IntermediateTopic 53 of 101Signals, Control & Comms
Frequency response methods
Bode and Nyquist plots analyse stability and margins.
In depth
Frequency response G(jω) shows gain and phase vs frequency. Bode plots (log scales) and Nyquist plots analyse stability margins and bandwidth; closed-loop bandwidth relates to speed and noise sensitivity. Experimental frequency response can model unknown plants.
Key points
- Resonant peak M_r
- Bandwidth
- Low-frequency gain sets accuracy
ExampleSweeping a sine input through a system measures its Bode plot.
What is Frequency response methods?
Bode and Nyquist plots analyse stability and margins.
Why is it important to understand frequency response methods?
Bode and Nyquist plots show stability and margins from the frequency response, which is how many loops are designed in practice.
What does a Bode plot show?
The magnitude and phase of the frequency response on logarithmic scales, which helps design and assess margins.
What does a Nyquist plot show?
The path of the open-loop frequency response in the complex plane, which can reveal instability encirclements.
How is Frequency response methods used in practice?
Typical applications include checking the stability of a motor speed loop using its Bode plot, reading the crossover frequency of a controller for bandwidth and using a Nyquist plot to assess a loop with a time delay.
What should I learn before Frequency response methods?
Study "Root locus" first (topic 52 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Frequency response methods?
Resonant peak M_r. Bandwidth. Low-frequency gain sets accuracy.
Can you give an example of Frequency response methods?
Sweeping a sine input through a system measures its Bode plot.
What comes after Frequency response methods?
The next topic is "Gain and phase margin", which builds directly on this one.
How difficult is Frequency response methods?
It is classed as Intermediate in Signals, Control & Comms (topic 53 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.