Question

4. (25 pts) Part A: A unity feedback system has $HG(s) = \frac{K(s+2)}{s(s+5)(s^2+2s+5)}$ a) Determine the range of K for stability. b) At what value of K does the system's dynamic behavior enters into a state of self- sustained oscillations? c) What is the frequency of oscillation for the condition of part (b)? Part B: A unity feedback system has the open loop transfer function $HG(s) = \frac{K(s+3)}{s(s-2)}$ Find K such that the damping ratio of the closed loop roots is equal to $1/\sqrt{3}$. Be sure that your K yields a stable closed loop system.

          4. (25 pts)
Part A:
A unity feedback system has $HG(s) = \frac{K(s+2)}{s(s+5)(s^2+2s+5)}$
a) Determine the range of K for stability.
b) At what value of K does the system's dynamic behavior enters into a state of self-
sustained oscillations?
c) What is the frequency of oscillation for the condition of part (b)?
Part B:
A unity feedback system has the open loop transfer function $HG(s) = \frac{K(s+3)}{s(s-2)}$
Find K such that the damping ratio of the closed loop roots is equal to $1/\sqrt{3}$. Be sure
that your K yields a stable closed loop system.

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4. (25 pts)
Part A:
A unity feedback system has HG(s) = (K(s+2))/(s(s+5)(s^2+2s+5))
a) Determine the range of K for stability.
b) At what value of K does the system's dynamic behavior enters into a state of self-
sustained oscillations?
c) What is the frequency of oscillation for the condition of part (b)?
Part B:
A unity feedback system has the open loop transfer function HG(s) = (K(s+3))/(s(s-2))
Find K such that the damping ratio of the closed loop roots is equal to 1/√(3). Be sure
that your K yields a stable closed loop system.

Added by Elena B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Rajendra Kumar

Step 1

To determine the range of K for stability, we need to find the values of K for which the system's poles are located in the left half of the complex plane. In other words, we need to find the values of K for which the real parts of the roots of the characteristic Show more…

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Part A: a. Determine the range of K for stability. b. At what value of K does the system's dynamic behavior enter into a state of self-sustained oscillations? c. What is the frequency of oscillation for the condition of part (b)? Part B: K = 5 + 3 A unity feedback system has the open loop transfer function HG(s) = s(s-2). Find K such that the damping ratio of the closed loop roots is equal to 1/3. Be sure that your K yields a stable closed loop system.

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