I have a transfer function G(s)=1/s(s+10) with sampling and holding, it is easy to relocate poles at 0.5 and -0.5 using a state feedback controller. But if the proportional controller is added to the transfer function, as in G(s)=K/s(s+10), how can the state feedback controller be designed?
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1$\begingroup$ There are a couple problems here. 1. Why are you putting one of your poles at 0.5? Presumably you're referring to a continuous-time system, in which case all of your poles need to be left of the imaginary axis (i.e. negative). 2. What are you trying to do? Are you designing a state space controller or a proportional controller? Is your problem how you re-design the state-space controller when a constant gain K is added to G(s)? Please clarify $\endgroup$– BarbalatsDilemmaJan 4, 2017 at 19:43
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Using given transfer function you can get your state space model by control canonical form and you get your A,B,C,D matrix after that you can derive your P gain or feedback control gain by this equation
P=1/(C*(B*K-1)^(-1)*B)
where K = Feedback control gain [-0.5 -0 5] and P = Proportional Control Gain (in your case it is K)
