EE611

Homework #26

Due Wednesday, Nov. 12

1. a) Draw the simulation diagram for:

b) Determine the stability of if

c) Show the region of the Z-plane which meets the following specs if T=0.2 sec.

i) ii) No overshoot iii) both i) and ii)

d) Find a similarity transformation, x_k=Tz_k, which decouples the following state variable model:

e) Draw a simulation diagram for your system in decoupled form

f) Determine which eigenvalues are i) stable ii) controllable iii) observable

g) Is the system stabilizable? Is it detectable?

2. Given the discrete-time system: where 

a) Determine the controllable eigenvalues of the system

b) Is the system stabilizable?

c) Design a feedback regulator such that the closed-loop controllable eigenvalues are {1/10}

d) Let T=1/100. What is the settling-time of the closed-loop system?

e) Now design a control such that ,, (i.e., find y_ref, N_x and N_u)

f) Draw a block diagram of your system.

g) Use dlsim() to simulate your closed-loop sytem over the period 0 to 2 seconds (see HW#17 for how to do this). If you have access to SIMULINK, you can use it instead of dlsim.

h) Obtain a plot of and . What is the actual settling time? What is the steady-state error?

i) Repeat part d) if we set N_u to zero