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. \(\omega_{BW4} = \)
