JNTU B.Tech II CONTROL SYSTEMS Previous Question Paper (March - 2022 - R16)

A closed-loop control system is one where the output has an effect on the input quantity to maintain the desired output value. Two common examples are:

1. Automatic Water Level Controller: In this system, a sensor measures the water level in a tank and provides feedback to a controller. If the level falls below a set point, the controller activates a pump. Once the water reaches the desired level, the sensor signals the controller to stop the pump, ensuring the output (water level) remains constant regardless of usage.
2. Air Conditioning System: An AC unit uses a thermostat as a feedback element. The user sets a desired temperature (reference input). The thermostat continuously measures the actual room temperature and compares it with the set point. If the room is too warm, the compressor is turned on; once the set temperature is achieved, the system cycles off, maintaining the desired thermal environment.

For a mechanical translational system, the transfer function is defined as the ratio of the Laplace transform of the output displacement to the Laplace transform of the input force, assuming zero initial conditions. The system is governed by Newton's Second Law, where the sum of forces equals the product of mass and acceleration.

1. Identify the forces acting on the mass: the applied force F(t), the spring force k*x(t), the viscous friction force f*dx/dt, and the inertial force m*d²x/dt².
2. Write the differential equation:
   m(d²x/dt²) + f(dx/dt) + kx = F(t)
3. Apply the Laplace transform to both sides, assuming zero initial conditions:
   (ms² + fs + k)X(s) = F(s)
4. Rearrange to find the transfer function G(s):
   G(s) = X(s) / F(s) = 1 / (ms² + fs + k)