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 3/71Section 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