JNTU B.Tech III CONTROL SYSTEMS Previous Question Paper (September 2021 - R18)

Feedback in control systems provides several critical advantages that improve system performance:

• Increased Accuracy: Feedback reduces the error between the reference input and the actual output by continuously comparing them and adjusting the control signal.
• Sensitivity Reduction: It makes the system less sensitive to variations in internal parameters and components, as the closed-loop gain is primarily determined by the feedback path rather than the forward path.
• Disturbance Rejection: Feedback systems can effectively suppress the effects of external noise and disturbances, ensuring the output remains close to the desired value.
• Bandwidth Improvement: Negative feedback increases the bandwidth of the system, allowing it to respond faster to input changes and improving the speed of response.
• Stability Control: Through proper design, feedback allows for the manipulation of system poles to achieve desired stability margins and transient response characteristics.

To derive the transfer function for a mechanical system with input f(t) and output V2, we apply Newton's second law to the masses and write the force balance equations in the Laplace domain.

Assuming a standard translational mechanical system with two masses M1 and M2, connected by springs (k) and dampers (b), the equations of motion are:

Since the output is velocity V2(s) = sX2(s), we solve the system of equations for X2(s) using Cramer's rule or substitution. The transfer function is defined as:

By calculating the determinant of the system matrix and the cofactor for X2(s), we obtain the final expression where the denominator represents the characteristic equation of the system, and the numerator is the product of the coupling terms and the Laplace operator s.