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Q1: The transfer function of a phase lead compensator is given by
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)The frequency (in rad/sec), at which ∠D(jω) is maximum, is   (2019)
(a) Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)
Ans: (b)
Sol: Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Frequency at which ∠T(jω) is maximum,
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)

Q2: The transfer function C(s) of a compensator is given below.
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is   (SET-2(2017))
(a) 0.1<ω<10.1 < ω < 1  
(b) 1<ω<101 < ω < 10
(c) 10 < ω < 100
(d) ω > 100
Ans:
(a)
Sol: Pole zero diagram of compensator transfer function is shown below.
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Maximum phase lead is between 0.1 and 1.
0.1 < ω < 1

Q3: For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase lag occurs is, ___________.   (SET-2(2016))
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)(a) 0.15
(b) 0.32
(c) 0.66
(d) 0.92
Ans:
(b)
Sol: Assuming
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)We can write,
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)
Q4: The transfer function of a compensator is given asPrevious Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)The phase of the above lead compensator is maximum at   (2012)
(a) √2 rad/s
(b) √3 rad/s
(c) √6 rad/s
(d) 1/√3 rad/s
Ans:
(a)
Sol: Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)
Q5: The transfer function of a compensator is given as
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Gc(s) is a lead compensator if   (2012)
(a) a = 1, b = 2
(b) a = 3, b = 2
(c) a =- 3, b =- 1
(d) a = 3, b = 1
Ans: 
(a)
Sol: Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)For Gc(s) to be a lead compensator
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Option (A) Satisfies the above equation.

Q6: The transfer functions of two compensators are given below :
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Which one of the following statements is correct ?   (2008)
(a) C1C1 is a lead compensator and C2 is a lag compensator
(b) C1 is a lag compensator and C2 is a lead compensator
(c) Both C1 and Care lead compensator
(d) Both Cand Care lag compensator
Ans:
(a)
Sol: Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Zero at s = -1
Pole at s = -10
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)As zero is closer origin, zero dominates pole. Hence  C1 is lead compensator.
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Zero at s = -10
Pole at s = -1
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)As pole is closer to origin, pole dominates zero. Hence C2 is lag compensator.

Q7: The system Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE) is to be compensated such that its gain-crossover frequency becomes same as its uncompensated phase crossover frequency and provides a 45° phase margin. To achieve this, one may use   (2007)
(a) a lag compensator that provides an attenuation of 20 dB and a phase lag of 45° at the frequency of 3 √3 rad/s
(b) a lead compensator that provides an amplification of 20 dB and a phase lead of 45° at the frequency of 3 rad/s
(c) a lag-lead compensator that provides an attenuation of 20 dB and phase lag of 45° at the frequency of √3 rad/s
(d) a lag-lead compensator that provides an attenuation of 20 dB and phase lead of 45° at the frequency of 3 rad/s
Ans: 
(d)
Sol: Let uncompensated syatem,
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Phase crossover frequency of uncompensated system = (ωpc), at this frequency phase of T(jω) is −180°
Put s = jω in T(s)
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Gain cross frequency of compensated system, (ωgc)= phase cross frequency of uncompensated system, (ωpc)1
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)phase angle of ∠T(jω) is −135° and phase of uncompensated systen is −180° at 3 rad/sec.  
Therefore, the compensator provides phase lead of 45° at the frequency of 3 rad/sec.
Let X dB is the gain provided by the compensator, so at gain cross frequency, ∣T(jω)∣com=1 or 0 dB. Gain of uncompensated system  Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Gain of compensated system,
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)So, the compensator provides an attenuation od 20dB. Hence option (D) is correct.

Q8: A lead compensator used for a closed loop controller has the following transfer function Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE) For such a lead compensator   (2003)
(a) a<ba<b
(b) a>ba>b
(c) a>Kb
(d) a<Kba<Kb
Ans: 
(a)
Sol: Transfer function Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)Zero of TF = -a
Pole of TF = -b
For a lead-compensator, the zero is nearer to origin as compared to pole, hence the effect of zero is dominant, therefore, the lead-compensator when introduced in series with forward path of the trnasfer function the phase shift is increased.
Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE)So, from pole-zero configuration of the compensator a < b.

The document Previous Year Questions- Design of Control Systems | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
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FAQs on Previous Year Questions- Design of Control Systems - Control Systems - Electrical Engineering (EE)

1. What are the basic components of a control system?
Ans.The basic components of a control system include the controller, the process or plant, the actuator, and the sensor. The controller processes the input signal and sends commands to the actuator, which affects the process. The sensor measures the output and feeds it back to the controller for adjustment.
2. How do feedback loops work in control systems?
Ans.Feedback loops in control systems involve taking a portion of the output signal and feeding it back to the input of the system. This helps in maintaining the desired output by comparing it with the reference input. If there is a difference, the controller adjusts the input to minimize the error, ensuring system stability and performance.
3. What is the significance of stability in control systems?
Ans.Stability in control systems is crucial as it determines whether the system will perform consistently and predictably over time. A stable system will return to equilibrium after a disturbance, while an unstable system may oscillate or diverge, leading to potential failure or inefficient operation.
4. What are the different types of control strategies used in control systems?
Ans.Different types of control strategies include Proportional (P), Integral (I), and Derivative (D) control, often combined in PID controllers. Other strategies include feedforward control, adaptive control, and robust control, each suited for specific applications based on system requirements and dynamics.
5. How can one assess the performance of a control system?
Ans.Performance of a control system can be assessed using various criteria, including transient response (rise time, settling time, overshoot), steady-state error, stability margins, and frequency response. Tools like Bode plots, Nyquist plots, and root locus techniques are commonly used for this assessment.
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