HOMEWORK_8 - HOMEWORK 8 Question 1 Show that the direct...

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HOMEWORK 8 Question 1 Show that the direct synthesis method for the following process, assuming a desired first order response, yields a PID controller Find the PID tuning parameters if a closed-loop time constant of 5 minutes is desired. Question 2 Consider the following first-order process: If the desired closed-loop response to a setpoint change is second order with the following form: find the feedback controller required, where the α and τ C are adjustable tuning parameters (they are both positive). What type of controller is this? If the controller is PID form (perhaps with a lag), find each of the tuning parameters (Kc, τ I τ D α). Show that τ C >0.5γ is required for the controller to be stable. Question 3 Consider a first-order process with a desired closed-loop response that is second order. Use the direct synthesis procedure with the following specified closed-loop transfer function (which is critically damped) to derive the controller. Perform simulations for several values of τ C and compare and contrast the closed-loop results with those shown in Figure 6-5 of your textbook.
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