Design of Smooth Second Order Sliding Mode Controller for Motion Control of Machine Tools

Lim, Yit Yuan (2023) Design of Smooth Second Order Sliding Mode Controller for Motion Control of Machine Tools. Final Year Project (Bachelor), Tunku Abdul Rahman University of Management and Technology.

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Abstract

The need for machinery with greater accuracy and precision is increasing as more industrial products and processes are automated. In order to improve the performance of a motor drive system in that respect, the controller is essential. Although classical controllers such as the proportional, integral, derivative (PID) controller and cascade controller remain useful, they have struggled to keep up with the performance demands of modern manufacturing. The sliding mode controller is one of the advanced control methods which are popular among researchers for its excellent robustness and disturbance rejecting capabilities. However, its inherent chattering phenomenon is a major drawback that renders it impractical for real-world applications. In this project, a smooth second order sliding mode controller (SOSMC) that reduces the chattering effect is designed by comparing and analysing the performance characteristics of different smoothening functions used to replace the signum function in the control law of SMC. From the literature, many methods to suppress chattering have been found, such as equivalent-control-dependent gain, state-dependent gain, boundary layer control, observer-based method, low-pass filter, and smoothening function. The method that is used in this project is the smoothening function method, which is to replace the discontinuous signum function with a smooth “S”-shaped curve so that the controller produces a smooth continuous control signal rather than a discontinuous one. The project began with system identification of the single axis positioning system, followed by the design of controller and stability test using Lyapunov stability theorem. After that, the signum function in the control law is replaced with the smooth continuous functions found in literature. The performance characteristics of the designed controller in terms of tracking error and chattering amplitude is analysed and compared using root mean square error (RMSE) and fast Fourier transform (FFT). It is found that the smoothening function that produces the best results with Super-twisting sliding mode controller (ST-SMC) is the Langevin function which is able to greatly reduce the chattering phenomenon in both high and low frequencies by more than 99% as well as minimize the tracking error by 64% compared to the original ST-SMC. The steepness of the curve used in the switching function is found to correlate with the chattering behaviour of the controller. Future research directions include implementing the proposed smoothening function on a 2 or 3-axis positioning system, testing its effectiveness in real-world scenarios, exploring alternative smoothening functions, applying the function to advanced sliding mode control, and conducting an in-depth analysis of the relationship between the steepness of the “S”-shaped curve and controller performance.