F11_ECH157_Quiz2

F11_ECH157_Quiz2 - University of California, Davis...

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Unformatted text preview: University of California, Davis Department of Chemical Engineering & Materials Science ECH 157 – Process Dynamics and Control Fall 2011 – Quiz # 2 Instructions: This is a 30-minute closed-book closed-notes quiz. Please print your name on all answer sheets, label the problems clearly and put them in the right order. Read all questions carefully; answer them concisely and neatly. Point values for each problem are based on 10 points total for the quiz. Good Luck!! Problem 1: The question has been raised whether an open-loop unstable process can be stabilized with a proportional-only controller. Ysp Gp = K 1−τ s G c = Kc Y Fig.1 (a) [3 points] For the process and controller shown in Fig.1, find the range of Kc values that yield a stable closed-loop response. (Note that τ is positive.) (b) [3 points] For K = 10 and τ = 20, find the value of Kc that yields a pole at s = - 0.1. What is the offset for these conditions? (c) [4 points] Suppose that you had designed the controller neglecting the dynamics of the measurement sensor. Would the controller still yield a stable closed-loop response when the sensor is in the loop? To check the "robustness" of your design, suppose that the sensor dynamics can be modeled by the following transfer function: 1 Gm ( s ) = τm +1 Find the general conditions on Kc and τm for stability if the system is as shown in Fig.2. Show for τm = 5, that your value of Kc from part (b) does or does not still yield a stable system. Ysp Gp = K 1−τ s G c = Kc Gm Fig.2 Y ...
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