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 + 1)/(10s + 1)
The system has time constants of one (1) second (numerator) and ten (10) seconds (denominator). The sampling period has to be 0.2 seconds or better, so assume it is 0.2 seconds.