Direct Fuzzy CMAC Sliding Mode Trajectory Tracking for Biaxial Position System

High-precision trajectory control is considered as an important factor in the performance of industrial two-axis contour motion systems. This research presents an adaptive direct fuzzy cerebellar model articulation controller (CMAC) sliding mode control (DFCMACSMC) for the precise control of the industrial XY-axis motion system. The FCMAC was utilized to approximate an ideal controller, and the weights of FCMAC were on-line tuned by the derived adaptive law based on the Lyapunov criterion. With this derivation in mind, the asymptotic stability of the developed motion system could be guaranteed. The two-axis stage system was experimentally investigated using four contours, namely, circle, bowknot, heart, and star reference contours. The experimental results indicate that the proposed DFCMACSMC method achieved the improved tracking capability, and so reveal that the DFCMACSMC scheme outperformed other schemes of the model uncertainties and cross-coupling interference.

Design of Adaptive TSK Fuzzy Self-Organizing Recurrent Cerebellar Model Articulation Controller for Chaotic Systems Control

The synchronization and control of chaos have been under extensive study by researchers in recent years. In this study, an adaptive Takagi–Sugeno–Kang (TSK) fuzzy self-organizing recurrent cerebellar model articulation controller (ATFSORC) is proposed, which is composed of a set of TSK fuzzy rules, a cerebellar model articulation controller (CMAC), a recurrent CMAC (RCMAC), a self-organizing CMAC (SOCMAC), and a compensation controller. Specifically, SOCMAC, RCMAC, and adaptive laws are adopted so that the association memory layers of ATFSORC can be modulated in accordance with the layer decision-making mechanism in order to reduce the structure complexity and improve the control performance of ATFSORC. Moreover, the Takagi–Sugeno–Kang fuzzy rules are introduced to increase the learning speed of ATFSORC, and the improved compensating controller is designed to dispel the errors between an ideal controller and the TFSORC. Moreover, the proposed ATFSORC is applied to chaotic systems in order to validate its performance and feasibility. Several simulation schemes are demonstrated to show the effectiveness of the proposed method. Simulation results show that the proposed ATFSORC can obtain a favorable control performance when the chaotic systems are operated at different parameters. Specifically, ATFSORC can achieve faster convergence of the tracking error than fuzzy CMAC (FCMAC) and CMAC.

Method to Expand the CMAC Model to Composite-Type Model

Neural networks (NNs) are effective for the learning of nonlinear systems, and thus they achieve satisfactory results in various fields. However, they require significant amount of training data and learning time. Notably, the cerebellar model articulation controller (CMAC), which is modeled after the cerebellar neural transmission system, proposed by Albus can effectively reduce learning time, compared with NNs. The CMAC model is often used to learn nonlinear systems that have continuously changing outputs, i.e., regression problems. However, the structure of the CMAC model must be expanded to apply it to classification problems as well. Additionally, the CMAC model finds it difficult to simultaneously classify categories and estimate their proportional linear measure because designated learning algorithms are required for both regression and classification problems. Therefore, we aim to build a composite-type CMAC model that combines classification and regression algorithms to simultaneously classify categories and estimate their proportional linear measures.

Fuzzy cerebellar model articulation controller-based adaptive tracking control for load-carrying exoskeleton

Load-carrying exoskeletons need to cope with load variations, outside disturbances, and other uncertainties. This paper proposes an adaptive trajectory tracking control scheme for the load-carrying exoskeleton. The method is mainly composed of a computed torque controller and a fuzzy cerebellar model articulation controller. The fuzzy cerebellar model articulation controller is used to approximate model inaccuracies and load variations, and the computed torque controller deals with tracking errors. Simulations of an exoskeleton in squatting movements with model parameter changes and load variations are carried out, respectively. The results show a precise tracking response and high uncertainties toleration of the proposed method.