How to draw Bode Plot?
Step 1: Write the given transfer function in the standard form.
Transfer function:
[Tex]G(s)= \frac{(s+a)(s+b)}{(s+p)(s+q)} [/Tex] —– (1)
Standard form of equation 1:
[Tex]G(s) = \frac{ab(1+ \frac{s}{a})(1+\frac{s}{b})}{pq (1+\frac{s}{p})(1+\frac{s}{q})} [/Tex]
Take [Tex]\frac{ab}{pq} [/Tex] as a constant k.
Step 2: Identify the slope of the first line for the bode plot. The slope of the first line is based on poles and zeros at the origin. Refer to the following table.
Poles at origin | Slope of 1st line |
|---|---|
1 | -20 dB/decay |
2 | -40 dB/decay |
Zeros at origin | The slope of 1st line |
1 | +20 dB/ decay |
2 | +40 dB/ decay |
Step 3: Find the gain of 1st line at ω=1 rad/sec
Gain|ω=1 = 20 log k
Where k = [Tex]\frac{ab}{pq}
[/Tex]
Step 4: Write all the corner frequencies in ascending order and define the slope of each line
Step 5: Write the phase equation and make a table of phase and frequency.
Φ = tan-1([Tex]\frac{w}{a} [/Tex]) + tan-1([Tex]\frac{w}{b} [/Tex]) – tan-1([Tex]\frac{w}{p} [/Tex]) – tan-1([Tex]\frac{w}{q} [/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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