ECE332 HOMEWORK 11 ECE332 HOMEWORK 11


1. [Phase lead and phase lag design with Bode plots] The open loop transfer function is

G(s) = 1
(s+0.5)(s+1)(s+2)
The closed loop system has unity feedback.
(a) Design a lead compensator using Bode plot techniques so that the steady state error to a unit step is less than 0.1 and the phase margin is at least 25 degrees.
(b) Design a lag compensator using Bode plot techniques to achieve the same performance.
(c) Find the following for the uncompensated and lead and lag compensated systems: step response, bandwidth, amplifier gain required. Try to relate these results to the general observations in Table 10.7 in Dorf.

2. [Phase lead design with root locus] The open loop transfer function of a numerically controlled machine tool is

G(s) = 1
s(s+1)
The closed loop system has unity feedback. The specification is that the closed loop poles should be at -1+ j1.732 and -1- j1.732.
(a) Show that the specification cannot be achieved by increasing the open loop gain.
(b) Design a cascade lead compensator using root locus techniques to satisfy the specification.

3. [Phase lag design with root locus] The open loop transfer function of a system is

G(s) = 1
s(s+2)
The closed loop system has unity feedback. Design lag compensation so that the dominant poles of the closed loop system are close to -1+ j and -1- j and the steady state error to a unit ramp input is less than 0.2.

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On 25 Apr 2002, 15:33.