Dynamic Joint Modeling And Control Of Flexible Joint Robots

Harmonic reducer is widely applied in the mechanical transmission systems of the joint-type robots because of its large transmission ratio,carrying capacity,small size,and high efficiency,etc.The existence of flexible components inside the harmonic reducer will cause a series of problems including flexible vibration,uncertainty and unknown disturbance and so forth,although it makes the benefit of additional degrees of freedom.In order to achieve excellent position control performance for the flexible joint robot,it is highly expected that the control law can not only suppress the flexible vibration and reject the disturbance as much as possible but also be robust to the uncertainties in the system.The mathematical modeling and control approaches of the flexible joint robot are investigated in this paper.The main works and innovations of the thesis are presented as follows:The dynamic model of a flexible joint robot with four degrees of freedom is established via Lagrange equation,which lays the foundation for the study on the control of flexible joint robot.A hierarchical sliding mode control(HSMC)law is proposed for the point-to-point position control of the flexible joint robot,under the assumption of bounded disturbance and full state feedback of system state,and the stability of the controller is proved by Lyapunov theory.To solve the issue of chattering in sliding mode control,two improved controllers based on hierarchical sliding mode are proposed.Firstly,by employing a power function to replace the sign function in HSMC the chattering is alleviated obviously.Furthermore,a hierarchical sliding mode control law based on the double power reaching law is presented,which can not only suppress the chattering but also achieve fast approaching speed and good dynamic and static performance for the system states.Simulation results demonstrate the effectiveness of the proposed algorithms.Aiming at tracking time-varying trajectory for the flexible joint robot,a dynamic surface sliding mode controller(DSSMC)is designed to simplify the process of differentiation of the virtual control in traditional back-stepping control,under the assumption of bounded disturbance and full state feedback.By employing Lyapunov theory it has been proved that he closed-loop system is semi-globally uniformly bounded.Furthermore,a fuzzy dynamic surface sliding mode controller(FDSSMC)is proposed to adjust the gain of the switching item in the sliding mode control,so as to compensate time-varying disturbances and reduce the chattering simultaneously.The effectiveness of the proposed algorithms is demonstrated via numerical simulation.To address the issue concerning with the time-varying stiffness,uncertainties of inertia and inner disturbances caused by flexible vibration in flexible joint system,active disturbance rejection controller(ADRC)design is investigated.Based on the modeling of Quanser rotary flexible joint experimental system,a fifth-order extended state observer is constructed to estimate the lump disturbance including the uncertainties of the parameters and flexible vibration in the system.Furthermore,a state error feedback control law with disturbance compensation is designed,which has only a few control parameters to be adjusted,and the debugging process is simple.Experimental results verify the effectiveness of the controller.