Research On The Control Of Harmonic Drive With Hysteresis Compensation

Harmonic drive is a type of precision mechanical transmission with high transmission ratio,small size and hifgh transmission precision.It plays important roles in precision electromechanical equipment,such as multi-axis robots,large spacecraft and semiconductor processing equipment.The complex transmission principle of harmonic drive makes it have manv nonlinear transmission characteristics such as kinematic errors,hysteresis,viscous friction,etc.These nonlinear characteristics seriously affect the transmission accuracies of the harmonic drive transmission system.So far,most of the researches about harmonic drive are focused on the compensation of single nonlinear disturbances based on continuous-time model.In this thesis,the continuous-time and discrete-time dynamics characteristics of harmonic drive under multiple nonlinear disturbances are studied and three corresponding control strategies under these characteristics are proposed.The methods are of theoretically significance and engineering application value.The major works in this thesis include two aspects:(1)A continuous-time mathematical model is established for harmonic drives considering hysteresis,flexible joints and viscous friction.Two schemes are used to optimize the model and correspondingly design the controllers.On one hand,the new model is considered as a linear system with mismatched interference and then the disturbance observer-based control(DOBC)is designed.On the other hand,the uniform smooth approximation function is employed to optimize the original model.By using coordinate transformation and state feedback linearization,then the degraded quasi-linear system is obtained.Combining the quasi-linear system with optimal theory,a compound optimal controller is proposed to realize the optimal tracking control.Simulation results show that compared with DOBC using a linear observer,the new compound optimal controller in this thesis presents a smoother control signal with the elimination of high-frequency oscillations.Furthermore,the tracking error in the steady state tracking is around 10-7 rad and no cyclic fluctuations appears.(2)The discrete Lagrangian-D'Alembert principie,is employed to constructs the discrete-time model of a harmonic drive transmission system uncder multi-intcerferencce With the variational integrator which can conserve the symmetry property of system dynamics,the discrete model conserves momentum mapping in the configuration space of the original continuous-time system during the whole control horizon.Based on discrete mechanics,the continuous-time hysteresis is discretized and the equivalent discrete performance index functions of the original continuous-time objective functions.By using discrete mechanics and optimal control(DMOC),we obtain trajectory tracking and energy optimal control of the harmonic drive,which is very challenging in continuous-time modeling.The optimal control input of these two control problems are calculated with the sequential quadratic programming to illustrate the superiority of the proposed DMOC.Numerical calculation results show that compared with continuous-time controller,the optimal tracking error of DMOC is around 10-7 rad and optimal energy control is realized for harmonic drive under multiple disturbance.