# Objective Questions on Control System – 4

1. For a transfer function H ( s ) = P ( s ) / Q ( s ), where P ( s ) and Q ( s ) are polynomials in s. Then

If the degree of the numerator P ( s ) and the denominator Q ( s ) are dependent with each other, then the poles and zeros of the system may gets placed on the same roots. Then the transfer function is wrong. So, the degree of the numerator P ( s ) and the denominator Q ( s ) should be independent with each other. This is the one of the necessary conditions for transfer function.

2. Transfer function of the control system depends on

The transfer function is nothing but the ratio to the Laplace transform of the output to the Laplace transform of the input. So, based on the input and output characteristics the system characteristics can be changed. But, if we adjust the system parameter, the output can change with respect to the input of the system. Hence, due to this action, the transfer function also can be changed. Thus, the transfer function of the control system depends on the parameters of the system alone.

3. Sparking between the contacts can be reduced by inserting

An arc between two electrodes can be initiated by ionization of atmospheric air. If we connect a capacitor across the contacts of the electrodes, there is a chance to make a short circuit by capacitor. Hence, there is no air gap between contacts and thereby sparking can be reduced.

4. Error constants of a system are measure of

In the steady state condition, the accuracy of the time response is the indication of how well the system response achieving the final settling stage. Ideally, the output y( t ) equals to the reference signal u( t ) and thereby the error e(t) is zero because error is the difference between the reference signal and the output signal. In practical, it is not possible. But, the objective is to force the output signal to reach our reference signal. For that purpose only, we are introduced the error constants to achieve the steady state response. So, if we adjust the error constants, then the system’s steady state response also varies.

5. Slope of asymptote in Bode plot of 2nd order system is ________ per octave.

Basically, the slope of asymptote in a Bode plot of any system are n × 20 dB per decade (or) n × 6 dB per octave (an octave is a change in frequency by a factor of 2). Here, ‘n’ is the order of the system. Hence, for a second order system there might be (2 × 6 = 12) dB per octave.

6. The graph of an electrical network has N nodes and B branches. The number of links, L with respect to the choice of a tree, is given by

For a graph with N nodes, the number of branches in each tree T must be; T = N – 1. An important relationship for circuit analysis is; B = L + T. where B is the number of branches in the graph and L is the number of links removed to form the tree. Hence, the number of links L = B – N + 1.

7. F( s ) = ( s2 – 1) / ( - s + 8). What type of function is this?

PR function tests reveals that all the quotients of polynomial in the numerator are not +ve and also there is a zero on the r.h.s of s-plane. This clearly proves that the given function is not a PR function. No more confirmatory testing is needed.

8. First Foster form of a LC network represents which element in the beginning?

In Foster 2 form last element is a capacitor.

9. What is the full form of SPICE ?

SPICE is a software that simulates different circuits and can perform various analysis of electrical and electronics circuits.

10. Based on relation between the arm impedances the filters can be categorized into how many types?

2 types are - constant k type / prototype filter and m-derived filter.

11. F( s ) = ( s2 – 1) / ( -s + 8). What type of function is this?

PR function tests reveals that all the quotients of polynomial in the numerator are not +ve and also there is a zero on the r.h.s of s-plane. This clearly proves that the given function is not a PR function. No more confirmatory testing is needed.

12. First Foster form of a LC network represents which element in the beginning?

In Foster 2 form last element is a capacitor.

13. What is the full form of SPICE ?

SPICE is a software that simulates different circuits and can perform various analysis of electrical and electronics circuits.

14. Based on relation between the arm impedances the filters can be categorized into how many types?

2 types are- constant k type/prototype filter and m-derived filter.

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