Problem 3.
Q: Can you define some of the terms for me?
A: On part (a), it is not stated, but you are supposed to be designing the inner control loop that only regulates theta. On part (c), C_theta is the controller for the inner theta loop you just designed, and T_theta and S_theta are the complementary sensitivity and sensitivity functions, respectively, of the inner closed loop. The idea is to design a fast inner loop that only cares about theta, and then a slow outer loop for x for which the theta loop is so fast it is nearly instantaneous.
Note: beware when adding two transfer function objects (eg. those generated by sys=tf(num,den)): even if they have identical poles, matlab will generate duplicate poles. One possible way around this is to extract the poles (eg., with zpkdata(sys)) and re-enter the transfer function manually or automatically. Dr. Macmynowsky has included in his lecture notes some details on how to perform this in state-space.
- Sawyer, 2009.01.11 10:30p Updated 2009.01.12 5:12p