Section 5.1 H2 PID Controllers for the First-Order Plant Q(s)should be proper.Use the following filter to roll the improper solution off: 1 J5)=λ5+1 where A is the performance degree.It is a positive real number. The suboptimal Q(s)is Q(s)=Qopt:(s)J(s)=K(A5+1) Ts+1 Since Q(0)=1/K,Q(s)satisfies the constraint for asymptotic tracking.The unity feedback loop controller is Q(s) 1(Ts+1)(1+0s/2) C(5)=1-G(5)Q(s)-K0Xs2/2+(+0)s 4口：4@4242定9QC Zhang.W.D..CRC Press.2011 Version 1.0 8/78Section 5.1 H2 PID Controllers for the First-Order Plant Q(s) should be proper. Use the following filter to roll the improper solution off: J(s) = 1 λs + 1 where λ is the performance degree. It is a positive real number. The suboptimal Q(s) is Q(s) = Qopt(s)J(s) = τ s + 1 K(λs + 1) Since Q(0) = 1/K, Q(s) satisfies the constraint for asymptotic tracking. The unity feedback loop controller is C(s) = Q(s) 1 − G(s)Q(s) = 1 K (τ s + 1)(1 + θs/2) θλs 2/2 + (λ + θ)s Zhang, W.D., CRC Press, 2011 Version 1.0 8/78