Abstract
A neural networks(NN) hysteresis compensator is proposed for dynamic systems. The NN compensator uses the back-stepping scheme for inverting the hysteresis nonlinearity in the feed-forward path. This scheme provides a general step for using NN to determine the dynamic pre-inversion of the reversible dynamic system. A tuning algorithm is proposed for the NN hysteresis compensator which yields a stable closed-loop system. Nonlinear stability proofs are provided to reveal that the tracking error is small. By increasing the gain we can reduce the stability radius to some extent. PI control without hysteresis compensation requires much higher gains to achieve similar performance. It is not easy to guarantee the stability of such highly nonlinear dynamical system if only a PI controller is used. Initializing the NN weights is simple. The initial weights of hidden layer are randomly selected and initial weights of output layer are set to zero. A PI loop with integerted an unity gain feedforward path keeps the system stable until the NN starts learning. Simulation results show its efficacy of the NN hysteresis compensator on a system. This work is applicable to xy table-like precision control system and also shows neural network stability proofs. Moreover, the NN hysteresis compensation can be further extended and applied to dead-zone, backlash, and other actuator nonlinear compensation.
Highlights
Industrial dynamical control systems have generally the structure of a nonlinear system in front of some nonlinearity in the actuator, for example, dead-zone, backlash, and hysteresis, etc
Hysteresis phenomena caused by magnetism, stiction or gear with backlash generally exist in control system [1,2,3] and often severely reduce system performance such as giving rise to oscillations and/or undesirable inaccuracy, even leading to instability
The compensator scheme has a dynamic inversion structure, and the NN of the feed-forward path approximating the hysteresis inversion error and filter dynamics required for back-stepping design
Summary
Industrial dynamical control systems have generally the structure of a nonlinear system in front of some nonlinearity in the actuator, for example, dead-zone, backlash, and hysteresis, etc. Developing an adaptive control scheme for systems with unknown hysteresis is a challenge of practical primary concern. Several rigorously guided adaptive schemes for compensation of actuator nonlinearities have been provided in detailed studies [4]. Adaptive control of plants with unknown hysteresis was developed using an adaptive inverse scheme [7]. A rigorous design procedure with validation is provided to generate a PI tracking loop using an adaptive neural network system in a feed-forward loop for hysteresis compensation. The authors derive practical limits for tracking errors through tracking error dynamics analysis, and investigate the performance of NN hysteresis compensator in the system from computer simulations
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