Active disturbance rejection control for nonlinear fractional‐order systems

Summary This paper investigates active disturbance rejection control involving the fractional-order tracking differentiator, the fractional-order PID controller with compensation and the fractional-order extended state observer for nonlinear fractional-order systems. Firstly, the fractional-order optimal-time control scheme is studied to propose the fractional-order tracking differentiator by the Hamilton function and fractional-order optimal conditions. Secondly, the linear fractional-order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional-order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional-order extended state observer. Thirdly, by this observed value, the nonlinear fractional-order plant is converted into a linear fractional-order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional-order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional-order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.

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