JNTU
JNTU B.Tech II CONTROL SYSTEMS Previous Question Paper (April - 2018 - R16)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit.
Part A
(25 Marks)
Write the Manson’s gain formula.
Answer
Mason's gain formula is used to determine the transfer function of a linear system represented by a signal flow graph. It is given by the expression:
Where:
- Pk is the path gain of the k-th forward path.
- Δ is the determinant of the graph, calculated as 1 - (sum of individual loop gains) + (sum of gain products of all combinations of two non-touching loops) - (sum of gain products of all combinations of three non-touching loops) + ...
- Δk is the cofactor of the k-th forward path, which is the value of Δ for that part of the graph not touching the k-th forward path.
What are the basic properties of SFG?
Answer
The basic properties of a Signal Flow Graph (SFG) are as follows:
- An SFG is a graphical representation of a set of linear algebraic equations, where nodes represent system variables and branches represent the gain or transmission between variables.
- The transmission of a signal along a branch occurs only in the direction indicated by the arrow; thus, an SFG is a directed graph.
- The value of a variable at a node is the sum of all signals entering that node, where each signal is the product of the incoming branch gain and the value of the node from which the branch originates.
- An SFG is applicable only to linear time-invariant systems.
What are the standard test signals used in control systems?
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Distinguish between type and order of a system.
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Define a stable system.
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Explain the basics of root locus plot.
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What is polar plot?
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Define gain and phase margins.
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What is state diagram?
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Mention any four advantages of state variable representation.
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Part B
(50 Marks)
Compare the AC and DC servomotors.
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For the system represented by the block diagram shown in figure 1. Find C/R.
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What are the characteristics of servomotors?
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Find the overall gain C(s)/R(s) for the signal flow graph shown in figure 2.
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The open-loop transfer function of a unity feedback control system is given by G(s) = 9 / (s(s+3)). Find the natural frequency of response, damping ratio, damped frequency and time constant.
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For unity feedback control system the open loop transfer function, G(s) = 10(s+2) / (s^2(s+4)). Find the ess when the input is r(t) = 3 - 2t + t^2/2. And find Kp, Kv, and Ka.
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Determine the RH stability of given characteristic equation: s^4 + 8s^3 + 18s^2 + 16s + 5 = 0.
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Sketch the root locus of the system, whose open loop transfer function is: G(s) = K(s+15) / (s(s+1)(s+5)).
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Given G(s) = Ke^(-0.2s) / ((s+2)(s+8)). Find K so that the system is stable with, a) GM=2db, b) PM=45 degrees.
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The open loop transfer function is given by G(s)H(s) = K(1+4s) / ((1+s)(1+2s)), Determine the stability of closed loop system.
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The open-loop transfer function of a system is given by G(s) = K / ((1+0.1s)(1+0.2s)). Design a lag-lead compensator to meet the Kv=100sec^-1 and Phase margin >= 30 degrees.
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Define: i) State ii) State variables iii) State space representation.
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Find the state transition matrix for the matrix A = [[0, 1], [-1, -1]].
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Obtain the state space representation for the differential equation y'' + 5y' + 7y = 114u.
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The state equation of a linear-time invariant system is given as, X' = [[0, 5], [-1, -2]]X + [[1], [1]]r and y = [1, 1]X, Find the transfer function and draw the state diagram.
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