Recently the need for high-precision servo system has been increased in many applications. In such servo systems, unmodeled friction is usually the cause of performance degradation. Moreover, the friction characteristics may be changed easily due to the environmental changes, for instance, the variations of the load, temperature and humidity. In the conventional control schemes, however, the friction has been often neglected or inadequately compensated.
In this study, robust tracking control schemes are proposed for a positioning table with external disturbances and nonlinear friction. Firstly, as a model-based friction compensation scheme, a friction identification method using evolution strategies (ES), and a robust control scheme are proposed. For the friction identification, an integrated friction model is employed based on the Karnopp's friction model, which can explain the rising static friction and spring-like property. Using the (μ+ λ)-ES, the system parameters are identified with the experimental input and output data. After the off-line identification phase, the friction can be compensated by applying the opposite signed instantaneous friction force to the controlled system. However, the friction may not be canceled out exactly due to the unstructured and structured modeling errors. Considering the modeling errors and the external disturbances, the sliding control input is introduced to guarantee the stability of the overall system. The gain of the sliding control input is updated adaptively by an estimation algorithm, so it is not necessary to know a priori the upper bound of such uncertainties.
Then, two kinds of non-model-based friction compensation schemes are proposed. Firstly, a robust adaptive control scheme using a state-dependent sliding control input is proposed. We introduce the sliding control input whose gain is computed from the estimated upper bound, i.e., a linear function of relative velocity, of the friction. Secondly, two robust control schemes are proposed using an explicit identifier which estimate the friction adaptively. Artificial neural networks such as a fuzzy neural network and a CMAC network are used for such an identifier. In the proposed schemes, the weights of the artificial neural networks are updated by a proposed estimation law based on the Lyapunov stability theory.
All of the proposed schemes are robust to the variation of the system and/or the friction characteristics, and the bounded external disturbances. Also, the stability of the overall system and the asymptotic convergence of the tracking errors to the pre-determined desired error tolerances are proved via Lyapunov stability theorem. The effectiveness of each proposed control scheme is demonstrated and compared via computer simulations and experiments on a positioning system called X-Y table.
