JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II CONTROL SYSTEMS Previous Question Paper (April - 2018 - R16)
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. Each question carries 10 marks.
Part A
Write the Mason’s gain formula.
Answer
Mason's gain formula is used to determine the overall transfer function of a signal flow graph. It is given by:
Where:
- T is the transfer function between the input and output nodes.
- Pk is the 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 possible non-touching loops taken two at a time) - (sum of gain products of all possible non-touching loops taken three at a time) + ...
- 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
A Signal Flow Graph (SFG) is a graphical representation of a system of linear algebraic equations. Its basic properties are as follows:
- SFG applies only to linear time-invariant systems.
- The graph consists of nodes, which represent system variables, and directed branches, which represent the gain or transfer function between nodes.
- Signals travel along branches only in the direction of the specified arrow.
- The value of a node variable 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 source node.
- A node with only outgoing branches is an input node (source), and a node with only incoming branches is an output node (sink).
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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Unit I
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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Unit II
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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Unit III
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 deg.
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Unit IV
The open loop transfer function is given by G(s)H(s) = K(1+4s) / (s(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 / (s(1+0.1s)(1+0.2s)). Design a lag-lead compensator to meet the Kv=100sec^-1 and Phase margin >= 30 deg.
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Unit V
Define: i) State ii) State variables iii) State space representation.
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Find the state transition matrix for the following matrix, A = [[0, 1], [-1, -1]].
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Obtain the state space representation for the following 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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