12.What is Bode plot?
The Bode plot is the frequency response plot of the transfer function of a system. A Bode plot consists of two graphs. One is the plot of magnitude of sinusoidal transfer function versus log Ï‰.The other is a plot of the phase angle of a sinusoidal function versus log Ï‰.
13.What are the main advantages of Bode plot?
The main advantages are:
i) Multiplication of magnitude can be in to addition. ii) A simple method for sketching an approximate log curve is available. iii) It is based on asymptotic approximation. Such approximation is sufficient if rough information on the frequency response characteristic is needed. iv) The phase angle curves can be easily drawn if a template for the phase angle curve of
1+ jÏ‰ is available.
14.Define Corner frequency?
The frequency at which the two asymptotic meet in a magnitude plot is called corner frequency.
15.What is Polar plot?
The Polar plot of a Sinusoidal transfer function G(jÏ‰) is a plot of the magnitude of G(jÏ‰) versus the phase angle/argument of G(jÏ‰) on polar or rectangular co-ordinates as Ï‰ is varied from zero to infinity.
16.What is minimum phase system?
The minimum phase systems are systems with minimum phase transfer functions. Inminimum phase transfer functions, all poles and zeros will lie on the left half of s-plane.
17.What is non-minimum phase transfer function?
A transfer function which has one or more zeros in the right half of s-plane is known as non- minimum phase transfer function.
18.What are M circles?
The magnitude of closed loop transfer function with unit feed back can be shown to be in the for every value if M.These circles are called M circles.
19.What is Nichols chart?
The chart consisting if M & N loci in the log magnitude versus phase diagram is called Nichols chart.
20.What are two contours of Nichols chart?
Nichols chart of M and N contours, superimposed on ordinary graph. The M contours are the magnitude of closed loop system in decibels and the N contours are the phase angle locus of closed loop system.
21.How is the Resonant Peak, resonant frequency, and bandwidth determined from Nichols chart?
i) The resonant peak is given by the value of .contour which is tangent to G(jÏ‰ ) locus. ii) The resonant frequency is given by the frequency of G(jÏ‰ ) at the tangency point. iii) The bandwidth is given by frequency corresponding to the intersection point of G(jÏ‰ ) and –3dB M-contour.
22.What are the advantages of Nichols chart?
The advantages are: i) It is used to find the closed loop frequency response from open loop frequency response. ii) Frequency domain specifications can be determined from Nichols chart. iii) The gain of the system can be adjusted to satisfy the given specification
23.What are N circles?
If the phase of closed loop transfer function with unity feedback is Î±, then tan Î± will be in the form of circles for every value of Î±. These circles are called N circles.
PART B
1. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over
frequencies. G(S) = 10/ S(1+0.4S) (1+0.1S) (16)
2. The open loop transfer function of a unity feed back system is G(S) = 1/ S(1+S) (1+2S).
Sketch the Polar plot and determine the Gain margin and Phase margin. (16)
3. Sketch the Bode plot and hence find Gain cross over frequency ,Phase cross over
frequency, Gain margin and Phase margin.
G(S) = 0.75(1+0.2S)/ S(1+0.5S) (1+0.1S) (16)
4. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over
frequency, Gain margin and Phase margin.
G(S) = 10(S+3)/ S(S+2) (S2+4S+100) (16)
5. Sketch the polar plot for the following transfer function .and find Gain cross over frequency
,Phase cross over frequency, Gain margin and Phase margin.
G(S) = 10(S+2)(S+4)/ S (S
2
-3S+10) (16)
6. Construct the polar plot for the function GH(S) =2(S+1)/ S
2
. find Gain cross over frequency ,Phase cross over frequency, Gain margin and Phase margin. (16)
7. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross
over frequencies G(S) =KS2 / (1+0.2S) (1+0.02S).Determine the value of K for a gain cross over frequency of 20 rad/sec. (16)
8. Sketch the polar plot for the following transfer function .and find Gain cross over
frequency, Phase cross over frequency, Gain margin and Phase margin.
G(S) = 400/ S (S+2)(S+10) (16)
9. A unity feed back system has open loop transfer function G(S) = 20/ S (S+2)(S+5).Using Nichol’s
chart. Determine the closed loop frequency response and estimate all the frequency domain specifications. (16)
10. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over
frequency, Gain margin and Phase margin.
G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S). (16)
11.Explain in detail about M and N Circles with necessary equations. (16)
UNIT-IV STABILITY OF CONTROL SYSTEM
PART- A (2 MARKS)
1.What is Nyquist contour?
The contour that encloses entire right half of S plane is called nyquist contour.
2.State Nyquist stability criterion.
If the Nyquist plot of the open loop transfer function G(s) corresponding to the nyquist control in the S-plane encircles the critical point –1+j0 in the counter clockwise direction as many times as the number of right half S-plane poles of G(s),the closed loop system is stable.
3.Define Relative stability.
Relative stability is the degree of closeness of the system, it is an indication of strength or degree of stability.
4.What are the two segments of Nyquist contour.
i. An finite line segment C1 along the imaginary axis. ii. An arc C2 of infinite radius.
5.What are root loci?
The path taken by the roots of the open loop transfer function when the loop gain is varied from 0 to Î± are called root loci.
6.What is a dominant pole?
The dominant pole is a air of complex conjugate pair which decides the transient response of the system.
7.What are the main significances of root locus?
i. The main root locus technique is used for stability analysis. ii. Using root locus technique the range of values of K, for as table system can be
determined.
8. What are the effects of adding a zero to a system?
Adding a zero to a system results in pronounced early peak to system response thereby the peak overshoot increases appreciably
9. State-Magnitude criterion.
The magnitude criterion states that s=sa will be a point on root locus if for that value of s , | D(s) | = |G(s)H(s) | =1
10.State – Angle criterion.
The Angle criterion states that s=sa will be a point on root locus for that value of s,∟D(s) = ∟G(s)H(s) =odd multiple of 180°
11. What is a dominant pole?
The dominant pole is a pair of complex conjugate pair which decides the transient response of the system.
12.Define BIBO stability.
A linear relaxed system is said to have BIBIO stability if every bounded input results in a bounded output.
13.What is the necessary condition for stability.
The necessary condition for stability is that all the coefficients of the characteristic polynomial be positive.
14.What is the necessary and sufficient condition for stability.
The necessary and sufficient condition for stability is that all of the elements in the first column of the routh array should be positive.
15.What is quadrantal symmetry?
The symmetry of roots with respect to both real and imaginary axis called quadrantal symmetry.
16.What is limitedly stable system?
For a bounded input signal if the output has constant amplitude oscillations Then the system may be stable or unstable under some limited constraints such a system is called limitedly stable system.
PART B
1. (i) Using Routh criterion determine the stability of the system whose characteristics equation is
S
4
+8S
3
+18S
2
+16S+5 =0. (8)
(ii).F(S) = S
6
+S
5
-2S
4
-3S
3
-7S
2
-4S-4 =0.Find the number of roots falling in the RHS plane and LHS plane. (8)
2. A unity feedback control system has an open loop transfer function
G(S)= K / S (S
2
+4S+13).Sketch the root locus. (16)
3. Sketch the root locus of the system whose open loop transfer function is
G(S)= K / S (S+2)(S+4).Find the value of K so that the damping ratio of the closed loop system is
0.5 (16)
4. A unity feedback control system has an open loop transfer function
G(S)= K (S+9) / S (S
2
+4S+11).Sketch the root locus. (16)
5. Sketch the root locus of the system whose open loop transfer function is
G(S)= K / S (S+4) (S
2
+4S+20). (16)
6. A Unity feedback control system has an open loop transfer function
G(S)= K (S+1.5) / S (S+1)(S+5).Sketch the root locus. (16)
7. Draw the Nyquist plot for the system whose open loop transfer function is
G(S)= K / S (S+2)(S+10).Determine the range of k for which closed loop system is stable. (16)
8. Sketch the Nyquist Plot for a system with the open loop transfer function
G(S) H(S)= K (1+0.5S)(1+S) / (1+10S)(S-1). Determine the range of k for which closed loop system is stable. (16)
9. (i) Determine the range of K for stability of unity feedback system whose open loop
transfer function is G(s) = K / s (s+1)(s+2) (8) (ii) The open loop transfer function of a unity feed back system is given by
G(s) = K (s+1) / s3+as2+2s+1. Determine the value of K and a so that the system oscillates at a frequency of 2 rad/sec. (8)
10.(i) Construct Routh array and determine the stability of the system represented by the characteristics
equation S5+S4+2S3+2S2+3S+5=0.Comment on the location of the roots of characteristic equation. (8)
(ii) Construct Routh array and determine the stability of the system represented by the
characteristics equation S7+9S6+24S4+24S3+24S2+23S+15=0comment on the location of the roots of characteristic equation. (8)
UNIT - V
COMPENSATOR DESIGN
PART- A (2 MARKS)
1.Define Phase lag and phase lead?
A negative phase angle is called phase lag. A positive phase angle is called phase lead.
2.What are the two types of compensation?
i. Cascade or series compensation ii. Feedback compensation or parallel compensation
3.What are the three types of compensators?
i. Lag compensator ii. Lead compensator iii. Lag-Lead compensator
4.What are the uses of lead compensator?
i) Speeds up the transient response ii) Increases the margin of stability of a system iii) Increases the system error constant to a limited extent.
5.What is the use of lag compensator?
Improve the steady state behavior of a system, while nearly preserving its transientresponse.
6.When is lag lead compensator is required?
The lag lead compensator is required when both the transient and steady state response of a system has to be improved.
7.What is a compensator?
A device inserted into the system for the purpose of satisfying the specifications is called as a compensator.
8.What is Compensation?
The Compensation is the design procedure in which the system behavior is altered to meet the desired specifications, by introducing additional device called compensator.
9.Why Compensation is necessary in feedback control system?
In feedback control systems compensation is required in the following situations.
i) When the system is absolutely unstable, then compensation is required to stabilize
the system and also to meet the desired performance. ii) When the system is stable, compensation is provided to obtain the desired
performance.
10.When lag/lead/lag-lead compensation is employed?
Lag compensation is employed for a stable system for improvement in steady state performance. Lead compensation is employed for stable/unstable system for improvement in transient- state performance. Lag-Lead compensation is employed for stable/unstable system for improvement in both steady- state and transient state performance.
PART B
1. What is compensation? Why it is need for control system? Explain the types of compensation? What
is an importance of compensation? (16)
2. Realise the basic compensators using electrical network and obtain the transfer
function. (16)
3. Design suitable lead compensators for a system unity feedback and having open loop transfer
function G(S)= K/ S(S+1) to meet the specifications.(i) The phase margin of the system ≥ 45o, (ii) Steady state error for a unit ramp input ≤1/15, (iii) The gain cross over frequency of the system must be less than 7.5 rad/sec. (16)
4. A unity feed back system has an open loop transfer function G(S)= K/ S(S+1) (0.2S+1). Design a suitable phase lag compensators to achieve following specifications Kv= 8 and Phase margin 40 deg with usual notation. (16)
5. Explain the procedure for lead compensation and lag compensation (16)
6. Explain the design procedure for lag- lead compensation (16)
7. Consider a type 1 unity feed back system with an OLTF G(S) =K/S (S+1) (S+4). The system is to be compensated to meet the following specifications Kv > 5sec and PM > 43 deg. Design suitable lag compensators. (16)
8. Using Electrical lead network derive the transfer function. (16)
9. Using Electrical lag network derive the transfer function (16)
10. Using Electrical lag-lead network derive the transfer function (16)
11. Design a lead compensator for a unity feedback system with open loop transfer function G(S) = K/
S(S+1) (S+5) to satisfy the following specifications (i) Kv > 50 (ii) Phase Margin is > 20 . (16)
12. Design a lead compensator for G(S) =K / S
2
(0.2S+1) to meet the following Specifications (i)Acceleration k
a
=10; (ii) P.M=35. (16)
13. Design a Lag compensator for the unity feedback system whose closed loop transfer function
C(s) / R(s) = K / (s (s+4) (s+80) + K) is to meet the following specifications P.M ≥33 o. And Kv ≥30. (16)
14. A unity feedback system has an OLTF G(s) = K / s(s+2)(s+60). Design a Lead-Lag
compensator is to meet the following specifications.
(i) P.M is atleast 40o , (ii) Steady state error for ramp input ≤ 0.04 rad. (16)