In motion control systems, friction effects can be critical and the absence of an effective friction compensation action may lead to undesired control behaviour, i.e. steady state errors, stick slip motion and limit cycles. Adequate compensation of friction however is not an easy task. Friction is a complicated phenomenon that is hard to model, highly non-linear, time-varying and application dependent, making the compensation of it a challenging task. A wide range of compensation schemes is proposed in literature, but growing performance demands reveal the limitations of many of these methods. In high precision applications, for example robotic surgery, a high degree of accuracy is required, to which the current methods do not comply.
The goal of this thesis is to develop and test adaptive friction compensation methods which meet the increasing performance demands. Additional requirements for the schemes are that they require little physical friction modelling and are applicable to various systems.
First, an adaptive, model-based compensation strategy based on the Coulomb friction model is designed. In the classical Coulomb friction model, the friction force is modelled as a constant times the sign of the velocity. In the proposed method, the constant is replaced by a time varying friction parameter and an update law for the on-line adaptation of this parameter is proposed. An important challenge with this method is the definition of the signum function because the general definition of it is not useful for friction modelling. Therefore, a modified signum function definition is used to model the friction force and an approximation of it is formulated for use in the compensator. Based on these definitions, global asymptotic stability of the scheme is proven. Simulations and experimental results confirm the theoretical findings: the compensator is able to eliminate steady state errors, to significantly decrease the stick slip effect and to compensate highly time-varying friction forces. The performance of the last skill however highly depends on the sampling rate and the tuning of the compensator.
Because it is difficult to model the friction force based on first principle knowledge, secondly, a learning-based compensation scheme is proposed. Local linear regression is used for on-line learning and estimation of the friction force. The resulting scheme is very well able to estimate and compensate the friction force. Again, the steady state errors are eliminated, the stick slip effect is almost completely removed and the scheme is very robust to variations in the friction force. An additional advantage is that the method is not restricted to friction compensation, it is also useful for the compensation of different kinds of disturbances.
It can be concluded that both developed methods are able to effectively compensate friction. The learning-based method is more robust with respect to varying friction forces, is less sensitive to the sampling rate and the performance at low velocities is slightly better compared to the model-based method. An additional advantage is that it is also suitable for the compensation of other disturbing forces like gravity. An advantage of the model-based strategy is that it requires no model of the friction-free system dynamics, which is required in the learning-based compensator.