# Control Systems - GATE practice papers - Electronics & Communication

1)   Consider the statements given below:

A. Beginning of root locus with an open-loop pole at k = 0
B. Location of root locus about the real axis

C. Determination of the branches of root
D. Estimation of an angle of asymptote
E. Monitors the liability for the existence of real axis
F. Termination of root locus either on open-loop zero or at infinity

Which is the correct chronological order of sequential steps obligatory for the construction of root loci? (Marks : 02)

- Published on 19 Oct 15

a. A, D, E,B,C, F
b. A, B, C, D, E, F
c. B, A, F, C, E, D
d. B, F, A, D, E, C
 Answer  Explanation ANSWER: B, A, F, C, E, D Explanation: Root locus is a graphical mechanism which is concerned to the plotting of roots of the characteristic equation in s-plane for several parameter values. It is mandatory to determine the root locus properly in proper sequential steps specified in option (c) so as to estimate the presence or location of any point on it by verifying the roots of characteristic equation with the assistance of angle and magnitude criteria.

2)   Which among the below stated conditions is/are precise for non-minimum phase function? (Marks : 02)
- Published on 19 Oct 15

a. It consists of at least one pole or zero at RHS of an imaginary axis
b. It consists of symmetric poles and zeros about imaginary axis in s-plane
c. It consists of at least one symmetric pair of pole & zero at RHS of real axis
d. It does not contain any poles or zeros in the RHS of an imaginary axis
 Answer  Explanation ANSWER: It consists of at least one pole or zero at RHS of an imaginary axis Explanation: If the transfer function possesses at least one pole or zero at RHS of an imaginary axis, then the system is said to be in ' Non-minimum Phase while options (b) &(d) represent the conditions of all-pass and minimum phase systems/transfer functions respectively

3)   What does the term/value 'ΔK' represents in an equation of Mason's Gain Formula? (Marks : 02)
- Published on 19 Oct 15

a. Path Factor
b. Forward Path Transmittance of kth path
c. Loop Gain
d. Graph Determinant
 Answer  Explanation ANSWER: Path Factor Explanation: Mason's Gain Formula is used to evaluate an overall transmittance (gain), which can be expressed as, T = k=1∑n PK ΔK / Δwhere, Pk = forward path transmittance of kth path Δ = graph determinant comprising closed loop transmittances & mutual interactions between non-touching loops. ΔK = path factor consisting of all isolated closed loops from the forward path in the graph.

4)   What action should be performed in accordance to the rule of signal flow theory, if the summing point is located after the take-off point in the direction of signal flow? (Marks : 02)
- Published on 19 Oct 15

a. Only Summing Point should be represented by a single node
b. Only Summing Point should be represented by separate node
c. Summing & Take-off Points should be represented by a single node
d. Summing & Take-off Points should be represented by separate nodes
 Answer  Explanation ANSWER: Summing & Take-off Points should be represented by separate nodes Explanation: According to the construction rule of signal flow graph, all summing & take-off points are absolutely represented by nodes. Therefore, a single node is sufficient to represent the summing and take-off points,if the position of summing point is before the take-off point. But, if the position of summing point lies after the take-off point, then both of them are represented with the assistance of separate nodes connected by a branch possessing unit value of transmittances.

5)   Which term associated with the signal flow theory is also renowned as 'Transfer Function'? (Marks : 01)
- Published on 19 Oct 15

a. Transmittance
c. Reluctance
d. Inductance
 Answer  Explanation ANSWER: Transmittance Explanation: Basically, signal flow graph is a graphical representation of a set associated with simultaneous equations & applicable for linear time invariant systems by reducing the time required for block reduction techniques. Sine the transmittance is normally represented or written on the branch near the arrow by specifying the input-output relationship, it is also referred as a transfer function.

6)   Which among the below specified block reduction techniques deal with an algebraic addition of block for the evaluation of transfer function? (Marks : 01)
- Published on 19 Oct 15

a. Associative Law
b. Blocks in Series
c. Blocks in Parallel
d. Summing Point Shift (behind the block)
 Answer  Explanation ANSWER: Blocks in Parallel Explanation: According to the drawing procedure of block diagram, sequential block reduction priorities are assigned for those connected in series , parallel,minor feedback loops and then summing point shift. However, the transfer function of the serially connected blocks is evaluated on the basis of multiplication while the transfer function of the blocks connected in parallel combination is evaluated on the basis of an algebraic addition. Associative law is only applicable when two or more directly connected summing points are interchangeable.

7)   Which control systems basically exhibit their output dependency upon input as well as the previous output stages? (Marks : 01)
- Published on 19 Oct 15

a. Open-loop Control System
b. Closed-loop Control System
c. Both a & b
d. None of the above
 Answer  Explanation ANSWER: Closed-loop Control System Explanation: In an open-loop system, the control characteristics are totally independent of the system output & hence are generally stable, while the output relies on the controlling action (input) along with the previous output in a closed-loop control system. As a result, closed loop systems may sometimes become unstable.

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