Question

Feedback control of dynamic systems

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I need only (B)

The solution of A uploaded below.

6ple Plant PCs) Tontoller A) Plunt is represented As belo State vecta eg ation Gce 4t) Ult) YiA-II o]it Find Gpl) Y Vs) (B) At the Above Systen. Controller Pis is to Stable the systen Rale of Drs is, when Tnput t)- 1, DIs) MAkes stendy-state euror to be o Design Pes) and Prot the systen can be stable usirn Root Lous -2 TS1-ABD = LI. ) -12 (st2) (stS2)-L12) Tis) S435-10 (S43542)-(2)

Answer 1

(B) fo to have essO centioller fs used K(- Tis) DUS) Tis Given, RCs) - ! and TIS) S435-10 ess lt S2o Ris) S ECS) lt s So t GC H Kkp CHT5 Erls)=k. Ds). Gp(s) Tis (st 3s-10) S-3o tKKptTis) Tis Cs35-10) sso Thus, P conrtsolles is toaken fn place of Ds) to have Ke and Ti of PI Thus, Values of CssO ase usex choice CCan be any values). det's Consides and Ti Ti But sustem con be unttaole coith PI, So, uoe go fos PID Contpilex coth DS) Ke b ess O On genesal Gr s43-10 Kke Cst bs sCs+5) Cs-2) G = K. D(S) - Gp(s) Sine these is a pole RHS K.e S2 this should be Contelled bou zero

G(Sta) bs+C ニ s+ (a-2) s2a Equating o-eficients, ba-2 Cニ-2a a lot2 Let's chooge that implies C-20 and aこt0, bこも Ond -20 KeC ss -20 DCs) s the eguired contolle S fos ess o Stable c Break-awa point Kkp (s-2)t Kke (stio (-) Sts)s s(sts) Centid o-5t 1o 23-3 P-2 e11so(t) Asymtde anfes (2t 1g0 18v 2-1 2-d

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