Section 5.1 H2 PID Controllers for the First-Order Plant 5.1 H2 PID Controllers for the First-Order Plant An analog of Hoo optimal control theory:H2 optimal control theory Assume that the plant is Ke-0s G(s)= Ts+1 Using the Youla parameterization,we have C(s)= Q(s) 1-G(s)Q(s) where Q(s)is a stable transfer function.It is difficult to treat e-s analytically.Approximate it by the 1/1 Pade approximant: G(S)≈K 1-0s/2 (rs+1)(1+0s/2) 4口+@4定4定0C Zhang.W.D..CRC Press.2011 Version 1.0 3/78Section 5.1 H2 PID Controllers for the First-Order Plant 5.1 H2 PID Controllers for the First-Order Plant An analog of H∞ optimal control theory: H2 optimal control theory Assume that the plant is G(s) = Ke−θs τ s + 1 Using the Youla parameterization, we have C(s) = Q(s) 1 − G(s)Q(s) where Q(s) is a stable transfer function. It is difficult to treat e −θs analytically. Approximate it by the 1/1 Pade approximant: G(s) ≈ K 1 − θs/2 (τ s + 1)(1 + θs/2) Zhang, W.D., CRC Press, 2011 Version 1.0 3/78