This paper presents the Takagi-Sugeno (TS) fuzzy control design for nonlinear stabilization and tracking control of a ball on plate system. To deal with the plant nonlinearity and the fuzzy convergence issue, we formulate the parallel distributed compensator (PDC) TS fuzzy model to characterize the global behaviour of the nonlinear system and synthesize a feasible control framework using a velocity compensation scheme. The nonlinear dynamics of the ball on plate system is obtained using the Euler-Lagrangian energy based approach. To identify the moving objects in the video stream, a background subtraction algorithm using thresholding technique is formulated. Moreover, the stability analysis of the TS fuzzy control is reduced to linear matrix inequality (LMI) problem and solved using the Lyapunov direct method. The potential benefits of the proposed control structure for real time test cases are experimentally assessed using hardware in loop (HIL) testing on a ball on plate system. Experimental results substantiate that the TS fuzzy scheme can significantly improve not only the tracking performance but also the robustness of the closed loop system.

中文翻译：

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Takagi-Sugeno模糊非线性控制设计应用于欠驱动视觉伺服系统

本文介绍了用于板球系统非线性稳定和跟踪控制的 Takagi-Sugeno (TS) 模糊控制设计。为了处理对象非线性和模糊收敛问题，我们制定了并行分布式补偿器 (PDC) TS 模糊模型来表征非线性系统的全局行为，并使用速度补偿方案合成一个可行的控制框架。使用基于欧拉-拉格朗日能量的方法获得板球系统的非线性动力学。为了识别视频流中的移动对象，制定了使用阈值技术的背景减法算法。此外，TS 模糊控制的稳定性分析被简化为线性矩阵不等式 (LMI) 问题并使用 Lyapunov 直接方法解决。所提议的控制结构对实时测试用例的潜在好处是使用硬件在环 (HIL) 测试对板球系统进行实验评估的。实验结果证实，TS模糊方案不仅可以显着提高跟踪性能，而且可以显着提高闭环系统的鲁棒性。