SCIENCE CHINA Information Sciences, Volume 64 , Issue 7 : 172211(2021) https://doi.org/10.1007/s11432-020-3096-0

Model predictive control with fractional-order delay compensation for fast sampling systems

More info
  • ReceivedJun 18, 2020
  • AcceptedOct 1, 2020
  • PublishedMay 20, 2021



This work was partially supported by National Key RD Program of China (Grant No. 2018YFA0703800), Science Fund for Creative Research Group of National Natural Science Foundation of China (Grant No. 61621002), National Natural Science Foundation of China (Grant No. 61873233), Zhejiang Key RD Program (Grant No. 2021C01198), and Ningbo Science and Technology Innovation 2025 Major Project (Grant No. 2019B10116).


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  • Figure 1

    (Color online) (a) Ideal case without delay; (b) computation delay; (c) sampling delay.

  • Figure 2

    (Color online) Magnitude frequency characteristics of Lagrange-interpolation-based fractional delay filters with order $n=1$.

  • Figure 3

    Topology and parameters of the BUCK converter.

  • Figure 6

    Topology of the wireless power transfer system.

  • Figure 7

    (Color online) Comparison of the influence of the computation delay and sampling delay on the system.

  • Figure 8

    (Color online) Comparison of the sampling delay compensation algorithms under the wireless power transfer system.

  • Figure 9

    (Color online) Coexistence of computation and sampling delays. (a) Controlled variable variations; (b) control signal variations.

  • Figure 10

    (Color online) Step response of the wireless power transfer system under the coexistence of computation and sampling delays.

  • Figure 11

    (Color online) Control effect under time-varying situation of $F$. (a) Controlled variable variations; (b) control signal variations.


    Algorithm 1 Fractional-order compensation of the computation delay

    Obtain the state variables of the current moment;

    Apply the optimal control signal $u(k)$ calculated before one period to the current time;

    At the current time $k$, calculate the optimal control signal $u(k+1)$ and output it at time $k+1$.

  • Table 1  

    Table 1Parameters of wireless power transfer

    Parameter Symbol Value
    Input voltage of the inverter $u_{\rm~in}$ 200 V
    Self-inductance of the primary-side coil $L_{1}$ 178 $\mu~{\rm{H}}$
    Self-inductance of the secondary-side coil $L_{0}$ 178 $\mu~{\rm{H}}$
    Primary-side resonant inductor $L_{f1}$ 45.5 $\mu~{\rm{H}}$
    Secondary-side resonant inductor $L_{f0}$ 45.5 $\mu~{\rm{H}}$
    Primary-side resonant capacitor $C_{f1}$ 77.05 nF
    Secondary-side resonant capacitor $C_{f0}$ 77.05 nF
    Primary-side compensation capacitor $C_{1}$ 24.46 nF
    Secondary-side compensation capacitor $C_{0}$ 24.46 nF
    DC-DC input capacitor $C_{d}$ 90 $\mu~{\rm{F}}$
    DC-DC inductor $L_{d}$ 3 mH
    Battery voltage $u_{b}$ 136 V
    Sampling cycle $T_{s}$ 50 $\mu$s

    Algorithm 2 Fractional-order compensation of sampling signal delay

    Calculate $M$ and $b$ in (8);

    Estimate the current state variable $x(k|k-\tau)$ by (23);

    Obtain the optimal control law by (24).


    Algorithm 3 Fractional-order compensation of hybrid delay

    Calculate $M_1$ and $b_1$ in (12);

    Estimate the current state variable $x(k|k-\tau)$ by (23);

    Obtain the optimal control law by (25).


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