List of top Control Systems Questions on Transient and Steady‐state analysis of linear time invariant systems

A 3-phase, 400 V, 4 pole, 50 Hz star-connected induction motor has the following parameters referred to stator: \[ R'_1 = 1 \, \text{ohm}, \, X_s = X'_1 = 2 \, \text{ohm} \] Stator resistance, magnetizing reactance, and core loss of the motor are neglected. The motor is run with constant \( v/f \) control. The output frequency from the drive is closest to:

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( S \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?

For the closed-loop system with \(G_p(s) = \frac{14.4}{s(1 + 0.1s)}\) and \(G_c(s) = 1\), the unit-step response shows damped oscillations. The damped natural frequency is \(\underline{\hspace{2cm}}\) rad/s. (Round off to 2 decimal places.)

In the given figure, plant \(G_p(s)=\dfrac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)}\) and compensator \(G_c(s)=K \left\{ \dfrac{1+T_1 s}{1+T_2 s} \right\}\). The disturbance input is \(D(s)\). The disturbance is a unit step, and the steady-state error must not exceed 0.1 unit. Find the minimum value of \(K\). (Round off to 2 decimal places.)