__ ECE 421, Homework #11 __

Due Tuesday, April 14, 1998

**For each problem, design a compensator G _{c }(s) such that all of the specifications are satisfied. Sketch the uncompensated and compensated root locus 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 £ 1;

2. the compensated settling time must be < 4 seconds;

3. the damping ratio for the dominant closed-loop poles must be ³ 0.707.

2. The transfer function for a certain system is

The following specifications must be satisfied by the compensated system:

1. the steady-state error for a unit ramp input must be £ 0.025;

2. the compensated settling time should be 2 seconds;

3. the percent overshoot for a step input should be 4% - 5%.

3. The transfer function for a certain system is

The following specifications must be satisfied by the compensated system:

1. steady-state error for ramp input = 0.01;

2. settling time for a step input must be £ 1 second ;

3. percent overshoot to a step input must be approximately 5%;

4. the design cannot produce any pole/zero cancellations.

4. The transfer function for a certain system is

The following specifications must be satisfied by the compensated system:

1. steady-state error for ** ramp** input = 0.1;

2. settling time for a step input should be = 4 seconds ;

3. damping ratio for dominant closed-loop poles should be 0.707.

5. The transfer function for a given unstable plant is

The following specifications must be satisfied by the compensated system:

1. one closed-loop pole must be located at s = s_{1} = -2.5 + j8.5;

2. the closed-loop system must be stable.

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