Abstract
Model predictive control (MPC) is widely used in fast sampling systems owing to its fast regulating ability. However, the sampling delay is a key issue and tends to be a fractional multiple of the sampling period. If the fractional-order delay is not accurately offset, the controller output will exhibit errors, thus resulting in oscillations in controlled system. Moreover, the MPC delay compensation algorithm is limited to the computation time. To address the problems of fractional delay and computational burden in fast sampling systems, we propose a new method to compensate for the fractional-order sampling delay. First, we use a finite-impulse-response fractional delay filter based on a Lagrange interpolation polynomial to approximate the fractional portion. Moreover, we prove that high accuracy and simplicity can be ensured when the polynomial order is one. Then, we estimate the current state variable using the delayed sampling signal and control signals of past moments. Further, we obtain the current control signal according to the estimated state variable. By considering the simultaneous existence of computational and sampling delays, a full compensation strategy is proposed. Computational simulation results validate the proposed MPC algorithm with fractional-order delay compensation and demonstrate its advantages.
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Mayne D Q, Rawlings J B, Rao C V, et al. Constrained model predictive control: stability and optimality. Automatica, 2000, 36: 789–814
Mayne D Q. Model predictive control: recent developments and future promise. Automatica, 2014, 50: 2967–2986
Yoon S Y, Lin Z L. Predictor based control of linear systems with state, input and output delays. Automatica, 2015, 53: 385–391
Teng L, Wang Y Y, Cai W J, et al. Efficient robust fuzzy model predictive control of discrete nonlinear time-delay systems via Razumikhin approach. IEEE Trans Fuzzy Syst, 2019, 27: 262–272
Martins M A F, Yamashita A S, Santoro B F, et al. Robust model predictive control of integrating time delay processes. J Process Control, 2013, 23: 917–932
Bhaskaran A, Rao A S. Predictive control of unstable time delay series cascade processes with measurement noise. ISA Trans, 2020, 99: 403–416
Jeong S C, Park P. Constrained MPC algorithm for uncertain time-varying systems with state-delay. IEEE Trans Autom Control, 2005, 50: 257–263
Liu J F, de la Peña D M, Christofides P D. Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements. Automatica, 2010, 46: 52–61
Liu J F, Chen X Z, de la Peña D M, et al. Iterative distributed model predictive control of nonlinear systems: handling asynchronous, delayed measurements. IEEE Trans Autom Control, 2012, 57: 528–534
Teng L, Wang Y Y, Cai W J, et al. Fuzzy model predictive control of discrete-time systems with time-varying delay and disturbances. IEEE Trans Fuzzy Syst, 2018, 26: 1192–1206
Liu Z, Xie L, Bemporad A, et al. Fast linear parameter varying model predictive control of buck DC-DC converters based on FPGA. IEEE Access, 2018, 6: 52434–52446
Falkowski P, Sikorski A. Finite control set model predictive control for grid-connected AC-DC converters with LCL filter. IEEE Trans Ind Electron, 2018, 65: 2844–2852
Guzman R, de Vicuna L G, Camacho A, et al. Receding-horizon model-predictive control for a three-phase VSI with an LCL filter. IEEE Trans Ind Electron, 2019, 66: 6671–6680
Cortes P, Rodriguez J, Silva C, et al. Delay compensation in model predictive current control of a three-phase inverter. IEEE Trans Ind Electron, 2012, 59: 1323–1325
Vafamand N, Khooban M H, Dragicevic T, et al. Networked fuzzy predictive control of power buffers for dynamic stabilization of DC microgrids. IEEE Trans Ind Electron, 2019, 66: 1356–1362
Zhang L Y, Zhou Z, Chen Q H, et al. Model predictive control for electrochemical impedance spectroscopy measurement of fuel cells based on neural network optimization. IEEE Trans Transp Electrific, 2019, 5: 524–534
Lee W R, Caccetta L, Rehbock V. Optimal design of all-pass variable fractional-delay digital filters. IEEE Trans Circ Syst I, 2008, 55: 1248–1256
Kwan H K, Jiang A. FIR, allpass, and IIR variable fractional delay digital filter design. IEEE Trans Circ Syst I, 2009, 56: 2064–2074
Dam H H. Design of variable fractional delay filter with fractional delay constraints. IEEE Signal Process Lett, 2014, 21: 1361–1364
Zou Z X, Zhou K L, Wang Z, et al. Frequency-adaptive fractional-order repetitive control of shunt active power filters. IEEE Trans Ind Electron, 2015, 62: 1659–1668
Bagheri P, Khaki-Sedigh A. Closed form tuning equations for model predictive control of first-order plus fractional dead time models. Int J Control Autom Syst, 2015, 13: 73–80
Laakso T I, Valimaki V, Karjalainen M, et al. Splitting the unit delay [FIR/all pass filters design]. IEEE Signal Process Mag, 1996, 13: 30–60
Zhou Z, Zhang L Y, Liu Z T, et al. Model predictive control for the receiving-side DC-DC converter of dynamic wireless power transfer. IEEE Trans Power Electron, 2020, 35: 8985–8997
Zhou Z, Zhang L Y, Liu Z T, et al. Design and demonstration of a dynamic wireless power transfer system for electric vehicles. Sci China Inf Sci, 2019, 62: 224201
Beccuti A G, Mariethoz S, Cliquennois S, et al. Explicit model predictive control of DC-DC switched-mode power supplies with extended kalman filtering. IEEE Trans Ind Electron, 2009, 56: 1864–1874
Acknowledgements
This work was partially supported by National Key R&D 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 R&D Program (Grant No. 2021C01198), and Ningbo Science and Technology Innovation 2025 Major Project (Grant No. 2019B10116).
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Zhou, Z., Liu, Z., Su, H. et al. Model predictive control with fractional-order delay compensation for fast sampling systems. Sci. China Inf. Sci. 64, 172211 (2021). https://doi.org/10.1007/s11432-020-3096-0
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DOI: https://doi.org/10.1007/s11432-020-3096-0