Gain Margin

The gain margin is the amount of open loop gain that can be increased before our system becomes unstable.

It can be calculated from the gain at the phase cross-over frequency.

Gain Margin (GM): [Tex]\frac{1}{|G(jw)H(jw)|}_{w=w_{pc}} [/Tex]

Phase crossover frequency:

It is the frequency where the phase angle of G(s) H(s) is -180 degrees as seen in the figure 1.


∠G(jω)H(jω)∣ω=ωpc= -180

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

Similar Reads

What are Bode Plots?

A graph is called as Bode plot which is frequently used in control system engineering to assess a control system’s stability. Two graphs, the Bode phase plot (which expresses the phase shift in degrees) and the Bode magnitude plot (which expresses the magnitude in decibels), are used to map the frequency response of the system....

Types of Bode Plot

1. Gain plot:...

1. Gain plot:

It represents the magnitude response of the system as a function of frequency. It is plotted on a logarithmic scale....

2. Phase plot:

It depicts the frequency-dependent phase shift of the system’s output signal compared to its input signal. It’s also drawn on a logarithmic scale....

How to draw Bode Plot?

Step 1: Write the given transfer function in the standard form....

How to read Bode Plots?

Blode plots show the frequency response, that is, the changes in magnitude and phase as a function of frequency....

Phase and Gain Margins

Phase Margin...

Phase Margin

The phase margin indicates how much more phases shift we may put in the open loop transfer function before our system becomes unstable....

Gain Margin

The gain margin is the amount of open loop gain that can be increased before our system becomes unstable....

Advantages of Bode Plots in Control System

It helps in identifying the stability of the system.It helps in identifying phases and gaining margins with minimum calculation.It can be used to calculate the system’s transfer function.It can show the amplification and attenuation in the gain plot which is helpful in designing the filters....

Disadvantages of Bode Plots in Control System

It is only applicable to LTI (linear time-invariant) system.It is not suitable for the system having extremely high or low frequencies.It focuses on the frequency response without considering the transient time effect....

Solved Examples of Bode Plots

Example: Find the transfer function from the bode plot given in the figure?...

Conclusion

In Conclusion, The Bode plots are similar to the asymptotic Bode plots since they display the magnitude and also the phase plots as straight lines. The Bode plots will only differ in that they will use simple curves rather than straight lines. For other terms of the open loop transfer function that are listed in the table, you can also create the required Bode graphs....

FAQs on Bode Plots in Control System

Which graph paper is used for Bode plots?...