JNTU
JNTU B.Tech III CONTROL SYSTEMS Previous Question Paper (February - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Explain about the analogous quantities in translational and rotational systems.
Answer
Analogous systems are physical systems that are governed by the same mathematical differential equations. By establishing an analogy between translational and rotational mechanical systems, we can use electrical network analysis techniques to solve mechanical problems.
In translational mechanical systems, the three basic elements are Mass (M), Spring (k), and Dashpot (f or B). In rotational mechanical systems, the corresponding elements are Moment of Inertia (J), Torsional Spring (K), and Torsional Damper (D). The analogy is typically established using the Force-Voltage (F-V) or Force-Current (F-I) analogy.
| Translational Element | Rotational Element | Analogous Quantity (F-V) | Analogous Quantity (F-I) |
|---|---|---|---|
| Force (F) | Torque (T) | Voltage (v) | Current (i) |
| Velocity (v) | Angular Velocity (ω) | Current (i) | Voltage (v) |
| Mass (M) | Moment of Inertia (J) | Inductance (L) | Capacitance (C) |
| Friction (f) | Damping (D) | Resistance (R) | Conductance (G) |
| Spring (k) | Torsional Spring (K) | Capacitance (1/C) | Inductance (1/L) |
Define Transfer function and explain the properties of Transfer function.
Answer
The Transfer function of a linear time-invariant (LTI) system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions are zero.
The properties of the transfer function are as follows:
- It is a property of the system itself and is independent of the input and the nature of the input.
- It includes the transfer functions of the individual components of the system.
- It provides a mathematical model to describe the system dynamics in the s-domain.
- The poles of the transfer function determine the stability of the system.
- If the transfer function is known, the output response can be determined for any given input by taking the inverse Laplace transform.
- It is defined only for linear time-invariant systems.
What is feedback? Explain its characteristics.
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Explain about the classification of control systems.
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Obtain the overall Transfer function of the given system (figure 1).
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Find the overall gain of the system whose signal flow graph is given below figure 2.
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Derive the expressions for Rise Time, Peak Time and Peak Overshoot of a second order system subjected to unit step input.
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Derive the expression for response of first order systems for unit step input.
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Discuss various types of steady state error constants for different inputs.
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Sketch the root locus for open loop system transfer function for unity feedback control system given below:
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Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over frequencies.
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