(Solved): For the unity feedback system shown below, design a PID controller that will yield the following spe ...

1. ( 30 points) For the unity feedback system shown below, design a PID controller that will yield the following specifications: a) Find the critical value of the gain, \( K_{c r} \), and the critical period, \( P_{c r} \), that will make the system unstable b) The PID should produce a \( \pm 5 \% \) settling time not exceeding 1 second. Provide the PID tuning values for this specification, e.g. \( K_{p}, T_{\text {i }} \), and \( T_{d} \). c) Plot the step response of the tuned PID controlled system \[ G(s)=\frac{K}{s(s+1)(s+3)} \]