Control Systems Questions and Answers – Integral Square Error & its Minimization

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Integral Square Error & its Minimization”.

1. A unity feedback system has an open loop transfer function G(s) =25/s(s+8). What is the percentage of it’s peak overshoot?
a) 0.13%
b) 1.13%
c) 1.26%
d) 1.52%

Explanation: Damping ratio is calculated from the characteristic equation and placing that value in the formula for peak overshoot Mp = e3.14DR (1- DR2) we get the answer. Peak overshoot arises especially in the step response of the systems such as low pass filters which are band limited.

2. What is the analogous electrical element of Frictional coefficient (B) in Force-Current Analogy for mechanical translational system?
a) Resistance
b) Conductance
c) Flux
d) Voltage

Explanation: As Resistance is the analogous element of B in F-V analogy so here it is the reciprocal of resistance, conductance is the answer. Force voltage analogy means both the equations will have differential equation of the same form.

3. What is the response of the feedback function with open loop transfer function G(s) = 4/s(s+5) and input is input step?
a) 1-1/3(4e-t – e-4t)
b) 1-1/2(6e-t – e-4t)
c) 1-1/3(6e-t – e-4t)
d) 1-1/2(4e-t – e4t)

Explanation: We should first get the response in s domain which is C(s)/R(s) = G(s)/1+G(s) = R(s) 4/(s+1)(s+4) and as the input is unit step which R(s)=1/s the equation becomes 4/s(s+1)(s+4). Then we apply partial fraction to the equation and we get values of A, B, C as 1, -4/3, 1/3 and then inverse Laplace transform is applied to C(s) and we get response as 1-1/3(4e-t – e-4t).

4. The response of a servomechanism is 1+0.2e-60t-1.2e-10t when subjected to a unit step input. What is the damping ratio?
a) 1.21
b) 1.43
c) 1.59
d) 1.74

Explanation: First we apply Laplace Transform to the system and as R(s) = 1/s we get closed loop transfer function as C(s)/R(s) = 600/s2+70s+600. Then we compare it with the standard equation for second order transfer function we got damping ratio = 70/2wn = 1.43.

5. The open loop transfer function for a unit feedback system is G(s) = K/s(sT+1). By what factor the amplitude gain K should be reduced so that the peak overshoot becomes 25% from 75%?
a) 75
b) 25
c) 20
d) 10

Explanation: The peak overshoot is decreased by increasing the damping ratio. The damping ratio is increased by reducing the gain K by same proportion and for decreasing the peak overshoot from 75% to 25% the factor of amplitude becomes 19.6% which is approximately 20%.

6. A performance index must offer selectivity.
a) True
b) False

Explanation: It must offer selectivity, that is, an optimal adjustment of parameters must clearly distinguish non optimal adjustment of parameters. If there was no selectivity we would not have been able to distinguish between parameters.

7. For a unity feedback control system, the open loop transfer function G(s) = 10(s+2)/s2(s+1). What is the acceleration error constant?
a) Infinity
b) 5
c) 10
d) 20

Explanation: As limit s tends to zero s2 G(s) H(s) = s2 G(s) = 10*2/1 = 20. Therefore we get the value of Ka as 20 and both kv and ks are infinity.

8. Actuator is the basic component of an automatic control system.
a) False
b) True

Explanation: There are 5 basic components of an automatic control system. They are error detector, amplifier, actuator, plant, and sensor. So, Actuator is a basic component of automatic control system.

9. What is the need for a controller?
b) Transmit control signals
c) Modify control signals
d) Create control signals

Explanation: Controller is needed to modify control signals for better control action. Some control signals are raw signals which can’t function properly so we use controllers for modifying them.

10. How many types of controllers and compensators are there respectively?
a) 4, 3
b) 3, 4
c) 4, 5
d) 5, 4

Explanation: There are 4 types of controllers namely PID, PI, PD. There are 3 types of compensators namely Lag, Lead & Lag-Lead compensators.

Sanfoundry Global Education & Learning Series – Control Systems.

To practice all areas of Control Systems, here is complete set of 1000+ Multiple Choice Questions and Answers.

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