-0.5s-1 to control the system 3.78s2+3.9s+1 It is desired such that the dynamics

Question

-0.5s-1 to control the system 3.78s2+3.9s+1 It is desired such that the dynamics of the closed loop system response are similar to those of the system s2+1.5s+1 with a PI controller, choosing the PI parameters 1 Attempt this by performing the following steps: i. Obtain a first order approximation of the original system. You can use Simulink to practice for the test. Using this approximate system, determine analytically the closed loop transfer function. Determine Kc and of the PI controller so that the poles of the closed loop system are the ii. same as those of the "desired" system response. iv. Simulate the closed loop system response of the approximate system and compare witlh that of the desired system response. Comment on the differences and how they arise. V. Simulate the closed loop response of the actual system. What is (are) the difference(s) compared with the desired system response and why?

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