(a) Define phase margin (PM) and gain margin (GM) of a system. For what type of linear system, the PM and GM considerations may not be appropriate in assessing relative stability?
(b) An approximate relationship for PM in terms of damping ratio ζ is given by:
Give the main steps of deriving this result using a damped oscillator model.
(c) A position control system, which uses a dc motor to drive an inertial load, is represented by the block diagram given in
Figure P9.23.
The forward transfer function is given by G(s) = 2/s(2s+1)
(i) Sketch the Nyquist diagram of G. On this basis, comment on the stability of the closed loop system.
(ii) Compute the phase margin and gain margin of the closed loop system.
(iii) Determine the exact damping ratio of the closed-loop system and check whether the result agrees with the approximate relation given in Part (a).
(iv) A reference position input of u = 3 sin t is applied to the system. Determine the position response y at steady state.
Figure P9.23
