Dynamics and Control of Geared Servomechanisms with Backlash and Friction Consideration

Abstract

The main objectives of this research are to develop a control- oriented dynamic model for geared servomechanisms with backlash and friction and to establish systematic methodologies of designing a feedforward plus feedback controller to achieve high precision.<P>First, the dynamic model for the purpose of real- time control is developed for a spur gear system with backlash and friction. The complicated variation of the meshing stiffness as a function of contact point along the line of action is studied. Then the mean value of the meshing stiffness is used as the stiffness constant in the proposed model. Without sliding friction, two, simulations, free vibration and constant load operation, are performed to illustrate the effects of backlash on gear dynamics. Comparisons are also given of the simulation results with those of Yang and Sun's model. Then the average friction torque instead of the instantaneous friction torque is, proposed for the model to simplify the complexity of the system. Another two simulations are performed to illustrate the effects of backlash and friction on gear dynamics. In addition, the effect of adding a damper on the driving shaft, is also studied.<P>Secondly, since the model for a geared servomechanism with backlash and friction is one example of nonsmooth dynamic systems, the traditional methods of examining existence and uniqueness properties and checking stability condition for such geared system are no longer valid. In this dissertation, Filippov's solution concept and his theorems are used to examine the existence and uniqueness properties for the proposed dynamic model. Furthermore, based on the extended stability theorems proposed by Shevitz and Paden, a general methodology is developed for the analysis of the stability, conditions of the equilibrium points for piece-wise continuous systems. The developed dynamic model is also examined using the above strategy.<P>Finally, conventional control methods for a geared servomechanism usually do not take backlash and friction into account. As a result, accurate position control can not be achieved. In this dissertation, a new open-loop, optimization- based controller is developed to achieve accurate position tracking of a geared servomechanism. Path generation, selection of appropriate control input function, and optimization techniques for the design of such a controller are discussed. A systematic method of finding appropriate state, feedback gains to reduce the effects of possible load disturbance and model errors is also proposed. Numerical simulation results indicate that the improvement is quite satisfactory.