IC8451 - Control Systems - Unit-3 Two marks

Subject Name: Control Systems

Subject Code: IC8451

B.E. EEE/EIE/ICE Dept - semester 04

Anna University Regulation 2017 B.E. EEE/EIE/ICE Dept 4th semester IC8451(Control Systems) 2 marks for 3rd unit is provided below. IC8451 all units 2 marks, Control Systems all units notes & syllabus are listed down for students to utilize it for scoring maximum marks with our study materials.

1.State any four advantages of frequency response.

Answer

i) The frequency method is easy to use for design of control systems and for finding absolute as well as relative stability of the system. Calculations are simple and methods of design are well tested. ii) When it is difficult to find transfer function of a given system by writing differential equations, the transfer function of the system can be determined practically in the laboratory by obtaining the frequency response of the system. iii) Frequency response tests are simple and can be made accurately by use of readily available signal generators and the precise measuring instruments. iv) Frequency response can be precisely applied to the system those do not have rational T.F. i.e. e-TS etc. Time domain methods can be applied to such elements only after making such elements rational (using certain approximation). v) The apparatus required for obtaining frequency response is simple and inexpensive, and easy to use.

2.Define frequency response of a system.

Answer

The steady state response of a system to a purely sinusoidal input is defined as frequency response of a system. In such method frequency of the input signal is to be varied over a certain range and the resulting response of system is to be studied. Such response is called frequency response. The frequency response means to sketch the variations in magnitude and phase angle of G(jω), when ω is varied from 0 to ∞.

3.List the frequency domain methods.

Answer

The commonly used frequency domain methods are, i) Bode Plot ii) Polar plot iii) Nyquist plot iv) M — ϕ plot

4.What are the advantages of Bode plot ?

Answer

* The magnitude are expressed in db, and so, a simple procedure is available to add magnitude of each term one by one. * The frequency domain specifications can be easily determined. * The bode plot can be used to analyse both open loop and closed loop system.

5.Define gain margin.

Answer

The gain margin (G.M.) is defined as the margin in gain allowable by which gain can be increased till system reaches on the verge of instability. Mathematically it can be defined as reciprocal of the magnitude of the G(jω)H(jω) measured at phase crossover frequency. G.M. = 1/(|G(jω)H(jω)|)

6.State any four frequency domain specifications.

Answer

i) Cut-off frequency : It is denoted by ωb. The frequency at which the magnitude of the closed loop response is 3 dB down from its zero frequency value is called cut-off frequency. ii) Resonant peak (Mᵣ) : It is the maximum value of magnitude of the closed loop frequency response. iii) Resonant frequency (ωᵣ) : The frequency at which resonant peak Mᵣ occurs in closed loop frequency response is called resonant frequency. iv) Gain crossover frequency : The frequency at which magnitude of G(jω)H(jω) is unity i.e. 1 is called gain crossover frequency. v) Phase crossover frequency : The frequency at which phase angle of G(jω)H(jω) is -180° is called phase crossover frequency.

7.What is meant by corner frequency in frequency response analysis ?

Answer

A frequency upto which the magnitude contribution of a factor is negligible and can be neglected is called its corner frequency. It is the frequency at which low frequency and high frequency asymptotes intersect each other. At the corner frequency, a change in the slope of a magnitude plot occurs.

8.What do you mean by minimum phase system ?

Answer

The system having transfer function with neither poles nor zeros in the right half of s plane is called minimum phase system. With any one pole or zero or both in right half, it is called non-minimum phase system.

9.Why did Bode suggest plotting the magnitude of a frequency response on log-log co-ordinates ?

Answer

Bode suggested plotting the magnitude of a frequency response on log-log co-ordinates so as to accommodate large range of frequency in the limited space due to which effect of wide range of frequency can be conveniently studied on the magnitude.

10.What is gain crossover frequency and phase crossover frequency ?

Answer

i) Gain crossover frequency : The frequency at which magnitude of G(jω)H(jω) is unity i.e. 1 is called gain crossover frequency. ii) Phase crossover frequency : The frequency at which phase angle of G(jω)H(jω) is -180° is called phase crossover frequency.

11.In terms of Bode plot, define stability of the system.

Answer

In terms of Bode plot, when gain cross over frequency is lessthan phase crossover frequency then P.M. and G.M. are positive and the system is said to be stable. When gain cross over frequency is greater than phase crossover frequency then P.M. and G.M. are negative and the system is said to be stable. When gain crossover frequency is equal to phase crossover frequency then P.M. and G.M. are zero and the system is said to be marginally or critically stable.

12.What will be the initial slope of the Bode magnitude plot for a system having no poles at the origin ?

Answer

A pole at the origin contributes a slope of -20 dB/dec at start. But if there are no poles at the origin then the initial slope of the Bode magnitude plot will be zero and it will be of straight line nature, parallel to Log ω axis.

13.If the very low frequency asymptote of the magnitude plot of an unity feedback system has a slope of -40 dB/decade, find which standard input or inputs it can follow without any steady state errors.

Answer

At very low frequency, the magnitude plot slope is -40 dB/decade i.e. there are two poles at the origin and hence the system is TYPE 2 system. The TYPE 2 system follows parabolic input with some error but it can follow step and ramp type standard inputs without any steady errors.

14.What is meant by +20 dB/dec slope change ?

Answer

The slope +20 dB/dec means an increase in the magnitude by 20 dB per decade (10 times) change in the frequency.

15.What is polar plot ?

Answer

Polar plot is the locus of tips of the phasors of various magnitudes of transfer function of the system, plotted at the corresponding phase angles for different values of frequencies from 0 to ∞.

16.How to determine stability from the polar plot ?

Answer

If critical point -1+j0 is enclosed by the polar plot of the system then that system is unstable and if it is not enclosed it is stable in nature. A portion is said to be enclosed within polar plot if it lies to the right hand side when one travels along the polar plot from the point corresponding to ω = 0 to point corresponding to ω = ∞

17.Define encirclement of a point.

Answer

A point is said to be encircled by a closed path if it is found to lie inside that closed path.

18.Define analytic function and singularities.

Answer

A mathematical function is said to be analytic at a point in a plane if its value and its derivative has finite existence at that point. If at a point in a plane, the value of function or its derivative is infinite, the function is said to be non analytic at that point and such a point is called singularity of the function. So all such points where given function is not analytic are called singularities of that function.

19.What is Nyquist path or Nyquist contour ? What is Nyquist contour ?

Answer

The contour that enclosed entire right half of s plane is called Nyquist contour.

20.Define phase margin. (or) What is phase margin ?

Answer

The phase margin is defined as the amount of additional phase lag at gain cross over frequency required to bring the system to verge of instability. Phase margin, γ = 180° + ϕgc.

21.State Nyquist stability criterion.

Answer

If the Nyquist plot of the open loop transfer function G(s) corresponding to the nyquist contour in the s plane encircle the critical point -1+j0 in the contour in clockwise direction as many time as the number of right half s plane poles of G(s), the closed loop system is stable.

22.What is Bode plot?

Answer

The Bode plot is the frequency response plot of the transfer function of a system. A bode plot consist of two graphs. One is the plot of magnitude of sinusoidal transfer versus log ω. The other is a plot of the phase angle of a sinusoidal function versus log ω.

23.What is closed loop frequency response ?

Answer

The closed loop frequency response is the graph of magnitude of C(jω)/R(jω) and phase angle of C(jω)/R(jω) against frequency ω.

24.What is Nichols chart ?

Answer

The constant M and N circles to log magnitude phase angle co-ordinates and the resultant chart is known as Nichols chart.

25.Mention the advantages of Nichols chart. (or) What are the advantages of Nichols chart

Answer

The advantages are, 1. It is used to find the closed loop frequency response from open loop frequency response. 2. Frequency domain specification can be determined from Nichols chart. 3. The gain of the system can be adjust to satisfy the given specification.

26.State the various frequency domain specifications. (or) What are the frequency domain specifications ?

Answer

1. Resonant peak 2. Resonant frequency 3. Bandwidth 4. Cut-off rate 5. Gain margin 6. Phase margin.

27.Define Resonant peak. (or) What is Resonant peak?

Answer

The maximum value of the magnitude of closed loop transfer function is called resonant peak.

28.What is dominant pole?

Answer

The dominant pole is a pair of complex conjugate pole which decides transient response of the system. In higher order systems the dominant poles are very close to origin and all other poles of the system are widely seperated and so they have less effect on transient response of the system.

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