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

2. Exercise 1: Linearization

3. Exercise 1

4. 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

5. Exercise 2: Steady State Value

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

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

8. Exercise 3: Reachability

9. 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

10. Exercise 4: State Feedback

11. Exercise 4: State Feedback