The mechanical motion rectifier (MMR) is a pivotal mechanical transmission device that can convert bidirectional motion into unidirectional motion. Incorporating the MMR into a rotary generator significantly enhances the energy recovery efficiency of a vibration energy-harvesting system. This study develops an energy-harvesting system featuring an MMR in a permanent magnet synchronous motor (PMSM) electromagnetic damper, leveraging electromagnetic conduction to recover vibration energy. Utilizing the electromechanical analogy principle, an equivalent circuit model for the energy-harvesting system is developed, and a direct control method for the electromagnetic torque of the PMSM is proposed to achieve maximum power point tracking control. Considering the motion of MMR constitutes a state-dependent switching system, a “time-scale transformation” method is designed to reconfigure the switching system with uncertain timings into one with fixed equivalent switching moments. In addition, an iterative optimization controller is proposed to ensure that the system operates at its maximum power point. Hardware-in-the-loop experiments are conducted to validate the effectiveness of the proposed iterative optimal control-based maximum power point tracking scheme.
AbolhasaniAPakdelianS (2020) Comparison of control strategies and electromechanical devices for the backpack energy harvesting system. IEEE Transactions on Industry Applications56: 6420–6435.
2.
AliAQiLFZhangTS, et al. (2021) Design of novel energy-harvesting regenerative shock absorber using barrel cam follower mechanism to power the auxiliaries of a driverless electric bus. Sustainable Energy Technologies and Assessments48: 16.
3.
BruzzoneLFanghellaPBerselliG (2020) Reinforcement learning control of an onshore oscillating arm wave energy converter. Ocean Engineering206: 107346.
4.
CaiMJLiaoWHCaoJY (2019) A smart harvester for capturing energy from human ankle dorsiflexion with reduced user effort. Smart Materials and Structures28(1): 10.
5.
CaiQLZhuSY (2020) Unified strategy for overall impedance optimization in vibration-based electromagnetic energy harvesters. International Journal of Mechanical Sciences165: 15.
6.
CaiQLZhuSY (2022) The nexus between vibration-based energy harvesting and structural vibration control: A comprehensive review. Renewable & Sustainable Energy Reviews155: 24.
7.
ChenCALiXFZuoL, et al. (2021) Circuit modeling of the mechanical-motion rectifier for electrical simulation of ocean wave power takeoff. IEEE Transactions on Industrial Electronics68(4): 3262–3272.
8.
ChenYBraunDJ (2019) Hardware-in-the-loop iterative optimal feedback control without model-based future prediction. IEEE Transactions on Robotics35: 1419–1434.
9.
ChenYQLiYZBraunDJ (2023) Data-driven Iterative optimal control for switched dynamical systems. IEEE Robotics and Automation Letters8(1): 296–303.
10.
CostanzoLLinTLinWH, et al. (2021) Power electronic interface with an adaptive MPPT technique for train suspension energy harvesters. IEEE Transactions on Industrial Electronics68(9): 8219–8230.
11.
CostanzoLLiuMLo SchiavoA, et al. (2022a) Backpack energy harvesting system with maximum power point tracking capability. IEEE Transactions on Industrial Electronics69: 506–516.
12.
CostanzoLLiuMLo SchiavoA, et al. (2022b) Voltage adaptation or resistance matching in backpack regenerative systems? In: 2022 IEEE 21st Mediterranean Electrotechnical Conference (MELECON), Palermo, Italy, 14–16 June 2022, pp.780–784. New York: Institute of Electrical and Electronics Engineers.
13.
DonelanJMLiQNaingV, et al. (2008) Biomechanical energy harvesting: Generating electricity during walking with minimal user effort. Science319(5864): 807–810.
14.
DongLWHuGBYuJ, et al. (2023) Maximizing onboard power generation of large-scale railway vibration energy harvesters with intricate vehicle-harvester-circuit coupling relationships. Applied Energy347: 20.
15.
FanKQXiaPWLiRC, et al. (2022) An innovative energy harvesting backpack strategy through a flexible mechanical motion rectifier. Energy Conversion and Management264: 13.
16.
GelosEMJudewiczMGCisilinoAP, et al. (2024) Generalized model of mechanical motion rectifiers. Mechanism and Machine Theory199: 105678.
17.
HaoDKongLZhangZ, et al. (2023) An electromagnetic energy harvester with a half-wave rectification mechanism for military personnel. Sustainable Energy Technologies and Assessments57: 103184.
18.
JiangBXLiXFChenS, et al. (2020) Performance analysis and tank test validation of a hybrid ocean wave-current energy converter with a single power takeoff. Energy Conversion and Management224: 14.
19.
LiWTodorovE (2007) Iterative linearization methods for approximately optimal control and estimation of non-linear stochastic system. International Journal of Control80: 1439–1453.
20.
LiXFChenCAChenS, et al. (2022) Dynamic characterization and performance evaluation of a 10-kW power take-off with mechanical motion rectifier for wave energy conversion. Ocean Engineering250: 10.
21.
LiXFChenCALiQF, et al. (2020) A compact mechanical power take-o ff for wave energy converters: Design, analysis, and test verification. Applied Energy278: 12.
22.
LiXFLiangCWChenCA, et al. (2020) Optimum power analysis of a self-reactive wave energy point absorber with mechanically-driven power take-offs. Energy195: 13.
23.
LinTPanYChenSK, et al. (2018) Modeling and field testing of an electromagnetic energy harvester for rail tracks with anchorless mounting. Applied Energy213: 219–226.
24.
LiuMYTaiWCZuoL (2018) Toward broadband vibration energy harvesting via mechanical motion-rectification induced inertia nonlinearity. Smart Materials and Structures27(7): 14.
25.
López-MartínezJGarcía-VallejoDAlcaydeA, et al. (2023) A comprehensive methodology to obtain electrical analogues of linear mechanical systems. Mechanical Systems and Signal Processing200: 110511.
26.
MiJLiQFLiuMY, et al. (2020) Design, modelling, and testing of a vibration energy harvester using a novel half-wave mechanical rectification. Applied Energy279: 13.
27.
MostafaviAZakerzadehMRSadighiA, et al. (2022) An efficient design of an energy harvesting backpack for remote applications. Sustainable Energy Technologies and Assessments52: 102173.
28.
NasiriMMilimonfaredJFathiSH (2014) Modeling, analysis and comparison of TSR and OTC methods for MPPT and power smoothing in permanent magnet synchronous generator-based wind turbines. Energy Conversion and Management86: 892–900.
29.
NocedalJWrightS (2006) Numerical Optimization. Berlin: Springer Science & Business Media.
30.
PanYZuoLAhmadianM (2022) A half-wave electromagnetic energy-harvesting tie towards safe and intelligent rail transportation. Applied Energy313: 13.
31.
QiLFSongJHWangY, et al. (2024) Mechanical motion rectification-based electromagnetic vibration energy harvesting technology: A review. Energy289: 23.
32.
RamJPBabuTSRajasekarN (2017) A comprehensive review on solar PV maximum power point tracking techniques. Renewable and Sustainable Energy Reviews67: 826–847.
33.
SalmanWQiLFZhuX, et al. (2018) A high-efficiency energy regenerative shock absorber using helical gears for powering low-wattage electrical device of electric vehicles. Energy159: 361–372.
34.
SalmanWZhangXTLiH, et al. (2022) A novel energy regenerative shock absorber for in-wheel motors in electric vehicles. Mechanical Systems and Signal Processing181: 18.
35.
SmithMC (2002) Synthesis of mechanical networks: The inerter. IEEE Transactions on Automatic Control47: 1648–1662.
36.
SunLNVansompelHZhangZR, et al. (2022) Circulating-current-excited switched reluctance generator system with diode rectifier. IEEE Transactions on Industrial Electronics69(8): 7859–7868.
37.
TanBTanXLiuJ, et al (2025) Cooperative compensation control for a novel semi-active electromagnetic suspension integrating with variable damper and variable inertance. Mechanical Systems and Signal Processing226: 112344.
38.
WangXZLiangHZQiaoDS, et al. (2023) Hardware-in-the-loop test for the optimal damping identification of oscillating buoy wave energy converters. Ocean Engineering287: 13.
39.
XuXAntsaklisPJ (2004) Optimal control of switched systems based on parameterization of the switching instants. IEEE Transactions on Automatic Control49(1): 2–16.
40.
YinXXLiXFZuoL (2021) Dynamic characteristics and test results of a wave power takeoff system with mechanical motion rectification and transmission. IEEE Transactions on Industrial Electronics68(12): 12262–12271.
41.
ZhangCLiDDingZ, et al. (2024) Wave energy converter with multiple degrees of freedom for sustainable repurposing of decommissioned offshore platforms: An experimental study. Applied Energy376: 124204.
42.
ZhangJQDuHFWangS, et al. (2025) A compact mechanical energy harvester for multi-scenario applications in smart transportation. Mechanical Systems and Signal Processing224: 23.
