Nonlinear Control of Dual-Axis Platform

Improving control accuracy in robotic platforms remains a highly relevant challenge, particularly in the presence of mechanical nonlinearities. One of the most common issues is backlash, which causes deviations from a straight trajectory during motion, and adversely affects the overall stability and precision of the control system. (Research purpose) The objective of this study is to develop a control system for a dual-axis platform with two degrees of mobility that effectively recognizes and compensates for the mechanical backlash effects. To achieve this, a system was designed to ensure stable platform motion while minimizing the impact of backlash on trajectory accuracy. (Materials and methods) A mathematical model of the control system was developed, representing backlash as a hysteresis effect. Several backlash compensation methods were investigated. The implemented control algorithms included linear controllers such as the Proportional–Integral–Derivative (PID) controller and a phase-shift controller, as well as nonlinear algorithms based on fuzzy logic (Fuzzy Logic Controller). The system model and control algorithms were simulated using MATLAB and the Simulink library. (Results and discussion) Simulation results demonstrate that the proposed control methods effectively compensate for mechanical backlash, ensuring more stable and accurate platform motion. The effectiveness of these methods was confirmed under both idealized and real-world operating conditions. (Conclusions) The developed control system significantly improves platform accuracy and stability, broadening its applicability across a wide range of robotic applications.

1. Izmaylov A.Yu., Lobachevskiy Ya. P., Dorokhov A.S. et al. Modern technologies and equipment for agriculture – trends from the Agritechnika 2019 exhibition. Tractors and Agricultural Machines. 2020. N6. 28-40 (In Russian). DOI: 10.31992/0321-4443-2020-6-28-40.

2. Shutenko, A. V., & Khort, D. O. (2024). Determination of the geometric parameters of a water jet depending on the type of nozzle and jet operation mode. Engineering Technologies and Systems. 34(1). 88-100 (In Russian). DOI: 10.15507/2658-4123.034.202401.088-100.

3. Smith J., Brown L. Advances in precision gear design: A review. Journal of Mechanical Engineering Science. 2020. 234(10). 1234-1245 (In English). DOI: 10.1177/0954406220901234.

4. Karba B. Developing a software for proper assembly of planetary gearbox components with low backlash. Master’s thesis. Gaziantep University. 2021 (In English). DOI: 10.13140/RG.2.2.16503.55209.

5. Filippov R., Khort D. Multifunctional robotic device with intelligent positioning system. E3S Web. 2024. 493. 01003 (In English). DOI: 10.1051/e3sconf/202449301003

6. Kutyrev A.I., Khort D.O., Smirnov I.G. et al. Robotic device for identifying and picking apples. Proceedings of IEEE Technology. 2022. 415-420 (In English). DOI: 10.1109/PICST57299.2022.10238646.

7. Lin W., Qian C. Linear openness and feedback stabilization of nonlinear control systems. Discrete and Continuous Dynamical Systems. 2018. 11(6). 1105-1120 (In English). DOI: 10.3934/dcdss.2018063.

8. Serkies P., Szabat, K. Model predictive control of the twomass drive system with backlash and friction. ISA Tran sactions. 2019. 93 . 1-12 (In English). DOI: 10.1016/j.isatra.2019.02.005.

9. Zhang Y., Wang Y. Backlash compensation in servo systems using adaptive control. IEEE Transactions on Industrial Electronics. 2019. 66(5). 3983-3992 (In English). DOI: 10.1109/TIE.2018.2856205.

10. Vered Y., Elliott S. J. Robust internal model control approach for position control of systems with sandwiched backlash. ISA Transactions. 2023 (In English). DOI: 10.48550/arXiv.2307.06030.

11. Wang L., Chen X. Adaptive fuzzy control for nonlinear systems with backlash-like hysteresis. IEEE Transactions on Fuzzy Systems. 2018. 26(3). 1312-1323 (In English). DOI: 10.1109/TFUZZ.2017.2737021.

12. Lima T.A., Madeira D. de S., Viana V.V., Oliveira R.C.L.F. Static output feedback stabilization for uncertain relative degree nonlinear systems with input saturation. Systems & Control Letters. 2022. 168 (In English). DOI: 10.1016/j.sysconle.2022.105359.

13. Zhang Y., Li X. Discrete-time adaptive fuzzy finite-time tracking control for nonlinear systems with uncertainties. IEEE Transactions on Fuzzy Systems (In English). 2023.

14. Li X., Zhang H. Position control of PMDC motors with backlash compensation using adaptive control. IEEE Transactions on Industrial Electronics. 2019. 66(12). 9462-9471 (In English). DOI: 10.1109/TIE.2018.2886789.

15. Zuo Q., Wang B., Chen J., Dong H. Model predictive control of aero-mechanical actuators with consideration of gear backlash and friction compensation. Electronics. 2024. 13(20). 4021 (In English). DOI: 10.3390/electronics13204021.

16. Smith, J., Brown, L. (2020). Advances in precision gear design: A review. Journal of Mechanical Engineering Science. 2020. 234(10). 1234-1245 (In English). DOI: 10.1177/0954406220901234.