Section 5.1 H2 PID Controllers for the First-Order Plant 0rs/2+(0+T) 8 (Ts+1)(1-0s/2)=1-0s/2 +5+1 Then W()S()0.( Temporarily relax the requirement on the properness of Q(s).To obtain the minimum,the only choice is Qion(句=R Consequently,the optimal Q(s)is 0m间=5k2 4口：4@4242定9QC Zhang.W.D..CRC Press.2011 Version 1.0 7/78Section 5.1 H2 PID Controllers for the First-Order Plant θτ s/2 + (θ + τ ) (τ s + 1)(1 − θs/2) = θ 1 − θs/2 + τ τ s + 1 Then kW (s)S(s)k 2 2 = θ 1 − θs/2 2 2 + τ τ s + 1 − K τ s + 1 Q1(s) 2 2 Temporarily relax the requirement on the properness of Q(s). To obtain the minimum, the only choice is Q1opt(s) = τ K Consequently, the optimal Q(s) is Qopt(s) = τ s + 1 K Zhang, W.D., CRC Press, 2011 Version 1.0 7/78