Question 8 Second Order Dominant Poles Model in s-Domain and in Frequency Domain (Open and Closed Loop), Step Response Specifications. Consider a certain closed loop control system under Proportional Control, as shown in Figure Q8.1. Open loop frequency response plots of the system (K = 1) are shown in Figure Q8.2 and closed loop frequency response plots of the system (K = 1) are shown in Figure Q8.3. R(s) K P Proportional Controller 100 s(s+ 5) Actuator/Plant Figure Q8.1 Y(s) The closed loop transfer function of the system (K = 1) has been calculated, and its three poles are factorized as follows: P = -0.7791 +j3.3524, P= -0.7791-j3.3524, P3 = -8.4418. 1) (5 marks) Determine if a second order dominant poles model applies to the closed loop transfer function and if so, derive the model transfer function, Gm1(S); 2) (5 marks) Assume the second order dominant poles model for the closed loop system, based on the information provided in the open loop frequency response plots (Figure Q8.2), and derive the model transfer function, Gm2 (s); 3) (5 marks) Assume the second order dominant poles model for the closed loop system, based on the information provided in the closed loop frequency response (magnitude only) plot (Figure Q8.3), and derive the model transfer function, Gm3 (S); 4) (5 marks) How do the three models compare? Use the one you consider the most accurate to estimate the following closed loop step response specifications: ess(step%), Trise (0-100%) and PO.