Assignment #2 Read Chapter 4

1. A closed loop first-order system and its unit step response are shown below. Find parameters K and t .

2. (a) For the system shown below, sketch the unit step response of the system without mathematically solving the time response c(t).

Indicate approximate numerical values on both the amplitude axis and the time axis.

(b) Run SIMULINK simulation of exactly this system, and compare the results to those in (a).

3. Shown below is a satellite attitude control system. The model is developed in Chapter 2 of the text. The moment of inertia, J, has been normalized to unity.

(a) Write the system transfer function for this attitude control system.

(b) The system is commanded to assume an attitude of 10^o [q_r(t) = 10u(t)]. After transients die out (steady

state), what is the attitude angle q_ss(t) ?

(c) The closed loop system is to respond to a step input in minimum time with no overshoot, which requires that

z = 1. Find K_v as a function of K such that this specification is satisfied.

(d) The system is to reach steady state approximately 6 sec after a command to change the attitude angle.

Find a value of K that satisfies this spec.

(e) Verify the results of (b) thru (d) above with a MATLAB simulation.

4. For the satellite control system above,

(a) Find the close-loop transfer function

(b) Find the closed-loop dc gain

(c) If K_v = 0, find the closed loop system gain (magnitude of frequency response) at resonance

(d) Design specifications of the system are that the peak closed-loop gain cannot be greater than 1.25 and

that the system time constant t = 1sec. Design the system by finding K and K_v such that the

specifications are satisfied. Note that the damping of the system has been increased by velocity

(rate or derivative) feedback.