4定4定0C Zhang.W.D..CRC Press.2011 Version 1.0 2/71
H∞ PID Controllers for Stable Plants 1 4.1 Traditional Design Methods 2 4.2 H∞ PID Controllers for the First-Order Plant 3 4.3 H∞ PID controller and the Smith Predictor 4 4.4 Quantitative Performance and Robustness 5 4.5 H∞ PID Controllers for the Second-Order Plant 6 4.6 All Stabilizing PID Controllers for Stable Plants Zhang, W.D., CRC Press, 2011 Version 1.0 2/71
Section 4.1 Traditional Design Methods 4.1 Traditional Design Methods PID Controllers Importance:95%controllers in practice are PID controllers Ideal PID: u0=k[o+元/0+n0] K-Gain Tj-Integral constant e(t)-Error Tp-Derivative constant u(t)-Controller output Assume that C(s)is the transfer function from e(s)to u(s).Using the Laplace transform,we have c=k(++T） 4口+@4定4定0C Zhang.W.D..CRC Press.2011 Version 1.0 3/71
Section 4.1 Traditional Design Methods 4.1 Traditional Design Methods PID Controllers Importance: 95% controllers in practice are PID controllers Ideal PID: u(t) = Kc e(t) + 1 TI Z e(t)dt + TD de(t) dt Kc—Gain TI—Integral constant TD—Derivative constant e(t)—Error u(t)—Controller output Assume that C(s) is the transfer function from e(s) to u(s). Using the Laplace transform, we have C(s) = Kc 1 + 1 TIs + TDs Zhang, W.D., CRC Press, 2011 Version 1.0 3/71
Section 4.1 Traditional Design Methods Practical PID Forms Ideal PID:Has a pure differentiator in it and therefore is not physically realizable An important method for realizing an improper transfer function:Introduce a low-pass transfer function to it Three practical forms: C(s)=Kc1+ TDS 1 TDs+1 C(s)= Ke C(s)= K1+ Usually TF=0.1Tp in a PID 4口，+@，4定4=定0C Zhang,W.D..CRC Press.2011 Version 1.0 4/71
Section 4.1 Traditional Design Methods Practical PID Forms Ideal PID: Has a pure differentiator in it and therefore is not physically realizable An important method for realizing an improper transfer function: Introduce a low-pass transfer function to it Three practical forms: C(s) = Kc 1 + 1 TIs + TDs TF s + 1 C(s) = Kc 1 + 1 TIs TDs + 1 TF s + 1 C(s) = Kc 1 + 1 TIs + TDs 1 TF s + 1 Usually TF = 0.1TD in a PID Zhang, W.D., CRC Press, 2011 Version 1.0 4/71
Section 4.1 Traditional Design Methods Practical PID Forms Ideal PID:Has a pure differentiator in it and therefore is not physically realizable An important method for realizing an improper transfer function:Introduce a low-pass transfer function to it Three practical forms: C(s)= ++） TDS C(s)=Kc(1+ TDs+1 Tis TEs+1 C(s)= TF5+1 Usually TF=0.1Tp in a PID 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 4/71
Section 4.1 Traditional Design Methods Practical PID Forms Ideal PID: Has a pure differentiator in it and therefore is not physically realizable An important method for realizing an improper transfer function: Introduce a low-pass transfer function to it Three practical forms: C(s) = Kc 1 + 1 TIs + TDs TF s + 1 C(s) = Kc 1 + 1 TIs TDs + 1 TF s + 1 C(s) = Kc 1 + 1 TIs + TDs 1 TF s + 1 Usually TF = 0.1TD in a PID Zhang, W.D., CRC Press, 2011 Version 1.0 4/71