PYQs Based test 15: Control Systems

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. the integration time step is h.

$\begin{array}{l}\frac{x_{k+1}-x_k}{h}=y_k\\ \frac{y_{k+1}-y_k}{h}=-x_k\end{array}$

For this discrete-time system, which one of the following statements is TRUE?

Consider a closed-loop system as shown. $G_p(s)=\frac{14.4}{s(1+0.1s)}$ is the plant transfer function and G${}_c$ (s) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is __________ rad / s. (Round off to 2 decimal places.)

In the given, figure, plant $G_p(s)=\frac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)}$ and compensator $G_c(s)=K\left(\frac{1+T_{1}s}{1+T_{2}s}\right)$. The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is ______. (Round off to 2 decimal places.)

Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

Consider the following system described by the following state space representation.

≤ft[ {*20c x_1 ≤ft( t )\\ x_2 ≤ft( t ) } ] = ≤ft[ {*20c 0&1\\ 0& - 2 } ]≤ft[ {*20c x_1≤ft( t )\\ x_2≤ft( t ) } ] + ≤ft[ {*20c 0\\ 1 } ]u≤ft( t )

y≤ft( t ) = ≤ft[ {*20c 1&0 } ]≤ft[ {*20c x_1≤ft( t )\\ x_2≤ft( t ) } ]

If u(t) is a unit step input and ≤ft[ {*20c x_1≤ft( 0 )\\ x_2≤ft( 0 ) } ] = ≤ft[ {*20c 1\\ 0 } ], the value of output y(t) at t = 1 sec (round off to three decimal places) is ________