Use MATLAB for simulating the system. Effect of Controller Gain on Open and Closed loop Responses in Frequency domain The objective of this assignment is to enable you to get a feel for the effect of controller gain on some important system characteristics in the frequency domain. For our plant, we will use a simple third- order system. The plant transfer function is: Gp(s) = Kpwn²(s+1) (Ts + 1)(s² + 23wns + wn²) Where, Kp= 3, T = 3, } = 0.5 and w₁ = 10 rad/sec The controller is a simple gain Kc in the forward path, upstream from the plant (before the plant). For the range of controller gain given below, obtain the Frequency Response characteristics of the system. This is best done by obtaining Bode plots of the open and closed loop systems. Use your frequency response curves to determine the following frequency response characteristics of the system: Bandwidth, Peak Resonance, and the Resonance Frequency of the system (use the bode command). Tabulate these characteristics in a table both for the open loop and closed loop cases for the following controller gains: Ke=0.2, 0.5, 1, 10 Note: Peak Resonance: This is obtained by finding the maximum of the function | Gp(jw) | (or the magnitude of the closed loop transfer function) with respect to frequency. Resonant Frequency: This is the frequency at which the peak resonance occurs. System Bandwidth: This represents the frequency range in which the magnitude of the transfer function drops no more than 3dB from its zero-frequency value. Hint: Use stf('s'); for simulating the transfer function. Report: Your report should be in the form of a brief technical memo stating the effect of controller gain on the open-loop and closed-loop response characteristics. Be sure to make observations, for example, "How does control gain affect the bandwidth in a closed-loop system, and how is this different than the effect on open-loop systems?" Attachments containing the various plots should be properly labeled and referenced. Your report should include the following: (1) Problem definition, (2) Models (codes) /simulation results/calculations and tables, (3) Discussions, (4) Conclusions.