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midterm99 - satisFes the following criteria 1 Rise time ≤...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F99 Midterm Exam Closed book and notes. No calculators. Show all work. Name: Problem 1: /10 Problem 2: /20 Problem 3: /20 Problem 4: /20 Total: /70 Problem 1 List at least two advantages of feedback control over open-loop control.
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Name: Problem 2 1. Use the Routh test (not the quadratic formula) to show that the roots of the second order polynomial s 2 + bs + c have negative real part if and only if b and c are positive. 2. Use the Routh test to give conditions on the coefficients of the polynomial s 3 + as 2 + bs + c that guarantee the roots have negative real part. 3. Use your answer to part 2 to decide whether the roots of the following polynomials have negative real part: (a) s 3 + 5 s 2 + 2 s + 12 (b) s 3 + 2 s 2 + 9 s + 16 (c) s 3 + 7 s 2 + 3 s + 10 4. Use your answer to part 2 to find the range of values for K such that the closed-loop formed by the controller C ( s ) = K in negative unity feedback with the plant P ( s ) = 1 ( s + 1) 3 is stable.
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Name: Problem 3 Design a controller C ( s ) so that, in negative unity feedback with the plant P ( s ) = 1 s + 1 , the closed-loop transfer function from reference to tracking error is type I and the step response
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Unformatted text preview: satisFes the following criteria: 1. Rise time ≤ 1 sec. (Recall, for second order complex poles, t r ≈ 1 . 8 /ω n ); 2. Overshoot ≤ percentage that corresponds to damping factor 0.7 for the second order complex pole case; 3. 1 % Settling time ≤ 3 seconds (Recall, for second order complex poles, t s = 4 . 6 /ζω n ); Name: Problem 4 The water height in a certain leaky tank is governed by the diferential equation ˙ h = u-10 √ h-1 where u represents water Fow into the tank. 1. ±ind the operating condition that yields a linearized model given by a trans²er ²unction with a single pole at s =-1. 2. Design a controller ²or the tank that measures h and produces values ²or u so that the linearized closed-loop model at the operating condition ²rom part 1 satis³es all o² the properties speci³ed in problem 3....
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