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. \frac{x _{k + 1} - x _{k}}{h} = y_{k} \frac{y _{k + 1} - y _{k}}{h} = - x_{k} 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 + 0.1 s )} 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 + 0.1 s ) ( 1 + 0.4 s ) ( 1 + 1.2 s )} and compensator G_{c} (s) = K (\frac{1 + T _{1} s}{1 + T _{2} s}) . 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.)

Topics Covered