Question

Given four 2nd order, unity-gain, closed-loop systems, with the following performance characteristics SYS 1: \(\zeta = 0.2\) and \(T_s = 3\) sec SYS 2: \(\zeta = 0.2\) and \(T_s = 3\) sec SYS 3: \(T_s = 4\) sec and \(T_p = 2\) sec SYS 4: \(\zeta = 0.3\) and \(T_s = 4\) sec a. Determine the closed-loop transfer function of each system. (One decimal place) b. Use a bode plot (i.e., -3dB freq.), or otherwise (see textbook Eqn. 10.5?), to determine the CL-bandwidth of each system (rad/s). (One decimal place) Answer: a. i. \(G_{CL1}(s) = \frac{?}{s^2 + ?s + ?}\) ii. \(G_{CL2}(s) = \frac{?}{s^2 + ?s + ?}\) iii. \(G_{CL3}(s) = \frac{?}{s^2 + ?s + ?}\) iv. \(G_{CL4}(s) = \frac{?}{s^2 + ?s + ?}\) b. i. \(\omega_{BW1} = \) ii. \(\omega_{BW2} = \) iii. \(\omega_{BW3} = \) iv. \(\omega_{BW4} = \)

          Given four 2nd order, unity-gain, closed-loop systems, with the following performance characteristics
SYS 1: \(\zeta = 0.2\) and \(T_s = 3\) sec
SYS 2: \(\zeta = 0.2\) and \(T_s = 3\) sec
SYS 3: \(T_s = 4\) sec and \(T_p = 2\) sec
SYS 4: \(\zeta = 0.3\) and \(T_s = 4\) sec
a. Determine the closed-loop transfer function of each system. (One decimal place)
b. Use a bode plot (i.e., -3dB freq.), or otherwise (see textbook Eqn. 10.5?), to determine the CL-bandwidth of each system (rad/s). (One decimal place)
Answer:
a. i. \(G_{CL1}(s) = \frac{?}{s^2 + ?s + ?}\)
ii. \(G_{CL2}(s) = \frac{?}{s^2 + ?s + ?}\)
iii. \(G_{CL3}(s) = \frac{?}{s^2 + ?s + ?}\)
iv. \(G_{CL4}(s) = \frac{?}{s^2 + ?s + ?}\)
b. i. \(\omega_{BW1} = \)
ii. \(\omega_{BW2} = \)
iii. \(\omega_{BW3} = \)
iv. \(\omega_{BW4} = \)

Given four 2nd order, unity-gain, closed-loop systems, with the following performance characteristics
SYS 1: ζ = 0.2 and Ts = 3 sec
SYS 2: ζ = 0.2 and Ts = 3 sec
SYS 3: Ts = 4 sec and Tp = 2 sec
SYS 4: ζ = 0.3 and Ts = 4 sec
a. Determine the closed-loop transfer function of each system. (One decimal place)
b. Use a bode plot (i.e., -3dB freq.), or otherwise (see textbook Eqn. 10.5?), to determine the CL-bandwidth of each system (rad/s). (One decimal place)
Answer:
a. i. GCL1(s) = (?)/(s^2 + ?s + ?)
ii. GCL2(s) = (?)/(s^2 + ?s + ?)
iii. GCL3(s) = (?)/(s^2 + ?s + ?)
iv. GCL4(s) = (?)/(s^2 + ?s + ?)
b. i. ωBW1 =
ii. ωBW2 =
iii. ωBW3 =
iv. ωBW4 =

Added by Timothy M.

Question

Please give Ace some feedback