Wednesday, Due February 20
EE/MFS599
D(s) = 1/s T
s
HW#8
W(s) + + Gc (z)
G zoh(s)
10 s+6
Y(s)
1. a) b) c)
Ts = 10 msec Re-write the problem so it is completely in the s-domain Make the disturbance zero and let Gc(s) = K. Find the sensitivity of Y(s)/W(s) to the gain K for both the open-loop and unity feedback case when the nominal value is K=100 and the input is a unit step. Predict how the steady-state response will change if K increases by 10% for both the openloop and closed-loop configurations.
2. a) Let the disturbance be a unit step (constant). Design a Robust digital compensator, Gc(z), which will meet the following specifications 1. Closed-loop system is stable 2. ts due to a step is less than 2 seconds 3. ess due to a step is zero 4. Mp < 5% (remember Mohannad's 4.32% means = 0.707 5. Steady-state error due to constant the disturbance d(t)=u(t) is minimized b) Use Simulink to verify your design (in the s-plane using Gc(s)). Initially, set the disturbance to zero and measure your transient (ts and Mp) and steady-state error specs. Then, set the disturbance to a unit step and verify that its effect is negligible c) Your book discusses the case when your disturbance occurs at the output. I made the statement in class that the model we use is the same as the model in the book if we simply put GzohG(s) as a p...