__ ECE 421 Homework
#15, Spring 2000 __

Due Tuesday, May 9

**In each problem below, design a compensator G _{c }(s) such that all specifications are
satisfied for the system, and plot the original and the final compensated Bode magnitude and phase plots.**

1. A certain plant is described by

The following specifications must be satisfied by the compensated system:

1. the steady-state error for a unit ramp input must be 0.01;

2. the compensated phase margin must be at least 60°;

3. the step response of the compensated system must ** not** be slower than the step
response of the uncompensated system.

2. The transfer function for a certain system is

The following specifications must be satisfied by the compensated system:

1. the compensated gain crossover frequency w_{x-compensated} must be between 0.1 and 1.0 radians per second;

2. the phase margin must be at least 30°;

3. the steady-state error for a parabolic input must be 1.

3. A given plant has the open-loop transfer function

The following specifications must be satisfied by the compensated system:

1. the steady-state error for a unit ramp input must be 0.05;

2. the compensated phase margin must be approximately 45°;

3. the compensated gain crossover frequency w_{x-compensated} must be > 10 r/s.

4. A given plant has the open-loop transfer function

The following specifications must be satisfied by the compensated system:

1. the steady-state error for a unit ramp input must be 0.05;

2. the compensated phase margin must be approximately 45°;

3. the compensated gain crossover frequency w_{x-compensated} must be < 10 r/s.

5. A certain plant is described by

The following specifications must be satisfied by the compensated system:

1. the steady-state error for a unit ramp input must be 0.01;

2. the compensated phase margin must be at least 50°;

3. the closed-loop bandwidth of the compensated system must be ** less** than the bandwidth for the uncompensated system.

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Friday, May 26, 2006 9:42 PM
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