SITUATION

The following system has already been designed, however the performance parameters need to be specified.

REQUIREMENT

Determine whether the following system is stable and predict the closed loop pole location for the system for K = 4. Also, find the system error.

SOLUTION

For system stability use Routh-Hurwitz method:

Characteristic Polynomial: s ³+2 s ²+ Ks+ K

Routhian Array:

The first column is positive for all positive values of K and the system is stable. The root locus is sketched by setting G = ?1 (that is, using the basic rules of root locus, G = 1, ? _G = n180 with n being any odd iteger) one obtains the following sketch:

The system is stable for all values of positives K's.

The system error is zero for both a step and ramp input, but is finite for an acceleration input (a/s ³):

Therefore the error is 0.5 of the acceleration input.

SITUATION

The open loop transfer function for a control system is approximated by:

It is desired to make the output signal (C) correspond as nearly as possible to some input signal, (R), in steady state, at the same time keeping the system stable.

REQUIRED

1. Sketch a block diagram for a feedback control system to accomplish the given objective. Carefully label the summation polarity of all signals coming into the feedback junction summing point. (Note that the given...