Interval Type-2 Fuzzy Logic Control of Linear Stages in Feedback-Error-Learning Structure Using Laser Interferometer

The output processer of interval type-2 fuzzy logic systems (IT2FLSs) is a complex operator which performs type-reduction plus defuzzification (TR+D) tasks. In this paper, a complexity-reduced yet high-performance TR+D for IT2FLSs based on Maclaurin series approximation is utilized within a feedback-error-learning (FEL) control structure for controlling linear move stages. IT2FLSs are widely used for control purposes, as they provide extra degrees of freedom to increase control accuracies. FEL benefits from a classical controller, which is responsible for providing overall system stability, as well as a guideline for the training mechanism for IT2FLSs. The Kalman filter approach is utilized to tune IT2FLS parameters in this FEL structure. The proposed control method is applied to a linear stage in real time. Using an identification process, a model of the real-time linear stage is developed. Simulation results indicate that the proposed FEL approach using the Kalman filter as an estimator is an effective approach that outperforms the gradient descent-based FEL method and the proportional derivative (PD) classical controller. Motivated by the performance of the proposed Kalman filter-based FEL approach, it is used to control a linear move stage in real time. The position feedback of the move stage is provided by a precision laser interferometer capable of performing measurements with an accuracy of less than $1\mathsf{\mu }\mathrm{m}$. Using this measurement system in a feedback loop with the proposed control algorithm, the overall steady state of the system is less than $20\mathsf{\mu }\mathrm{m}$. The results illustrate the high-precision control capability of the proposed controller in real-time.