CONTROL SYSTEM – KEC-602
Section-wise Important Questions & Ready Answers
SECTION A
(Attempt all questions – 2 marks each)
(a) Eigen Vector
An eigenvector of a matrix is a non-zero vector that, when multiplied by the matrix, results only in a scalar multiple of itself. In control systems, eigenvectors describe the mode shapes associated with system dynamics.
(b) Damping Ratio
Damping ratio is a dimensionless quantity that indicates the amount of damping in a system. It determines whether the system response is overdamped, underdamped, critically damped, or undamped.
(c) Open Loop vs Closed Loop System
An open-loop system operates without feedback and does not correct errors automatically. A closed-loop system uses feedback to compare output with input and automatically correct errors, resulting in improved accuracy and stability.
(d) Resonant Peak and Resonant Frequency
Resonant peak is the maximum value of the frequency response magnitude of a system. Resonant frequency is the frequency at which this peak occurs. Both depend on damping ratio and natural frequency.
(e) Incremental Encoder
An incremental encoder generates pulses as the shaft rotates. These pulses are counted to determine position, speed, and direction, making it useful in motion control systems.
(f) Servomechanism
A servomechanism is an automatic closed-loop control system that controls mechanical position, velocity, or acceleration with high precision using feedback.
(g) Transfer Function
The transfer function of a system is the ratio of the Laplace transform of output to input under zero initial conditions. It represents the dynamic behavior of a linear time-invariant system.
(h) Static Velocity and Acceleration Error Constants
The static velocity error constant determines steady-state error for ramp input, while the static acceleration error constant determines steady-state error for parabolic input.
(i) Characteristic Equation
The characteristic equation is obtained by setting the denominator of the closed-loop transfer function equal to zero. It determines system stability and transient response.
(j) Characteristics of an Ideal Control System
An ideal control system has high accuracy, fast response, good stability, low sensitivity to parameter variations, and minimal steady-state error.
SECTION B
(Attempt any three – 10 marks each)
2(a) Transfer Function Using Signal Flow Graph
Using Mason’s Gain Formula, the overall transfer function is obtained by calculating forward path gains, loop gains, and non-touching loop combinations. The final expression is derived by substituting these values into Mason’s formula.
2(b) Controllability and Observability
Controllability is checked by forming the controllability matrix and verifying its rank. Observability is checked using the observability matrix. If both matrices have full rank, the system is completely controllable and observable.
2(c) Steady-State Error in Type-1 Systems
Steady-state error is the difference between input and output as time approaches infinity. For a type-1 system, steady-state error is zero for step input and finite for ramp input. Mathematical expressions are derived using error constants.
2(d) Effect of Adding a Zero in Forward Path
Adding a zero increases system speed and reduces rise time. However, it may increase overshoot and reduce system stability if not placed carefully.
2(e) Routh-Hurwitz Stability Criterion
The Routh-Hurwitz criterion determines system stability without solving the characteristic equation. A system is stable if all elements in the first column of the Routh array are positive. Applying this method to the given equation confirms system stability or instability.
SECTION C
(Attempt any one)
3(a) Effect of Feedback
Feedback improves system stability by reducing oscillations. It reduces sensitivity to parameter variations and controls overall gain, making the system more robust.
3(b) Transfer Function of Given System
By writing force-balance equations and applying Laplace transforms, the required transfer function is obtained by eliminating intermediate variables.
