Fractional Proportional Derivative Controller Research Articles

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Rehabilitation Exoskeleton is becoming more and more important in physiotherapists’ routine work. To improve the treatment performance, such as reducing the recovery period and/or monitoring and reacting to unpredictable situations, the rehabilitation manipulators need to help the patients in various physical trainings. A special case of the active disturbance rejection control (ADRC) is applied to govern a proper realisation of basic limb rehabilitation trainings. The experimental study is performed on a model of a flexible joint manipulator, whose behaviour resembles a real exoskeleton rehabilitation device (a one-degree-of-freedom, rigid-link, flexible-joint manipulator). The fractional (FADRC) is an unconventional model-independent approach, acknowledged as an effective controller in the existence of total plant uncertainties, and these uncertainties are inclusive of the total disturbances and unknown dynamics of the plant. In this work, three FADRC schemes are used, the first one using a fractional state observer (FSO), or FADRC1, second one using a fractional proportional-derivative controller (FPD), or FADRC2, and the third one a Multi-loop fractional in PD-loop controller and the observer-loop (Feedforward and Feedback), or FADRC3. The simulated Exoskeleton system is subjected to a noise disturbance and the FADRC3 shows the effectiveness to compensate all these effects and satisfies the desired position when compared with FADRC1 and FADRC2. The design and simulation were carried out in MATLAB/Simulink.

Improving dynamics of integer-order small-world network models under fractional-order PD control

The optimal control of dynamics is a popular topic for small-world networks. In this paper, we address the problem of improving the behavior of Hopf bifurcations in an integer-order model of small-world networks. In this study, the time delay is used as the bifurcation parameter. We add a fractional-order proportional-derivative (PD) scheme to an integer-order Newman-Watts (N-W) small-world model to better control the Hopf bifurcation of the model. The most important contribution of this paper involves obtaining the stability of the system and the variation of the conditions of the Hopf bifurcation after a fractional PD controller is added to the integer-order small-world model. The results demonstrate that the designed PD controller can be used to restrain or promote the occurrence of Hopf bifurcations by setting appropriate parameters. We also describe several simulations to verify our research results.

Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ωo and controller bandwidth ωc on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.