an engine to be G(s)=(s+0.5)(s+1)1 design a control system to regulate the output of the engine such that - the settling time is less than 2 seconds, - the maximum overshoot is less than 20%, and - the maximum steady-state error is less than 2% of the commanded output. 4. Design a PI controller GPI(s)=Kp+sKi to improve the steady-state error of the closed-loop system, if needed. Note that the PI controller is a lag controller since it adds negative phase-shift to the Bode phase plot of the loop transfer function. Hint: Instead of a pure integrator, implement s+ps+z, where p0.01. Use the FVT to compute the zero location by satisfying the steady-state error requirement. The FVT yields e=1+GPI(s)GPD(s)G(s)1s=0 Pure integrators are not recommended in real systems since a pure integrator's output diverges if a constant nonzero input (usually bias) is applied to the integrator. 5. Simulate the closed-loop system with the designed controller. Does your design satisfy the time-domain specifications? Note that the designed controller is the product of the PD and the PI controller that you designed in the previous two steps. an engine to be G(s)=(s+0.5)(s+1)1 design a control system to regulate the output of the engine such that - the settling time is less than 2 seconds, - the maximum overshoot is less than 20%, and - the maximum steady-state error is less than 2% of the commanded output. 4. Design a PI controller GPI(s)=Kp+sKi to improve the steady-state error of the closed-loop system, if needed. Note that the PI controller is a lag controller since it adds negative phase-shift to the Bode phase plot of the loop transfer function. Hint: Instead of a pure integrator, implement s+ps+z, where p0.01. Use the FVT to compute the zero location by satisfying the steady-state error requirement. The FVT yields e=1+GPI(s)GPD(s)G(s)1s=0 Pure integrators are not recommended in real systems since a pure integrator's output diverges if a constant nonzero input (usually bias) is applied to the integrator. 5. Simulate the closed-loop system with the designed controller. Does your design satisfy the time-domain specifications? Note that the designed controller is the product of the PD and the PI controller that you designed in the previous two steps