Fractional order PI λ D μ controller design for satisfying time and frequency domain specifications simultaneously

Zheng, Weijia; Luo, Ying; Wang, Xiaohong; Pi, Yiming; Chen, YangQuan

doi:10.1016/j.isatra.2017.02.016

Cited by 57 publications

(27 citation statements)

References 26 publications

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“…Fractional‐order PID control attracts an increasing amount of interest from the control domain, which is based on the use of a fractional integrator of order μ and a fractional differentiator of order λ , instead of the classical integer order integrator and differentiator. Previous studies have proved that such generalization can realize an improved shaping of the closed‐loop system dynamical responses thanks to the introduction of the 2 supplementary tuning parameters.…”

Section: Adaptive Fractional‐order Pid Control Designmentioning

confidence: 99%

“…The proposed AFOPID control is applied on PMSG for MPPT, while the PMSG‐based WECS parameters are tabulated in Table . The control performance of AFOPID control is evaluated and compared to that of conventional PID control, FOPID control, and FLC, respectively. Here, to achieve a fair comparison, the parameters of these 4 controllers are all optimally tuned by PSO.…”

Section: Case Studiesmentioning

confidence: 99%

“…In addition, a fuzzy FOPI+I controller was reported in Beddar et al which offers effective control performance for MPPT and grid unity power factor. Besides, work designed an FOPID controller based on analytical calculation and differential evolution algorithm for a permanent magnetic synchronous motor (PMSM) servo system. Nevertheless, the control performance of FOPID still degrades under varied operation conditions because of the inherent flaws of linear control framework.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Yang

Shu

et al. 2018

Int Trans Electr Energ Syst

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Summary This paper designs a novel adaptive fractional‐order PID (AFOPID) control of a permanent magnetic synchronous generator (PMSG)‐based wind energy conversion system, which attempts to extract the maximum wind power by using a linear perturbation observer. The combinatorial effect of generator nonlinearities and parameter uncertainties, unmodelled dynamics, and stochastic wind speed variation is aggregated into a perturbation, which is then estimated in real time by a linear extended‐state observer called high‐gain state and perturbation observer. Besides, the perturbation estimate is used as an auxiliary control signal which is fully compensated by a fractional‐order PID (FOPID) controller to achieve a globally robust control consistency, simple structure and high reliability, as well as an improved tracking performance compared to that of PID control. In addition, AFOPID does not require an accurate PMSG model while only the measurement of d‐axis current and mechanical rotation speed is required, in which parameter is optimally tuned by particle swarm optimization. Four case studies are carried out, including step change of wind speed, low‐turbulence stochastic wind speed, high‐turbulence stochastic wind speed, and generator parameter uncertainties, respectively. Simulation results verify the effectiveness and superiority of AFOPID compared to that of PID, FOPID, and nonlinear control.

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Section: Adaptive Fractional‐order Pid Control Designmentioning

confidence: 99%

Section: Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Yang

Shu

et al. 2018

Int Trans Electr Energ Syst

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“…Example Consider the following fractional‐order model of permanent magnet synchronous motor (PMSM) system, which is used in the work of Zheng et al

G ((), s) = \frac{47979.2573}{s^{2.9544} + 127.38 s^{2.0463} + 9995.678 s^{1.0463}} e^{- 0.2 s} .

The objective is to get the stabilizing region of the PD μ controller for the PMSM system.…”

Section: Simulation Examplesmentioning

confidence: 99%

General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

Yang

Liu

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, an effective method is proposed to get the stabilizing regions of fractional‐order PIλDμ controllers for an arbitrarily given fractional‐order system with time delay. For each known proportional gain (kp), integral gain (ki), or derivative gain (kd) in the PIλDμ controllers, the stabilizing region with respect to the other two control gains is derived respectively. The boundaries of the stabilizing regions are firstly obtained based on singular frequencies. Then, the main results are presented to directly determine the stabilizing region from an analytical viewpoint. The results avoid the time‐consuming stability test since the stabilizing region is usually determined by manually choosing lots of test points from all the divided regions by the resultant boundaries. Besides, the stabilizing (ki, kd) regions of the PIλDμ controllers for λ + μ = 2 can be determined and the linear programming characteristic of the stabilizing (ki, kd) region for the case λ + μ = 2 is obtained. Furthermore, the robust stabilizing region is analyzed. The results in this paper provide the basis for both the tuning of the PIλDμ controller in practice and the design of the PIλDμ controller satisfying different performance criteria. Numerical examples and an application example are presented to check the validity of the proposed method.

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“…However, the magnitude and phase margin may be reduced by inserting the IOF into the control system, which means that the system tends to be unstable. In recent years, the Fractional-Order Filter (FOF) has been increasingly used in dynamic systems [ 22 , 23 , 24 ], which provides greater flexibility to optimize both the magnitude and phase responses in comparison with the IOF [ 25 ]. Though the analysis of the mutual restriction between vibration and deformation transmissibility, a novel piecewise frequency control (PFC) system based on FOFs is presented in this paper to effectively weaken the contradiction between the AVI and positioning of the supporting system.…”

Section: Introductionmentioning

confidence: 99%

A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System

Tao

Jiang

Han

et al. 2020

Sensors

Self Cite

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A piecewise frequency control (PFC) strategy is proposed in this paper for coordinating vibration isolation and positioning of supporting systems under complex disturbance conditions, such as direct and external disturbances. This control strategy is applied in an active-passive parallel supporting system, where relative positioning feedback for positioning and absolute velocity feedback for active vibration isolation. The analysis of vibration and deformation transmissibility shows that vibration control increases low-frequency position error while positioning control amplifies high-frequency vibration amplitude. To overcome this contradiction across the whole control bandwidth, a pair of Fractional-Order Filters (FOFs) is adopted in the PFC system, which increases the flexibility in the PFC design by introducing fraction orders. The system stability analysis indicates that the FOFs can provide a better stability margin than the Integral-Order Filters (IOFs), so the control gains are increased to get a better performance on the AVI and positioning. The PFC based on FOFs can suppress the peak amplitude at the natural frequency which cannot be avoided when using the IOFs. The constrained nonlinear multivariable function is formed by the required performance and the stability of the system, then the controller parameters are optimized effectively. Lastly, the effectiveness of the proposed method is verified by experiments.

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Fractional order PI λ D μ controller design for satisfying time and frequency domain specifications simultaneously

Cited by 57 publications

References 26 publications

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System

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Fractional order PI λ D μ controller design for satisfying time and frequency domain specifications simultaneously

Cited by 57 publications

References 26 publications

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers

General stabilization method of fractional‐order PIλDμ controllers for fractional‐order systems with time delay

A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System

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General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay