Introduction to Non Linear Control Systems

Cuthbert Nyack

Linear systems can be described by the Laplace Transforms and Transfer Function approach or by the state vector approach.

Linear systems are ideal systems and the concept of linearity is an approximation to real nonlinear systems.

Electrical systems have nonlinearity in the form of saturation, nonlinear charcateristics and waveforms, nonlinear dielectric and permeability effects, current and frequency dependent input and output impedances etc.

Thermal systems may have nonlinear radiative and convective losses.

Mechanical systems may have nonlinear friction, nonlinear elasticity and flexing, deadband, backlash, hysteresis etc.

Dynamical effects which occur with nonlinear systems include limit cycle oscillations, distorted waveform response, harmonic and subharmonic responses, stability dependent on size of input, chaotic behaviour etc.

For analysis, the Describing function approach attempts to derive an amplitude dependent transfer function, Phase plane approach can be used to visualise the dynamics or the state vector approach can be used for simulation.

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