Adaptiv reglering av system med glapp

Abstract: Backlash is common in mechanical and hydraulic systems. It severely limits the overall system performance. Many mechanical solutions have been developed to overcome backlash, for example by using spring-loaded split gear assemblies or dual motor systems. These mechanical solutions can satisfactorily handle the backlash problem but they give rise to other problems like decreased accuracy and reduced control speed. They are also more expensive, they consume more energy and they increase the weight of the system. Therefore it would be very nice to find ways to do backlash compensation that is not based on mechanical devices. In this thesis it is attempted to approach the problem by adaptive control. Two different types of backlash compensations are examined; one linear, phase lead compensation, and one nonlinear, backlash inverse. The nonlinear backlash compensation gives better performance and is used in the controller. The parameter values in the backlash inverse are crucial to the control performance and they need to be estimated if the backlash is unknown or varying. Two different schemes for estimating the backlash parameters has been considered, a model reference adaptive system and a recursive least squares estimator. Both methods require that the state of the backlash (i.e. if it is in the deadzone or not) is known. The recursive least square estimator is expanded so that the plant parameters can be estimated too. The adaptive controller is tested by simulation on a second order plant with known or unknown parameters and an unknown backlash acting on the input of the system. The simulations show that both the backlash and the plant parameters can be estimated if you know the state of the backlash.