Here is a system
to be controlled (Gp(s)) and there is a compensator and
a variable gain, K.
It is been decided that the compensator will have a transfer function of:
Gc(s) = (s + .2)/(s + 2)
The system has time constants of five (5) seconds (numerator) and one-half (0.5) seconds (denominator). The sampling period has to be 0.1 seconds or better, so assume it is 0.1 seconds.