Question 3: Consider the following 4th order system. G(s) (s 1) a. It is desired to find a 2nd order transfer function which represents the above system as accurately as possible. For this purpose, perform the model order reduction via optimization toolbox (use genetic algorithms) and take the following transfer function as a model reference (Choose the bounds of the parameters P1 and P2 in the interval of D. () (p 1) (p 1) Plot the step responses for the real and reduced order systems on the same figure. Comment on the results. b. Design a Pl controller which minimizes the following objective, ice) y(e)ldt via the reduced order transfer function you have found. Here, y(t) is the desired transient response, which can be obtained via the following transfer function: T(s) Again use the genetic algorithms in the optimtool and choose the search space for the PI parameters as K,,K; E [0,5]. Plot the closed-loop system step response with the resulting controller parameters. c. Use the Pl controller, which is designed through the reduced order transfer function in 3.b., to control the real (4th order) system. Plot the closed-loop step response and compare with the one you obtained in 3.b. Is the Pl controller able to control the real system (s) successfully? Give your comments. Question 3: Consider the following 4th order system. G(s) (s 1) a. It is desired to find a 2nd order transfer function which represents the above system as accurately as possible. For this purpose, perform the model order reduction via optimization toolbox (use genetic algorithms) and take the following transfer function as a model reference (Choose the bounds of the parameters P1 and P2 in the interval of D. () (p 1) (p 1) Plot the step responses for the real and reduced order systems on the same figure. Comment on the results. b. Design a Pl controller which minimizes the following objective, ice) y(e)ldt via the reduced order transfer function you have found. Here, y(t) is the desired transient response, which can be obtained via the following transfer function: T(s) Again use the genetic algorithms in the optimtool and choose the search space for the PI parameters as K,,K; E [0,5]. Plot the closed-loop system step response with the resulting controller parameters. c. Use the Pl controller, which is designed through the reduced order transfer function in 3.b., to control the real (4th order) system. Plot the closed-loop step response and compare with the one you obtained in 3.b. Is the Pl controller able to control the real system (s) successfully? Give your comments