Consider the antenna control system of Problem 5.3-15 and Fig. P5.3-15. Let D(z) = 1, T = 0.05 s , and K = 20 .

(a) Using the closed-loop transfer function, derive a discrete state model for the system in the observer canonical form of Fig. 2.6-1.

(b) Derive a discrete state model for the plant from the plant transfer function. Then derive a state model for the closed-loop system by adding the feedback path and system input to a flow graph of the plant.

(c) Calculate the system transfer function from the state model found in part (b), to verify the state model.

(d) Verify the results in part (c) using MATLAB.

Problem 5.3-15

Consider the antenna control system of Fig. P5.3-15. The unit of the antenna angle w(t) is degrees, and the
range is ±135°.

(a) The input signal r(k) is generated in the computer. Find the required values of r(k) to command the
satellite attitude angle w(t) to be ±60°.

(b) Let G_p(s) = 10>(s² + 4s), the transfer function of the motor, gears, and pedestal. Find the system transfer function as a function of the transfer functions D(z), K, and so on.

(c) Evaluate the system transfer function for D(z) = 1, T = 0.05 s, and K = 20.

(d) Verify the results in part (c) using MATLAB.

Transcribed Image Text:

R(z) r(k) + Computer Digital controller D(z) Binary data Vo(z) DIA M(s) 0.5 Amplifier K Sensor T Motor, gears, and pedestal 10 +4s (s) 0(t)