The design of cruise control systems in heavy vehicles,

Chapter 10, Problem 43

(choose chapter or problem)

An experimental holographic media storage system uses a flexible photopolymer disk. During rotation, the disk tilts, making information retrieval difficult. A system that compensates for the tilt has been developed. For this, a laser beam is focused on the disk surface and disk variations are measured through reflection. A mirror is in turn adjusted to align with the disk and makes information retrieval possible. The system can be represented by a unity feedback system in which a controller with transfer function

\(G_C(s)\) = \(\frac{78.575(s+436)^2}{(s+132)(s+8030)}\)

and a plant

P(s) = \(\frac{1.163 \times 10^8}{s^3+962.5 s^2+5.958 \times 10^5 s+1.16 \times 10^8}\)

form an open loop transmission L(s) = G_c(s)P(s) (Kim, 2009).

a. Use MATLAB to obtain the system’s Nyquist diagram. Find out if the system is stable.

b. Find the system’s phase margin.

c. Use the value of phase margin obtained in b. to calculate the expected system’s overshoot to a step input.

d. Simulate the system’s response to a unit step input and verify the %OS calculated in c.