PYQs Based Test - 04 : Control Systems

Consider the following state variable equations:

ẋ₁(t) = x₂ (t)

ẋ₂ (t) = -6x₁ (t) – 5x₂ (t)

The initial conditions are x₁ (0) = 0 and x₂(0) = 1. At t = 1 second, the value of x₂(1) (rounded off to two decimal places) is

In the control system shown in the figure below, a reference signal r(t) = t² is applied at time t = 0. The control system employs a PID controller C(s) = K${}_P$ + K${}_I$ / s + K${}_D$ s and the plant has a transfer function P(s) = 3/s. If K${}_P$ = 10, K${}_I$ = 1 and K${}_D$ = 2, the steady state value of e is

A second order system has closed loop poles located at s = -3 ± j4. The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places) is

A system is represented in state-space is X = Ax + Bu,where A = ≤ft[ {*20c 1&2\\ α &6 } ]andB = ≤ft[ {*20c 1\\ 1 } ]. The value of α for which the system is not controllable is _______.

A unity feedback system has the following open loop frequency response:The gain and phase margin of the system are