Abstract:
The increasing demand for high performance in mechanical systems has increased the interest and study into the control of such systems with friction. Friction induces negative effects such as; increased tracking errors, large settling times and stick-slip oscillations. If friction is taken into account in the controller design it is expected that many high performance motion systems will gain both speed and accuracy resulting in greater performance. This thesis contributes to the artalysis of these controlled mechanical systems with friction by providing extended modelling methods and simulation techniques. The problems encountered in the simulation of model with friction are that system can be; discontinuous, numerically stiff and implicit in the accelerations. It is found that if the system models are discontinuous the location of the discontinuity must be found during simulation. If the system models are found to be numerically stiff then implicit numerically methods should be used to for simulation. When the system model is implicit in the accelerations, the normal force is changing direction and is a nonlinear function of the position, velocity and acceleration of the system. At each time step during simulation the acceleration must therefore be found using an iterative method that is expensive to perform. Problems are encountered when the iteration fails to converge or converges on the incorrect solution for the acceleration. The first original contribution of this thesis is the development of two simple extensions that can be used with the commonly used friction models allowing them to model the experimentally observed phenomenon of the normal force lag. The second original contribution is the development of techniques that allow the system models that are implicit in the acceleration to be transformed to an explicit representation. The first of these techniques involves the differentiation of the system model with respect to time allowing the system model to be written explicitly in the jerk, the time rate of change of acceleration. The second technique involves the replacement of the normal force with the effective normal force determined from the extensions that model normal force lag. This technique allows the system model to be written explicitly in terms of acceleration. Both techniques are found to significantly reduce the problems encountered in simulation as well as making simulation less expensive.