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Trajectory tracking control based on fractional calculus of a new linear motor is presented and experiments are verified in this paper. Design details and principle analyses of the new motor are exhibited. Fractional calculus is used to improve the tracking performance, and the motion controller is composed of a fractional-order proportional-derivative controller, a first-order and a second-order extended state observer. The proposed method is compared with an active disturbance rejection controller, and simulations and experiments are performed to verify the effectiveness. Good trajectory tracking performance of the new linear motor has been realized in spite of parameter variations and external disturbances. more...

The numerical implementation of fractional calculus is an important factor in applying the fractional calculus theory to engineering application. In most existing research, the order in model or controller is constant, so it is relative easy to implement the fractional calculus because its coefficients are constant values. But in many application fields the order is variable, which bring difficulty to achieve the real-time implementation of fractional calculus. In this paper, based on the impulse response invariant discretization(IRID) and polynomial fitting, a fast numerical implementation for variable order fractional calculus operator is proposed, and the simulation results illustrate the effectiveness of the proposed method. more...

Fractional calculus and its application has been widely researched, and in most case the order is considered as a constant value. In many application fields the order is variable, and the fast implementation of variable order fractional calculus is important. In this paper a fast frequency domain approximation method for variable order fractional calculus operator is presented based on polynomial fitting. Firstly, the approximated integer order transfer functions for fractional calculus operator at several discrete order with equal interval are obtained by using the oustaloup method. Secondly, the coefficients from the same position in the approximated transfer functions corresponding to different order are taken out to construct coefficients matrix, then the column vectors of the coefficient matrix are used to make the polynomial fitting. Finally, for variable order, the approximated transfer functions in frequency domain can be achieved directly and quickly through the fitting function. The simulation results show the effectiveness of the proposed method. more...