IntermediateTopic 55 of 101Signals, Control & Comms
Nyquist stability criterion
Uses the open-loop frequency response to determine closed-loop stability.
In depth
Nyquist plots G(jω) in the complex plane; closed-loop stability requires N=Z-P encirclements of -1 (Z unstable closed-loop poles, P open-loop RHP poles). Handles systems with delay and unstable open-loop poles; margins visible as distance to -1.
Key points
- Contour in s-plane
- Clockwise encirclements
- Conditionally stable systems
ExampleA system with an open-loop unstable pole needs one counter-clockwise encirclement to be stabilised.
What is Nyquist stability criterion?
Uses the open-loop frequency response to determine closed-loop stability.
Why is it important to understand nyquist stability criterion?
The Nyquist criterion relates closed-loop stability to the open-loop frequency response, which is useful even when the model is not exact.
What does the Nyquist criterion count?
The number of encirclements of minus one by the open-loop Nyquist plot, which must match the number of open-loop unstable poles.
Why is it powerful?
It works with frequency response data directly, including systems with delay that are hard to handle with polynomials.
How is Nyquist stability criterion used in practice?
Typical applications include checking whether a loop with a time delay is stable, determining stability from measured frequency response data and verifying a design for a process with a nonminimum phase element.
What should I learn before Nyquist stability criterion?
Study "Gain and phase margin" first (topic 54 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Nyquist stability criterion?
Contour in s-plane. Clockwise encirclements. Conditionally stable systems.
Can you give an example of Nyquist stability criterion?
A system with an open-loop unstable pole needs one counter-clockwise encirclement to be stabilised.
What comes after Nyquist stability criterion?
The next topic is "PID control", which builds directly on this one.
How difficult is Nyquist stability criterion?
It is classed as Intermediate in Signals, Control & Comms (topic 55 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.