Feedback linearization controller design for a geared transmission system considering asymmetric backlash and friction

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

Shima Mirshahzadeh ¹ (Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran)
Hamed Khodadadi ² (Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran)

Received: 2022-11-30 Accepted : 2023-01-18 Published : 2023-03-01

Keywords: Backlash, Geared Transmission System, Feedback Linearization Control, Mechatronics,

Abstract :

This study is focused on the mathematical modeling, analysis, and controlling of a Geared Transmission System (GTS). Although GTS is used widely in mechanical equipment and mechatronics, the existence of nonlinearities such as backlash and friction made some challenges for its position control. In this paper's proposed method for GTS, the stribeck friction nonlinearity is estimated based on the motor velocity by a linear model. By this approach, the GTS model is reduced to a two-piecewise function. In addition, the asymmetric non-differentiable dead zone is approximated by a differentiable function. Additionally, using the differentiable function for the approximation leads to a reduction in the number of the piecewise function and therefore the number of switching in GTS output. Afterward, a feedback linearization controller is designed for the introduced model, and its stability and tracking of the reference trajectory are investigated. Simulation results indicate the designed controller on the proposed model has a good performance compared to the other models and complete tracking is realized without any steady-state error. Furthermore, due to the structure of the proposed model, position tracking is performed at the lowest time and by the minimum switching number.

References:

 

[1] Kikuuwe, R. (2023). Dynamics modeling of gear transmissions with asymmetric load-dependent friction. Mechanism and Machine Theory, 179, 105116.

[2] Jiang, S., Li, W., Xin, G., Sheng, L., & Wang, Y. (2022). Study on dynamic reliability of permanent magnet gear transmission system with wear and failure correlation. Engineering Failure Analysis, 131, 105802.

[3] Ozawa, R., Mishima, Y., & Hirano, Y. (2016). Design of a transmission with gear trains for underactuated mechanisms. IEEE Transactions on Robotics, 32(6), 1399-1407.

[4] Fernandez-del-Rincon, A., Garcia, P., Diez-Ibarbia, A., De-Juan, A., Iglesias, M., & Viadero, F. (2017). Enhanced model of gear transmission dynamics for condition monitoring applications: Effects of torque, friction and bearing clearance. Mechanical Systems and Signal Processing, 85, 445-467.

[5] Yang, H., Shi, W., Chen, Z., & Guo, N. (2022). An improved analytical method for mesh stiffness calculation of helical gear pair considering time-varying backlash. Mechanical Systems and Signal Processing, 170, 108882.

[6] Margielewicz, J., Gąska, D., & Litak, G. (2019). Modelling of the gear backlash. Nonlinear Dynamics, 97(1), 355-368.

[7] Wang, W., Xie, B., Zuo, Z., & Fan, H. (2018). Adaptive backstepping control of uncertain gear transmission servosystems with asymmetric dead-zone nonlinearity. IEEE Transactions on Industrial Electronics, 66(5), 3752-3762.

[8] Márton, L., & Lantos, B. (2009). Control of mechanical systems with Stribeck friction and backlash. Systems & Control Letters, 58(2), 141-147.

[9] Zuo, Z., Li, X., & Shi, Z., (2015). L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity. ISA Transactions, 58, 67-75.

[10] Shi, Z., Zuo, Z., & Liu, H. (2017). Backstepping control for gear transmission servo systems with unknown partially nonsymmetric deadzone nonlinearity. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(14), 2580-2589.

[11] Shi, Z., & Zuo, Z. (2014). Backstepping control for gear transmission servo systems with backlash nonlinearity. IEEE Transactions on Automation Science and Engineering, 12(2), 752-757.

[12] Zuo, Z., Ju, X., & Ding, Z. (2016). Control of gear transmission servo systems with asymmetric deadzone nonlinearity. IEEE Transactions on Control Systems Technology, 24(4), 1472-1479.

[13] Zhao, W., Ren, X., & Gao, X. (2016). Synchronization and tracking control for multi‐motor driving servo systems with backlash and friction. International Journal of Robust and Nonlinear Control, 26(13), 2745-2766.

[14] Huang, S., Liang, W., & Tan, K. K. (2019). Intelligent friction compensation: A review. IEEE/ASME Transactions on Mechatronics, 24(4), 1763-1774.

[15] Azar, A. T., & Serrano, F. E. (2017). Stabilization of mechanical systems with backlash by PI loop shaping. In Artificial Intelligence: Concepts, Methodologies, Tools, and Applications (pp. 2333-2360). IGI Global.

[16] Montague, R., & Bingham, C. (2013). Nonlinear control of magnetically-geared drive-trains. International Journal of Automation and Computing, 10(4), 319-326.

[17] Tarbouriech, S., Prieur, C., & Queinnec, I. (2010). Stability analysis for linear systems with input backlash through sufficient LMI conditions. Automatica, 46(11), 1911-1915.

[18] Vörös, J. (2010). Modeling and identification of systems with backlash. Automatica, 46(2), 369-374.

[19] Su, C. Y., Stepanenko, Y., Svoboda, J., & Leung, T. P. (2000). Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE transactions on automatic control, 45(12), 2427-2432.

[20] Zou, X., Luo, J., & Cao, C. (2014). Adaptive control for uncertain hysteretic systems. Journal of Dynamic Systems, Measurement, and Control, 136(1).

[21] dos Santos Coelho, L., & Cunha, M. A. B. (2011). Adaptive cascade control of a hydraulic actuator with an adaptive dead-zone compensation and optimization based on evolutionary algorithms. Expert Systems with Applications, 38(10), 12262-12269.

[22] Khan, M. B., Malik, F. M., & Munawar, K. (2010, December). Switched hybrid speed control of elastic systems with backlash. In 2010 IEEE International Conference on Industrial Engineering and Engineering Management (pp. 1641-1644). IEEE.

[23] Rostalski, P., Besselmann, T., Barić, M., Belzen, F. V., & Morari, M. (2007). A hybrid approach to modelling, control and state estimation of mechanical systems with backlash. International Journal of Control, 80(11), 1729-1740.

[24] Corradini, M. L., Manni, A., & Parlangeli, G. (2007, December). Variable structure control of nonlinear uncertain sandwich systems with nonsmooth nonlinearities. In 2007 46th IEEE Conference on Decision and Control (pp. 2023-2028). IEEE.

[25] Jacobson, B. (2003). The Stribeck memorial lecture. Tribology International, 36(11), 781-789.

[26] Khodadadi, H., Motlagh, M. R. J., & Gorji, M. (2011, June). Robust control and modeling a 2-DOF inertial stabilized platform. In International Conference on Electrical, Control and Computer Engineering 2011 (InECCE) (pp. 223-228). IEEE.

[27] Arab Zade, M., & Khodadadi, H. (2019). Fuzzy controller design for breast cancer treatment based on fractal dimension using breast thermograms. IET systems biology, 13(1), 1-7.

[28] Geibollahi, M., & Moshayedi, A. J. (2018). Dynamic Modeling, Assembly and implementing Quadrotor UAV Using PID Controller. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 11(1), 15-22.

[29] Khodadadi, H., Khaki-Sedigh, A., Ataei, M., & Jahed-Motlagh, M. R. (2018). Applying a modified version of Lyapunov exponent for cancer diagnosis in biomedical images: the case of breast mammograms. Multidimensional Systems and Signal Processing, 29(1), 19-33.

 

[30] Moshayedi, A. J., Roy, A. S., & Liao, L. (2019). PID Tuning Method on AGV (automated guided vehicle) Industrial Robot. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 12(4), 53-66.

[31] Zeini, M., & Pirmoradian, M. (2021). Design and construction of a unicycle robot controlled by its center of gravity. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 13(2), 59-73.

[32] Heidarpoor, S., Tabatabaei, M., & Khodadadi, H. (2017, June). Speed control of a DC motor using a fractional order sliding mode controller. In 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe) (pp. 1-4). IEEE.