JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II CONTROL THEORY Previous Question Paper (August/September - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Explain about State-Space Representation of Dynamic Systems.
Answer
State-space representation is a mathematical model of a physical system as a set of input, output, and state variables related by first-order differential equations. Unlike transfer functions which are limited to linear time-invariant (LTI) systems, state-space models can represent non-linear, time-varying, and multi-input multi-output (MIMO) systems.
The standard state-space equations are:
Where x(t) is the state vector of dimension n, u(t) is the input vector of dimension m, and y(t) is the output vector of dimension p. The matrices A (system matrix), B (input matrix), C (output matrix), and D (feedforward matrix) define the internal dynamics and the relationship between inputs and outputs.
A linear time-invariant multivariable system with inputs r1(t) and r2(t) and outputs y1(t) and y2(t) is described by the following set of differential equations. Find the transfer function Y1(s)/R1(s) for R2 = 0.
Answer
To find the transfer function when the system is described by differential equations, apply the Laplace transform to each equation assuming zero initial conditions. For a system with inputs r1(t), r2(t) and outputs y1(t), y2(t), the resulting algebraic equations in the s-domain are represented as:
Where G(s) is the transfer function matrix. To find Y1(s)/R1(s) with R2(s) = 0, follow these steps:
- Take the Laplace transform of the given differential equations.
- Substitute R2(s) = 0 into the equations.
- Solve the resulting system of linear algebraic equations for Y1(s) in terms of R1(s) using Cramer's rule or substitution.
- The ratio Y1(s)/R1(s) is the required transfer function.
The final result is obtained by isolating the variable Y1(s) and dividing by R1(s) after eliminating Y2(s) from the equations.
Discuss the similarities and differences between Closed-Loop Control and Open-loop Control systems.
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Draw a signal-flow diagram for the system with the following state-space representation.
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Discuss about Steady-State Errors in Unity-Feedback Control Systems for different input signals.
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Using the Routh-Hurwitz criterion, determine the stability of the system whose characteristic equation is as follows: S4 + 2S3 + 8S2 + 10S + 0 = 0.
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Explain the Effects of Derivative Control Actions on System Performance.
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The following transfer function is given for a single-loop non unity-feedback control system. Find the steady-state errors due to a unit-step input, and a unit-ramp input.
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What are Conditionally Stable Systems? Explain with examples.
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The characteristic equation of linear control system are given as follows. Construct the root locus for K ≥ 0.
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Explain briefly about Root Loci for Systems with Transport Lag.
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The forward-path transfer function of a unity-feedback control system is given in the following. Construct the root locus for K ≥ 0.
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Discuss briefly about the procedure to draw Nyquist Plots.
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The forward-path transfer function of unity-feedback control system is given in the following equation. Using Bode diagram find the value of K so that the gain margin of the system is 20 dB.
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Explain about the Frequency Response Methods that are used in control system design.
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With the help of root locus method, analyze lead-lag compensation.
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