State Feedback Disturbance Controller Plant/Process Output u y S kr

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Presentation transcript:

State Feedback Disturbance Controller Plant/Process Output u y S kr x -K kr State Feedback Prefilter State Controller u Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo State Feedback

Exercise 1: Linearization

Exercise 1

Exercise 2: Steady State Value Compute the steady state response for the system below subject to a step input: m k b massless cart u x

Exercise 2: Steady State Value

Exercise 2: Steady State Values >> sys = ss(A,B,C,D) a = x1 x2 x1 0 1 x2 -0.6667 -0.1333 b = u1 x1 0.1333 x2 0.6489 c = x1 x2 y1 1 0 d = y1 0 Continuous-time state-space model. >> step(sys) From Matlab: >> A=[0 1;-k/m -b/m] A = 0 1.0000 -0.6667 -0.1333 >> B=[b/m;k/m-(b/m)^2] B = 0.1333 0.6489 >> C=[1,0] C = 1 0 >> D=0 D =

Exercise 3: Reachability Determine the Reachability of m k b massless cart u x

Exercise 3: Reachability

Exercise 4: State Feedback Design a state feedback controller that will move the eigenvalues from to for the purpose of reducing the amount of oscillation of the mass. m k b massless cart u x

Exercise 4: State Feedback

Exercise 4: State Feedback