G-A1- (7 R(B2s +K) b) Design a PID controller via root-locus to satisfy the following requirements for the controlled system. Sections 3, 9 pos- 6.2 1-0.42 The following notation has been used for the system parameters: Percent Overshoot (%)-pos Settling time (s) T, Peak time (s)-Tp Text Start by manual calculations for the locations of the poles and zeros of the PID controller to satisfy the requirements. Find the required location of the zero for PD control and introduce PI control. Afterwards, use the Sisotool in MATLAB to simulate the response of the system and to refine your design parameters until the desired response is achieved. Do the analytical results match those of simulations? Elaborate on the reasons of your answer. Clearly describe and elaborate on all the simulations steps in the final report, and include the response plots for each stage of the design process. G-A1- (7 R(B2s +K) b) Design a PID controller via root-locus to satisfy the following requirements for the controlled system. Sections 3, 9 pos- 6.2 1-0.42 The following notation has been used for the system parameters: Percent Overshoot (%)-pos Settling time (s) T, Peak time (s)-Tp Text Start by manual calculations for the locations of the poles and zeros of the PID controller to satisfy the requirements. Find the required location of the zero for PD control and introduce PI control. Afterwards, use the Sisotool in MATLAB to simulate the response of the system and to refine your design parameters until the desired response is achieved. Do the analytical results match those of simulations? Elaborate on the reasons of your answer. Clearly describe and elaborate on all the simulations steps in the final report, and include the response plots for each stage of the design process