Solved Examples of Bode Plots
Example: Find the transfer function from the bode plot given in the figure?
Solution:
Step 1: Corner frequency: ω= 1, 10, 100
Step 2: Calculation of the slope
Slope | Increasing or decreasing |
---|---|
0 dB/dec | Initial value |
+20 dB/dec | Increasing |
0 dB/dec | Decreasing |
-20 dB/dec | Decreasing |
Therefore, if the slope is increasing then it is a zero else it is a pole.
ω = 1 (zeros) ω = 1 (pole) ω = 1 (pole)
Step 3: Calculating the gain of the first line at ω = 1
Gain = 20 log(k) + (slope of 1st line) log(ω) -20 = 20log(k) + 0 k = 0.1
Step 4: Writing the transfer function
[Tex]T(s) = \frac{k(1+\frac{s}{1})}{(1+\frac{s}{10})(1+\frac{s}{100} )} [/Tex]
k= 0.1
[Tex]T(s) = \frac{0.1(1+\frac{s}{1})}{(1+\frac{s}{10})(1+\frac{s}{100} )} [/Tex]
[Tex]T(s) = \frac{100(s+1)}{(s+10)(s+100)} [/Tex]
Bode Plots in Control System
Bode plots describe the linear time-invariant systems’ frequency response (change in magnitude and phase as a function of frequency). It helps in analyzing the stability of control system. It applies to the minimum phase transfer function i.e. (poles and zeros should be in the left half of the s-plane).
In this article, we are going to learn what is Bode Plot and Types of Bode Plots and how to draw Blode plot and parameters of Bode plot, we are going to learn what is Phase and Gain Margin and what are the advantages and disadvantages of Bode plots in Control System.
Table of Content
- What are Bode Plots?
- Types of Bode Plot
- How to draw Bode Plot?
- How to read Bode Plots?
- Phase and Gain Margins
- Advantages
- Disadvantages
- Solved Examples
- FAQs
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