Parameter identification and hybrid mathematical modelling techniques applied to non-linear control systems

The study is concerned with the mathematical modelling and parameter identification of nonlinear
motion control systems. The control systems under review are the axis motion control
systems for a 3-axis CNC machine tool.

The modelling process commences with lumped parameter methods applied to each element
and then to each axis in turn. Comparing the dynamic performance of the simulated axis drive
with the machine tool axis performance identifies the need for a modular load and the
introduction of measured non-linear effects.

In order to achieve a realistic dynamic performance, a hybrid model incorporating a
distributed load, explicit damping factors and measured non-linear effects was developed. The
influence of factors like damping coefficients, the moving mass, velocity and positional gains,
time constants of the servo control system on the servo characteristics of machine tool has
been determined. Different friction models have been investigated and an effective simulation
method has been developed for simulation purposes. This model represents to a large extent
the dynamic behaviour of the drives from the actual machine, a fact proven by the comparison
between the simulated and measured results.

For multi-axis control, measured geometric errors at the machine were needed to be included
in the model in order to achieve realistic contouring performance. The models were validated
by comparison with measurements at the machine.

A feature of this work is the developed measurement methods for parameter identification.
This together with the definition of the stimuli provides a solid base for a universal
identification process for application to non-linear machine tool axis drives. A novel wavelet
algorithm for the determination of damping coefficients for CNC machine tools is introduced
and this together with other developed parameter adjustment routines allows for the
performance to be optimised.