Objective  The photoelectric tracking system is affected by frictional torque during operation, resulting in jitter and climbing during the tracking process, which seriously affects the tracking accuracy. For the accurate compensation of frictional torque, this paper proposes a method of least squares method combined with particle swarm optimization algorithm for parameter identification with reference to Stribeck friction model, and uses the disturbance separation active disturbance rejection control (DSADRC) algorithm to compensate the identified friction model.

  Methods  First, the turntable system is modeled to analyze the disturbance of friction on the system. According to the characteristics of Stribeck friction model, the corresponding data were measured by constant speed-torque experiment, and the minimum squares method and particle swarm algorithm were used to identify the moment data, and the Stribeck model was established and added to the system. Then the identified friction model is compensated by using DSADRC. Last, the compensator is designed based on DSADRC. Experimental results show that the average error between the friction model identified by the combination of least squares method and particle swarm algorithm and the measured data is 3.4%. Then PID control, active disturbance rejection control and disturbance separation active disturbance rejection control algorithms are used to control and compensate the friction torque. The results show that the maximum speed error of the disturbance separation active disturbance rejection control is 77.72% and 58.78% (Fig.8, Tab.4) lower than that of the PID control and the active disturbance rejection control respectively. The friction torque suppression of the disturbance separation active disturbance rejection control improves the PID control and the classical ADRC by 73.59% and 60.59% (Fig.9, Tab.5) respectively. The steady state error of the tracking system is reduced, and the tracking performance of the system is improved.

  Results and Discussions   By comparing the results of parameter identification of Stribeck model (Tab.3) with experimental results by using the least squares method and particle swarm algorithm, the average error between the identified friction model and the measured data is 3.4% (Fig.7). And then PID control, active disturbance rejection control and disturbance separation active disturbance rejection control algorithms are used to control and compensate the friction torque. The results show that the single-side maximum speed error of the disturbance separation active disturbance rejection control is 77.72% and 58.78% (Fig.8, Tab.4) lower than that of the PID control and the active disturbance rejection control respectively. The friction torque suppression of the disturbance separation active disturbance rejection control improves the PID control and the ADRC by 73.59% and 60.59% (Fig.9, Tab.5) respectively.

  Conclusions  The parameters of the linear and nonlinear parts of the Stribeck friction model were identified by combining the least squares method and particle swarm algorithm, and the average error between the identification results and the experimental data was 3.4%, which could better reflect the friction model. The friction model is compensated by using disturbance separation ADRC and compared with PID control and ADRC control. The comparison results show that the single-side maximum speed error of the disturbance separation ADRC is 77.72% and 58.78% lower than that of PID control and ADRC control. Compared with PID control and ADRC control on friction torque suppression, the proposed method increases by 73.59% and 60.59% respectively. Through experimental results, it is proved that the disturbance separation self-rejection can not only make full use of the basis of the known information of the system, reduce the waste of information caused by the design, save time, but also reduce the steady-state error of the system, improve the tracking performance of the system, and have certain application value in engineering.