|عنوان فارسی مقاله:||کنترل دفع اختلال فعال جز به جز|
|عنوان انگلیسی مقاله:||Fractional active disturbance rejection control|
|رشته های مرتبط:||ریاضی، ریاضی کاربردی، تحقیق در عملیات و آنالیز عددی|
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|نشریه||الزویر – Elsevier|
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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.
Fractional calculus is the generalization of ordinary integer order calculus. Systems described by fractional order calculus are known as fractional order systems (FOS). Fractional calculus provides a preferable method to describe complicated natural objects and dynamical processes such as electrical noises, chaotic system, and organic dielectric materials [1–6]. As a consequence, scientists show more and more interests in identification of FOS [7,8]. Commensurate linear FOS is a special kind of FOS, with a simple model and proportional orders [9,10]. Controllers with fractional order operator are naturally suitable for the FOS [11,12]. There are mainly four kinds of fractional order controllers, which are CRONE (Contrôle Robuste d’Order Non Entier) controller, TID (Tilt Integral Derivative) controller, fractional order PID controller, and fractional order lead-lag compensator [13–19]. Considering the industrial universal controller design requirements, such as compact structure, repeatability, model independence, easy parameter turning and strong robustness, active disturbance rejection control (ADRC) provides an alternative paradigm for FOS control [20–22]. The central objective of ADRC is to treat the internal and external uncertainties as the total disturbance and to reject them actively. Compact frame, effortless turning and sufficiently good performance make ADRC popular in the world of industrial control [23–25]. ADRC was firstly used to control FOS in , where fractional order is regarded as a part of the total disturbances, and an extended state observer (ESO) is used to estimate and reject it. Because the known or available model information is neglected and underused, it would require higher observer bandwidth for accurate state estimation. In this paper, a distinct fractional active disturbance rejection control (FADRC) is proposed as a generalized and enhanced ADRC solution for the FOS. ESO is redesigned as a fractional one according to the highest fractional order of FOS. The modified fractional extended states observer (FESO) not only accurately estimates the total disturbance but also the fractional order dynamic states, leading to a reduced observer bandwidth. In addition, a fractional order PD controller is used to replace the tracking differentiator and the nonlinear state error feedback. Although FADRC is designed for commensurate linear FOS originally, the robustness analyses demonstrate that FADRC is also appropriate for incommensurate linear FOS. Simulation results show that FADRC has more inherent superiority and potential for FOS control. Due to the difficulty brought by the nonlinearity and uncertainty, theoretical studies of ADRC are still lagging behind its industrial applications. Recent research focuses on time domain convergence, frequency response and describing function in analyzing nonlinearity [27–29]. Stability analysis has been substantially studied for FOS in . An extended root locus method by Patil  provides a simple way to construct root locus of general FOS and is employed for FADRC analysis and design. The FOS is translated into its integer order counterpart and then analysis method of general integer system can be directly adopted. The rest of this paper is organized as follows. In Section 2, an introduction of commensurate linear FOS and fractional order state observer with full-dimensionality are presented. In Section 3, the framework of FESO and FADRC and the corresponding algorithm are introduced. Section 4 presents the stability and frequency-domain characteristics of FADRC. Simulation results of FADRC and ADRC are then compared in Section 5. Finally, conclusions are given in Section 6.