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Master Control Systems using Aktu’s Quantum Notes. Access critical insights and frequently asked questions to excel in your B.Tech courses. Your journey to success begins here! **Unit-4 Frequency Response Analysis**

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**Q1. What do you understand by frequency response ? What are its various methods ? Discuss their advantages, disadvantages and limitations.**

**Ans. A. Frequency response:**

- 1. The frequency response is the magnitude and phase relationship between a system’s sinusoidal input and steady-state output.
- 2. Linear system with sinusoidal input

**B. Various methods of frequency response:**

1. Polar plots 2. Inverse polar plots

3. Nyquist stability criterion 4. Bode plot

**C. Advantages of frequency domain approach:**

- 1. The frequency response of a stable open loop system can be obtained experimentally without knowing the transfer function.
- 2. These methods are simple to apply for control design and determining absolute and relative system stability.
- 3. Even with substantial nonlinearity, the system can be represented by an approximation transfer function.
- 4. There is a close relationship between a system’s frequency response and its step response.

**D. Disadvantages of frequency response:**

- 1. The frequency test is difficult to perform for systems with very large time constants because the time necessary for the output to achieve steady-state for each frequency of the test signal is disproportionately long.
- 2. Non-interruptible systems cannot be subjected to the frequency response test.

**E. Limitations of frequency response methods :**

- 1. These methods can be applied only to linear systems.
- 2. For an existing system, obtaining frequency response is possible only if the time constants are up to few minutes.
- 3. Obtaining frequency response practically is fairly time consuming.

**Q2. Sketch the polar plot of the following function, also determine Gain Margin, Phase Margin, H(s) = 1**

**Ans. **

10. As GM and PM are positive, system is stable.

**Q3. Sketch the polar plot for the following transfer function **

** G(s) = (1 + 4s)/s ^{2} (s + 1) (2s + 1)**

**Ans. **

6. Polar plot makes an intercept on the negative real axis at point X.

7. The intercept OX is calculate as given below :

Equating imaginary part to zero

**Q4. Sketch Nyquist plot for G(s) H(s) = 6/s**^{2} (s + 2) comment, on stability.

^{2}(s + 2) comment, on stability.

**Ans. Given: **G(s) H(s) = 6/s^{2}(s +2)

**To Sketch: **Nyquist plot.

1. In frequency domain the given transfer function will become,

2. Magnitude (M),

Z= 2 (Number of zeros on right-hand side)

So the system is unstable because its value lies in the right half s-plane.

**Q5. Sketch the Nyquist plot for the system with open loop transfer function**

**and comment on stability. **

**Ans. **

**Q6. The forward path transfer function of unity feedback control system is G(s) = 100/s(s + 6.45). Find the resonance peak M**_{r}, resonant frequency ω_{r}, and bandwidth of the closed loop system.

_{r}, resonant frequency ω

_{r}, and bandwidth of the closed loop system.

**Ans. **

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