Design of Second Order Sliding Mode Controller Using Smoothening Method for Machine Tools

Low, Kah Seng (2020) Design of Second Order Sliding Mode Controller Using Smoothening Method for Machine Tools. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

Demand for the requirements of industrial machine tools for high-performance drive control systems, the classic controller gradually eliminated due to the inability to meet the requirements of good tracking performance and high disturbance rejection for the system, but the super twisting sliding mode controller (ST-SMC) as a nonlinear control method can effectively improve the high accuracy and precision requirements of the machine tool and become an attractive and potential controller. However, the chattering phenomenon still exists caused by high-frequency oscillation from the signum function of the control laws mathematical formula, although the ST-SMC has demonstrated the effectiveness of high tracking performance. In this thesis, in order to enhance and optimize the ST-SMC method for reducing chattering to achieve the high accuracy of tracking performance, proposed the smoothing function substitution of the control law. In ST-SMC, the gain parameters L, W, and Lambda are optimized and adjusted, and the optimal values were 2x10-5, 0.05, and 800, respectively. According to the modification of the original ST-SMC control law, four different smoothing controllers are replaced the signum function and formulated namely: arctangent ST-SMC (ARC-ST-SMC), gompertz ST-SMC (GOM-ST-SMC), hyperbolic tangent ST-SMC (HT-ST-SMC), and algebraic ST-SMC (ALG-ST-SMC). The different variant types of ST-SMC were analysed the control performance and compared the result based on the root mean square of tracking error (RMSE), maximum tracking error and chattering amplitude. The HT-ST-SMC produced the overall control performance with 92.17% (chattering suppression), 0.54% (maximum tracking error) and 0.24% (RMSE) compared to the other variants of ST-SMC-based controller. ARC-ST-SMC produced degradation percentage of -0.54% and -1.13% of the maximum tracking error, as well as the RMSE value of the tracking error. However, compared to the original ST-SMC, chattering suppression produced a percentage improvement of 19.15% which was the worst performance among all the variant types of ST-SMC. GOM-ST-SMC and ALG-ST-SMC produced the percentage improvement of chattering suppression with 90.7% and 87.4% respectively. When compared the maximum tracking error and RMSE values of tracking error between ALG-ST-SMC with GOM-ST-SMC, ALG-ST-SMC produced the percentage improvement higher than GOM-ST-SMC by 0.14% and 0.03 %. There was a trade-off between tracking performance and chattering suppression, but HT-ST-SMC achieved the best performance. Finally, this thesis has demonstrated the hyperbolic tangent function replaced the signum function in the control laws of ST-SMC produced the best control performance in maximum tracking error, RMSE value of tracking error and chattering suppression.