IntermediateTopic 66 of 101Signals, Control & Comms
Nonlinear systems
Do not obey superposition; show limit cycles and multiple equilibria.
In depth
Nonlinear systems violate superposition and show phenomena like limit cycles, multiple equilibria, bifurcation, chaos, saturation, dead zones, backlash and hysteresis. Analysis tools: phase plane, describing functions, Lyapunov methods, simulation. Controlled by gain scheduling, feedback linearisation, sliding mode.
Key points
- Equilibrium points
- Phase portraits
- Describing function
- Saturation
ExampleA relay thermostat causes a limit cycle in room temperature.
What is Nonlinear systems?
Do not obey superposition; show limit cycles and multiple equilibria.
Why is it important to understand nonlinear systems?
Nonlinear systems show behaviour that linear models cannot, so you must know what to look for in real machines and processes.
What is a limit cycle?
A sustained oscillation of fixed amplitude and period that a nonlinear system settles into, which can appear in relay or saturating loops.
Why can a nonlinear system have several equilibria?
Nonlinear terms allow different balance points, and the stable one reached depends on the starting conditions.
How is Nonlinear systems used in practice?
Typical applications include explaining why a valve with stiction causes hunting in a loop, predicting the limit cycle in a relay controller and identifying multiple operating points in a chemical reactor.
What should I learn before Nonlinear systems?
Study "Discretisation methods" first (topic 65 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Nonlinear systems?
Equilibrium points. Phase portraits. Describing function. Saturation.
Can you give an example of Nonlinear systems?
A relay thermostat causes a limit cycle in room temperature.
What comes after Nonlinear systems?
The next topic is "Linearisation", which builds directly on this one.
How difficult is Nonlinear systems?
It is classed as Intermediate in Signals, Control & Comms (topic 66 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.