A PID controller output p(t), in time domain, is given by p(t)=30+5e(t)+1.25∫₀^te(t)dt+15(de(t)/dt) where e(t) is the error at time t. The transfer function of the process to be controlled is G_p(s)=10/(200s+1). The measurement of the controlled variable is instantaneous and accurate.
The transfer function of the controller is