Nonlinear friction compensation and dynamic model proposed of a three-axis cartesian system for improved trajectory tracking control

The precision and stability of Cartesian systems can be significantly affected by the friction present in their mechanical transmission systems. This paper presents a friction compensation model that integrates three different phenomena commonly found in such systems: Coulomb friction, viscous friction, and the Stribeck effect. The compensation is applied after analyzing the impact of these phenomena on the system, by using a mathematical function integrated into the dynamic model of the XYZ tree-axis cartesian system and allowing the study of their effects on the robot's behavior. By incorporating the compensation, the control is improved, reducing position error and enhancing the system performance. Afterward, the position control algorithm is compared with the trajectory control resulting in a further reduction of the error and achieving a maximum of 0.05-millimeter error on the X-axis, which is the degree of freedom with the highest load and where the friction phenomena are most pronounced. The results highlight the importance of friction compensation in robot control systems, especially in applications requiring high precision. The integration of a dynamic friction model with an optimized control algorithm provides a viable strategy for improving the performance of Cartesian system, enabling their use in industrial and precision applications without the need for expensive specialized hardware