GATE 2024 Control Systems Foundation Quiz 76

A state-space representation of a system is given by and . The zero input time response of the system is sin The value of is ______.

The state equation of an LTI system is

The state transition matrix will be

Given

The response for step input is

A controlled process is modelled by the following equations

The control u(t) is obtained from state feedback such that

u(t) = –K₁x₁(t) – K₂x₂(t)

Where, K₁ and K₂ are real constants. The closed loop system is stable in the region

The state space representation of a separately excited DC servo dynamics is given as

where w is the speed of the motor, i_a is the armature current, and u is the armature voltage.

The transfer function  of the motor is