*Answer the following questions (2 x 10)*

### What is the effect of the addition of a zero to the forward path transfer function?

The effects of the addition of zeros are as follows:

- There is a change in the shape of the root locus and it shifts towards the left of the s-plane.
- The stability of the system is enhanced.
- Range of K increases.
- Setting time speeds up.

### What correlation exists between time domain and frequency domain specification?

- The performance of a control system is normally measured in terms of its time-domain characteristics. It may equally be measured in frequency-domain since there are correlations between the frequency-domain and time-domain performances in a linear system so that the time-domain properties of the system can be predicted based on the frequency-domain analysis.
- Besides, the frequency domain approach provides an alternative perspective to the complex analysis and design problems of linear control systems in addition to the time-domain studies.
- The frequency-domain analysis of a linear control system assumes that the input is sinusoidal, even though, it does not necessarily imply that the system will be subjected to a sine-wave input only. Rather, the engineer will be able to project the time-domain performance of the system from the frequency-domain studies.

For the input (r(t)=Rsinω

_{0}t) and output (y(t)=Ysin(ω_{0}t + Φ)) signals, the amplitude of the output sinusoid isY=R|G(jω

_{0})and the phase of the output is

Φ = ∠G(jω

_{0})### When the complete row becomes zero, how the Routh’s array is completed?

When all the elements of any row of the Routh array are zero. In this case, we can say the system has the symptoms of marginal stability. Let us first understand the physical meaning of having all the elements zero of any row. The physical meaning is that there are symmetrically located roots of the characteristic equation in the s plane. Now in order to find out the stability in this case we will first find out the auxiliary equation. The auxiliary equation can be formed by using the elements of the row just above the row of zeros in the Routh array. After finding the auxiliary equation we will differentiate the auxiliary equation to obtain elements of the zero row. If there is no sign change in the new Routh array formed by using the auxiliary equation, then in this we say the given system is limited stable. While in all the other cases we will say the given system is unstable.

### What are the properties of the breakaway and break-in points in the root locus?

The breakaway points on the root loci are points at which multiple-order roots lie.

We have noted that the locus starts at the poles with K = 0 and terminates at the finite zeroes or at ∞ with K = ∞.

We have also found in the figure that the part of the real axis between the pole s = 0 and the pole s = – 5 is lying on the root loci. So the two branches of loci start at the poles with K = 0 and approach each other as K is increased until the two branches meet at point B in the given figure.

Any further increase of K will cause the roots to

**break away**from the real axis. Therefore, so far as the real axis loci are concerned, as we move from one pole on the real axis towards the other pole, the value of K gradually increases and reaches a maximum value and then decreases to zero at the other pole.Similarly, in case a portion of the real axis lying between two finite zeros is a part of the root locus, two branches of loci will

**break in**on the real axis and move towards the finite zeros as K approaches infinity.### What should be the electric strength of new insulating oil?

Dielectric Strength is simply the maximum electric field that a material can withstand without experiencing failure of its insulating properties. It’s measured in megavolts per meter (MV/m). The higher the Dielectric Strength, the better a material is to prevent electrical conductivity.

The dielectric strength of transformer oil should be 24 MV/m.

### Give the method for testing permanent magnets.

**Flux Density Check**

This test uses a gaussmeter to measure the flux density of a magnet at a determined distance. Typically, the measurement is made either at the magnet's surface or at the distance at which the flux will be used in the magnetic circuit. Flux density testing verifies that the magnet material used for our custom magnets will perform as predicted when the measurement matches the calculated values.

### Give the precaution and techniques for reducing errors in an AC bridge.

**Precautions**

The following precautions may be taken to avoid errors :

- High-quality components must be used for the elements of the bridge.
- The layout of the bridge must be made to avoid interaction of the bridge arms.
- The sensitivity of the bridge must be more.
- The bridge components and other pieces must be mounted on an insulation stand to prevent stray conductance effects.
- The presence of large conducting masses near the bridge arms must be avoided to prevent eddy current effects.
- The residual error can be avoided by identifying the nature, evaluating them and compensating them.
- Wave filters that eliminate the unwanted harmonics from the source or tuned detectors in place of headphones may be used to avoid the difficulty of frequency and waveform errors.

**Techniques to reduce errors**

- In the bridge networks, which are used for measurement of inductances, the leads should be twisted together in order to avoid such loops whereas in the bridge networks employed for measurement of capacitances the leads should be separated from one another in order to avoid capacitance between them.
- A statically wound inductance coil should be used in order to avoid magnetic coupling between the arms. The errors due to magnetic coupling between the arms can also the avoided by placing a magnetic screen (a thin sheet of high permeability material) in between the arms. The magnetic screen placed in between the arms short circuits stray fields and prevent them from reaching the components of other arms of the bridge.
- Sometimes direct induction effects between the source of the supply to the bridge and the detector circuit might exist and cause a current to flow in the detector even when the bridge is truly balanced. Such effects are eliminated by placing the source of supply at some distance from the bridge network and using an inter-bridge transformer.
- In ord bridge and earth capacitances, use of electrostatic screen is necessary.
- Leakage errors are avoided by using high-grade insulation and mounting the apparatus on insulating stands.
- To avoid eddy current errors, the presence of large masses near the bridge network is avoided.

### Classify resistances from the point of view of measurements.

Resistance is classified into three categories for the sake of Measurement. Different categories of Resistance are measured by the different techniques. They are classified as

- Low Resistance: Resistance having a value of 1Ω or below are kept under this category.
- Medium Resistance: This category includes Resistance from 1Ω to 0.1 MΩ.
- High Resistance: Resistance of the order of 0.1 MΩ and above is classified as High resistance.

The different methods used for the measurement of low resistance are as follows:

- Kelvin’s Double bridge method
- Potentiometer method
- Ducter ohmmeter

The different methods used for the measurement of Medium resistance are as follows:

- Ammeter Voltmeter method
- Substitution Method
- Wheatstone Bridge Method
- Ohmmeter Method

The different methods used for the measurement of High resistance are as follows:

- Direct deflection method
- Loss of charge method
- Megohm bridge
- Megger

### How does frequency affect the power factor for RL load?

The power factor is defined as the cosine of the phase angle between alternating e.m.f. and current in a.c. current.

The power factor of an a.c. the circuit is given by

Power factor depends upon the frequency (f) of the a.c. source.

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