ES 581: Homework 7

Due: Th 04/03

  1. Do problem 7.2 in textbook.
    -  See Problem 3.6 for numeric values (and state vector) and Problem 2.1 for original problem statement.
  2. Referring to problem 1.) For the system having an initial condition of x0 = [0.5, -0.5, Pi/8, -1] and the observer having an initial condition of [0,0,0,0]. Plot and compare the ZIR of the system's states and the observer's state response.
  3. Problem 7.3 in textbook.
  4. Referring to problem 3.) For the system having an initial condition of x0 = [0.5, -0.5, Pi/8, -1] and the reduced order observer having an initial condition of [0,0,0]. Plot and compare the ZIR of the system's states and the observer's state response.
  5. BONUS PROBLEM (+20%): Refering to problem 1.) compare:
    a. Observer based state-feedback to place all of the system's closed loop poles at -2+-2j. Plot the ZIR with above IC's.
    b. State-feedback (using actual states) to place all of the system's closed loop poles at -2+-2j. Plot the ZIR with above IC.