Consider the digital control system shown in Figure 4-69, where the plant is of the first order and has a dead time of 5 sec. By choosing a reasonable sampling period T, design a digital PI controller such that the dominant closed-loop poles have a damping ratio zeta of 0.5 and the number of samples per cycle of damped sinusoidal oscillation is 10. After the controller is designed, determine the response of the system to a unit-step input. Consider the digital control system shown in Figure 4-69, where the plant is of the first order and has a dead time of 5 sec. By choosing a reasonable sampling period T, design a digital PI controller such that the dominant closed-loop poles have a damping ratio zeta of 0.5 and the number of samples per cycle of damped sinusoidal oscillation is 10. After the controller is designed, determine the response of the system to a unit-step input