The Research of Nonlinear Friction Compensation on Rotary Shack Drive
Abstract
The rotary shack drive is widely used in various engineering applications such as machine tools and robotics. The friction between the rotating shaft and the motion system produces nonlinearities, which causes the output response to deviate from the desired value. To reduce the effect of these nonlinearities on the system performance, a friction compensator is used to accurately control the motional system. This paper presents a novel rotary shack drive with nonlinear friction compensation. The proposed system comprises a PID controller, a friction compensator consisting of a linear feedback gain and a nonlinear static gain, and an adjustable friction compensator model. The characteristics of the system are analyzed in detail and compared with the existing rotary shack drive. Simulation results show that nonlinear friction compensation can significantly increase the tracking accuracy of the rotary shack drive and reduce the influence of friction on the system.
Keywords: Rotary shack drive; Nonlinear friction compensation; PID controller; Linear feedback gain; Nonlinear static gain; Adjustable friction compensator model.
1. Introduction
Rotary shack drive is an important component in the design of engineering systems. Its main function is to move the object while providing a certain degree of speed and accuracy. It is used in a wide variety of applications, such as machine tools, robotics, and automation. The most common form of a shack drive is a ball-screw driven by a motor, which is capable of providing a high degree of positioning accuracy. However, due to unexpected perturbations and friction, the motion of the drive may deviate from the desired motion. Therefore, a proper control strategy is required to maintain the accuracy and stability of the system.
In order to accurately control the motion of the rotary shack drive, it is necessary to consider the nonlinearities associated with the system. In particular, friction between the rotating shaft and the motion system introduces significant nonlinearities that can lead to deviations from the desired motion. As a result, it is important to account for the nonlinearities associated with the system in order to properly control the response of the system.
For this purpose, a friction compensator is typically used to effectively compensate for the nonlinearities associated with the system. Generally, a friction compensator consists of a PID controller, a linear feedback gain, and a nonlinear static gain. By combining these components, it is possible to accurately control the response of the system and reduce errors due to friction. In recent years, some researchers have proposed adjustable friction compensator models which are able to account for the nonlinearities associated with the system and improve the performance of the control system.
2. Modeling of Rotary Shack Drive
In this section, we present the model of a rotary shack drive. The model consists of a motor, a ball-screw, and a load. The motor is used to generate a torque in order to drive the ball-screw and the load. The motion of the drive is governed by the equation:
where T is the motor torque, F is the load force, η is the friction coefficient, and u is the motor control signal.
Friction is an unavoidable phenomenon that exists in the motion system. It introduces nonlinearities that can lead to deviations from the desired motion. In order to accurately control the motion of the drive, it is necessary to take the friction into consideration in the model.
3. Nonlinear Friction Compensation
In this section, we propose a nonlinear friction compensator based on a PID controller, a linear feedback gain, and a nonlinear static gain. The proposed controller is able to effectively compensate for the nonlinearities due to friction and improve the accuracy of the system.
The PID controller is used to generate the control signal. It consists of three parameters, namely the proportional gain (Kp), the integral gain (Ki), and the derivative gain (Kd). The parameters are tuned in order to obtain a desired performance.
The linear feedback gain is used to adjust the magnitude of the control signal. It is expressed as:
where ξ is the linear feedback gain.
The nonlinear static gain is used to account for the nonlinearities associated with the friction. It has the form:
where k is the nonlinear static gain and b is the friction coefficient.
4. Simulation Results
In this section, we present a simulation study of the proposed system. The performance of the system is evaluated by comparing the tracking accuracy in different conditions. The simulation results are shown in Figure 1.
Figure 1 shows that the proposed system is able to significantly improve the tracking accuracy of the drive. When compared to the existing rotary shack drive, the proposed system is able to achieve a much higher accuracy. Moreover, the errors due to friction are reduced and the system performs better in the presence of external perturbations.
5. Conclusion
In this paper, we have proposed a novel rotary shack drive with nonlinear friction compensation. The proposed system is based on a PID controller, a linear feedback gain, and a nonlinear static gain. The proposed system is able to effectively compensation for the nonlinearities introduced by friction and significantly improve the tracking accuracy of the drive. Simulation results show that the proposed system is able to achieve a higher accuracy than the existing rotary shack drive. In addition, the errors due to friction are reduced and the system performs better in the presence of external perturbations.
