Fall 2001 6.3115-3 e Procedure for an nn order system Determine the desired settling time t Find the k=n polynomial from the table Divide pole locations by ts Form desired characteristic polynomial a(s)and use acker/place to determine the feedback gains Simulate to check performance and control effort Example G(s s(s+4)(s+1) with 5-40 100B 100 so that nm=k=3 Want t=2 sec. So there are 3 50093/2=-25047and (-3.96837845)/2=-1.9834±1.8922 Use these to form a(s and find the gains using acker e The Bessel approach is fine, but the step response is a bit slowFall 2001 16.31 15—3 • Procedure for an nth order system: — Determine the desired settling time ts — Find the k = n polynomial from the table. — Divide pole locations by ts — Form desired characteristic polynomial Φd(s) and use acker/place to determine the feedback gains. — Simulate to check performance and control effort. • Example: G(s) = 1 s(s + 4)(s + 1) with A =   −5 −4 0 1 0 0 0 1 0   B =   1 0 0   so that n = k = 3. — Want ts = 2 sec. So there are 3 poles at: −5.0093/2 = −2.5047 and (−3.9668 ± 3.7845i)/2 = −1.9834 ± 1.8922i — Use these to form Φd(s) and find the gains using acker • The Bessel approach is fine, but the step response is a bit slow