Loop Shaping Research Articles

H‐infinity loop shaping control of wireless power transfer system based on generalized state space averaging model

SummaryThe transmission distance and the output load of wireless power transfer (WPT) system are particularly prone to change, which results in higher requirements for the robustness and dynamic performance of the control. In order to reduce the influence of these characteristics, an H∞ loop shaping controller based on generalized state space averaging (GSSA) method is proposed in this paper. Based on the GSSA model, an appropriate compensation function is constructed for the WPT system to the target loop transfer function. The nominal coprime factorization of WPT system is carried out, and on this basis, H∞ controller is achieved by Riccati equation to minimize the infinite norm from disturbance to error output. The designed controller meets the requirements of robust. Furthermore, the obtained high‐order controller is discretized by a reasonable discretization method, and the details and limitations of its practical application are discussed based on the hardware computational capacity. The experimental results show that the proposed controller has better robustness and dynamic performance and flexibility than the mixed sensitivity H∞ controller and the Z‐N PI controller.

Interaction of 1/2〈111〉 interstitial dislocation loop with hydrogen and helium in tungsten: molecular dynamics simulation

The interaction of hydrogen and helium atoms with 1/2 〈111〉 interstitial dislocation loop in tungsten is investigated by molecular dynamics simulation. The binding energies of hydrogen and helium atoms around dislocation loop are calculated by molecular statics method. The results show that the outer region of the loop is attractive to the two atoms and the inner region is repulsive. Notably, the maximum binding energies are located in the core region of the dislocation loop. We have also studied the influence factors of the interaction between the dislocation loop and two atoms: free volume, lattice distortion degree, the radius and shape of the dislocation loop. The results show that large free volume benefits the retention of hydrogen and helium atoms, especially for helium. The less lattice distortion caused by the impurity atom, the more favorable for the dislocation loop to trap it. In addition, the larger dislocation loop with higher defect concentration results in stronger capture ability for the hydrogen and helium atoms. The different dislocation loop shapes lead to different binding energy distribution patterns. And the hydrogen and helium atoms tend to occupy the groove region of the concave dislocation loop. Finally, we employ the nudged elastic band theory and dynamics method to investigate the diffusion pattern of the hydrogen atom in the dislocation loop and find that the hydrogen atom tends to migrate spirally around dislocation line. Based on the obtained results, a reasonable interpretation of the interaction behaviors between the dislocation loop with hydrogen and helium atoms are discussed, which can provide essential parameters for mesoscopic scale simulations.

Damping of coronal oscillations in self-consistent 3D radiative magnetohydrodynamics simulations of the solar atmosphere

Context. Oscillations are abundant in the solar corona. Coronal loop oscillations are typically studied using highly idealised models of magnetic flux tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of a realistic magnetic field topology and the density structuring. Aims. We analyse the damping of coronal oscillations using a self-consistent 3D radiation-magnetohydrodynamics simulation of the solar atmosphere spanning from the convection zone into the corona, the associated oscillation dissipation and heating, and finally, the physical processes that cause the damping and dissipation. The simulated corona that forms in this model does not depend on any prior assumptions about the shape of the coronal loops. Methods. We analysed the evolution of a bundle of magnetic loops by tracing the magnetic field. Results. We find that the bundle of magnetic loops shows damped transverse oscillations in response to perturbations in two separate instances, with oscillation periods of 177 s and 191 s, velocity amplitudes of 10 km s−1 and 16 km s−1, and damping times of 176 s and 198 s. The coronal oscillations lead to the development of velocity shear in the simulated corona, which results in the formation of vortices seen in the velocity field that are caused by the Kelvin-Helmholtz instability. This contributes to the damping and dissipation of the transverse oscillations. Conclusions. The oscillation parameters and evolution we observed are in line with the values that are typically seen in observations of coronal loop oscillations. The dynamic evolution of the coronal loop bundle suggests that the models of monolithic and static coronal loops with constant lengths might need to be re-evaluated by relaxing the assumption of highly idealised wave guides.

A damage-coupled viscoplastic constitutive model considering tension-compression asymmetry for modeling low cycle fatigue mechanical behaviors of Inconel 617 at elevated temperature

Design and analysis based on the advanced constitutive models capable of simulating the complex mechanical behaviors of materials would improve the operational reliability and safety of high-temperature engineering components that experience thermo-mechanical fatigue loading in aerospace and power industries. Inspired by the experimental observations of a set of low cycle fatigue tests of nickel-based superalloy Inconel 617 at 700 °C, a damage-coupled unified viscoplastic constitutive model considering tension-compression asymmetry is proposed. For a better description of the hysteresis loop shape, the cyclic hardening behavior is modeled by the kinematic hardening rule. The damage is measured by the degradation of elastic modulus, and a low cycle fatigue damage model is employed to describe the cyclic softening behavior and predict the fatigue life. Due to the similarity in the evolution of damage and compressive hardening ratio, a compressive hardening factor, which is a function of damage, is incorporated into the kinematic hardening model to simulate the tension-compression asymmetry, i.e. the mean stress evolution. The strain-range dependence of cyclic hardening and tension-compression asymmetry is also considered. The simulation results show that the proposed model can effectively model the low cycle fatigue mechanical behaviors of the material at elevated temperatures.

Performance investigation and control design of SSI grid-connected system for PV applications with maximum power extraction

Split-source inverter (SSI) has been recently developed as an alternative to the commonly used ZSI where it can serve an interface between the renewable energy sources and the common grid. This paper presents a mathematical model and control strategy for grid-connected SSI system with either constant voltage source or photovoltaic (PV) source. The control strategy is based on linear PI controllers which are fine-tuned by the frequency loop shaping method with the help of the derived mathematical model to ensure the stability of the system with robust dynamic behavior. The derived mathematical model provides a straightforward and efficient understanding of the dynamics resulting from the interaction between the PV and the SSI grid-connected system. The simulation results indicate that the system has a robust dynamic behavior when subjected to various transient conditions. Finally, a downscaled prototype of SSI grid-connected system is implemented to experimentally validate both the mathematical model and control strategy.

Comparative Analysis of Structural Effect of Single Jersey and its Derivative Fabrics on Mechanical and Comfort Properties of Knitted Fabric

The physical, mechanical, and comfort properties of knitted fabrics depend on the type, shape, and number of loops per unit area. Physical properties, namely areal density depend on the ratio of knit, tuck, and miss stitches. The higher the ratio of touch stitches, the higher would be the areal density of the knitted fabric. Double Lacoste had a higher ratio of touch stitches and single jerseys had a zero ratio of tuck stitches. Noticeably, the double Lacoste had the highest areal density, whereas the single jersey had the lowest areal density among all knitted fabrics. Therefore, areal density was inversely proportional to the loop length. Mechanical properties such as tensile strength and bursting strength also depend upon the type and length of the loop. The knit loop had the highest tensile and bursting strength, which decreased as the ratio of touch stitches increased. Air permeability increased with the increasing ratio of tuck stitches and reduced when the fabric contains 100% of the knit loops.

Advanced polynomial trajectory design for high precision control of flexible servo positioning systems

This paper develops a new approach for the design of polynomial-based reference and feedforward control trajectories for the high precision control of flexible servo actuators. First, a robust frequency-domain controller is designed for reference tracking and disturbance rejection. This controller is designed to achieve a desirable loop shape with reasonable bandwidth and stability margins. Then, the polynomial trajectories are derived based on a simplified rigid body representation of the system. To avoid the excitation of the system's resonant modes, this paper proposes the design and implementation of a set of feedforward notch filters. We further investigate the main cause of tracking error resulted from the rigid body approximation, and propose an alternative model for the derivation of the polynomial input trajectories. This model accounts for the cumulative DC gain of the resonant modes ignored in the rigid body approximation. A method for deriving the new polynomial trajectories with the appropriate initial and final time conditions is developed and evaluated for a representative flexible servo system model. Simulation results indicate that the proposed scheme provides significant improvement in the performance of system compared to the conventional methods.

Dynamic performance improvement of proton exchange membrane fuel cell system by robust loop shaping and artificial intelligence optimized fractional order PI controllers

ABSTRACT Due to inherent nonlinear behavior, the Proton Exchange Membrane (PEM) Fuel Cell system yields in poor power quality. The sudden change in stack current causes uncertainty in PEMFC behavior resulting in degraded output. This necessitates the control of supply manifold pressure on the cathode side to prevent oxygen starvation. In this work, three techniques, namely, robust loop shaping, smith predictor, and Fractional Order Proportional Integral (FOPI) controllers, are designed after incorporating parametric uncertainty in system description. Further, the Particle Swarm Optimization (PSO) artificial intelligence technique is implemented to optimize the parameters of smith predictor and Fractional Order PI controllers. By stabilizing the system across the entire parameterized uncertainty range, the proposed control strategies, namely, loop shaping, PSO-Smith Predictor, and PSO-FOPI controller effectively compensate uncertainty effects. The simulation result shows that the PSO-tuned FOPI controller has best overshoot at operating points 3, 4, and 5 having a value of 0.505% in comparison with PSO-Smith Predictor where overshoot (ranging from 19.88% to 40.141%) is too high; and loop shaping controller having high values of overshoot (more than 40% at every operating point) Thus, PSO-FOPI controller exhibits the best performance with far superior overshoot and steady-state stability.

A unified framework for multi-lead ECG characterization using Laplacian Eigenmaps

Background. The analysis of multi-lead electrocardiographic (ECG) signals requires integrating the information derived from each lead to reach clinically relevant conclusions. This analysis could benefit from data-driven methods compacting the information in those leads into lower-dimensional representations (i.e. 2 or 3 dimensions instead of 12). Objective. We propose Laplacian Eigenmaps (LE) to create a unified framework where ECGs from different subjects can be compared and their abnormalities are enhanced. Approach. We conceive a normal reference ECG space based on LE, calculated using signals of healthy subjects in sinus rhythm. Signals from new subjects can be mapped onto this reference space creating a loop per heartbeat that captures ECG abnormalities. A set of parameters, based on distance metrics and on the shape of loops, are proposed to quantify the differences between subjects. Main results. This methodology was applied to find structural and arrhythmogenic changes in the ECG. The LE framework consistently captured the characteristics of healthy ECGs, confirming that normal signals behaved similarly in the LE space. Significant differences between normal signals, and those from patients with ischemic heart disease or dilated cardiomyopathy were detected. In contrast, LE biomarkers did not identify differences between patients with cardiomyopathy and a history of ventricular arrhythmia and their matched controls. Significance. This LE unified framework offers a new representation of multi-lead signals, reducing dimensionality while enhancing imperceptible abnormalities and enabling the comparison of signals of different subjects.

Time-dependent thixotropy of dysphagia management-oriented polysaccharide solutions

During dysphagia management, the required foods are often thixotropic yield fluids (YSFs) in which polysaccharide gums are used as thickeners or gelling agents. Thixotropy is a prevalent hysteresis phenomenon in YSFs, so it always occurs as an apparently time-dependent stress or modulus response. The yielding behavior of the food bolus is inseparable from the mastication and swallowing process, among which time-dependent thixotropy is integral. Nevertheless, standardizing and generalizing the thixotropy levels has always been a challenge in the manufacturing application of YSFs. Moreover, the existing thixotropic approaches cannot guarantee the accuracy and comparability of the measurement process due to technicalities. Along these lines, in this work, the thixotropic stress-shear rate hysteresis loops were investigated based on the utilization of dysphagia management-oriented model polysaccharide solutions that exhibited different time-dependent thixotropy levels. More specifically, xanthan gum (XG), carboxymethylated curdlan (CMCD), and konjac glucomannan (KGM) solutions were selected to mimic dysphagia diet construction, whereas the relationship between their technically mechanical properties and structural changes was analyzed. Compared with the KGM solutions, both XG and CMCD solutions presented significant thixotropy levels with different timescale responses and concentration dependence. The recorded discrepancy in their loop area and shape were attributed to their different intermolecular association and networks.

Study of hysteresis in the ferromagnetic random field 3-state clock model in two and three dimensional periodic lattices at zero temperature and in the presence of dilution and an absorbing state

We numerically study hysteresis in the ferromagnetic random field 3-state clock model in two and three dimensional periodic lattices at zero temperature and in the zero frequency limit of the driving field. The on-site quenched disorders are continuous and are drawn froma uniform distribution. We numerically analyzed the effects of disorder on the dynamics of the model and hence on the shape of the hysteresis loops. We also study the model in the presence of dilution and an absorbing state.

Structural, Magnetic, and Magneto-Optical Properties of Thin Films of BaM Hexaferrite Grown by Laser Molecular Beam Epitaxy.

Thin films of BaM hexaferrite (BaFe12O19) were grown on α-Al2O3(0001) substrates by laser molecular beam epitaxy. Structural, magnetic, and magneto-optical properties were studied using medium-energy ion scattering, energy dispersive X-ray spectroscopy, atomic force microscopy, X-ray diffraction, magneto-optical spectroscopy, and magnetometric techniques, and the dynamics of magnetization by ferromagnetic resonance method. It was shown that even a short time annealing drastically changes the structural and magnetic properties of films. Only annealed films demonstrate magnetic hysteresis loops in PMOKE and VSM experiments. The shape of hysteresis loops depends on thickness of films showing practically rectangular loops and high value of remnant magnetization (Mr/Ms~99%) for thin films (50 nm) and much broader and sloped loops in thick (350-500 nm) films. The magnitude of magnetization 4πMs ≈ 4.3 kG in thin films corresponds to that in bulk BaM hexaferrite. Photon energy and sign of bands in magneto-optical spectra of thin films correspond to ones observed earlier in bulk samples and films of BaM hexaferrite. FMR spectra of 50 nm films at 50 GHz consist of a number of narrow lines. The width of main line ΔH~20 Oe is lower than has been reported up to now.

Comparison of rare earths doping (neodymium and samarium) on structural and magnetic properties of Ni–Zn–Bi nanoferrites

Excellent magnetic properties in ferrites are required for high-frequency applications and for wastewater treatment. Thus, the present study shows the comparison of magnetic and structural properties of Nd and Sm substituted Ni–Zn–Bi ferrites with the series Ni0.5Zn0.5Bi0.04NdxFe1.96–xO4 (with step size 0.002) and Ni0.5Zn0.5Bi0.04SmxFe1.96–xO4 (with step size 0.02) prepared using citrate precursor method. The impact of the substitution of rare earth ions (Nd and Sm) on magnetic properties of the synthesized samples is observed using a vibrating sample magnetometer (VSM). The saturation magnetization values enhance considerably from 52 to 58 emu/g for Nd3+ ions and 39 to 57 emu/g for Sm3+ ions, thus, making these materials magnetically hard. Further, the higher value of coercivity is also observed ranging from 133 to 167 Oe for Nd3+ ions and 81 to 155 Oe for Sm3+ ions. The shape of hysteresis loops indicates a super paramagnetic and ferromagnetic behavior in the obtained samples. The squareness ratio value is <0.5, suggesting the uniaxial anisotropy of particles and hence, these ferrites are suitable for microwave-absorbing and in permanent magnetic materials. The X-ray diffraction (XRD) pattern shows the formation of pure cubic crystallites, where, lattice parameters range from 0.840 to 0.839 nm and from 0.838 to 0.839 nm for Nd3+ and Sm3+ ions substitution, respectively. The crystallite size ranges between 28.63 to 29.89 nm and 18.33 to 26.23 nm, for substitution of Nd3+ and Sm3+ ions, respectively. Field emission scanning electron microscopy (FESEM) shows the formation of homogeneous grains, whereas, energy dispersive spectrometer (EDS) counts describe the purity of the samples. The Sm concentration x = 0.10 has the maximum surface area with value of 42.6 m2/g which proves to be having good data storage application due to high surface area. The zero-field cooled (ZFC) and field cooled (FC) data show that Nd-doped Ni–Zn–Bi nanoferrites show superparamagnetic behaviour in the room temperature range which makes them suitable for practical applications.

Enhancing Dynamic Stability Performance of Hybrid AC/DC Power Grids Using a New Robust Controller

This research investigates the dynamic performance of a multi-terminal DC (MTDC) network linked to a wind farm side converter. The suggested approach is based on loop shaping, mutual quality decomposition, and an effective H controller architecture (MQDM). The transfer function was built as the wind power plant shifted from the Master-Slave control approach to the conventional feedback control method. The singular value curves of the original open-loop system and the suggested solution are compared in order to derive the weighting functions of the robust H controller. The control gain is then calculated by utilizing the MQDM approach to get the system's transfer function from the state space. By using the single value order reduction approach and frequency response analysis to generate a robust controller's gain, the suggested methodology was put into practice. The suggested method for controlling the DC grid voltage on the MTDC converter on the wind farm side has now been implemented in the MATLAB environment. Applying various uncertainties to the DC grid, wind turbines, and AC grid using simulation data demonstrates how reliable the suggested approach is.

Band-stop-filter-based repetitive control of fast tool servos for diamond turning of micro-structured functional surfaces

Fast tool servo (FTS) is a promising technique for the high-speed diamond turning of micro-structured functional surfaces due to its fast response capacity. However, the inherent actuator non-linearity, the lightly damped vibration mode and the external disturbance of the FTS would degrade its tracking performance severely and thus restrict its machining ability. To overcome this limitation, a band-stop-filter-based repetitive control (BSF-RC) scheme is proposed in this article to improve the operating performance of the FTS. Firstly, the spectra of the FTS tool paths (FTS-TPs) for machining typical micro-structured functional surfaces with the cylindrical coordinate machining method are analyzed in detail. The results reveal that the frequency components concentrate on the tiny neighborhoods of the rotational frequency of the spindle and its harmonic frequencies. Afterwards, the comb-like band-stop filter used by the BSF-RC is elaborately designed via the cascade of three comb-like notch filters to generate a comb-like band-stop loop shape for covering main spectral components of the FTS-TPs. The analytical expression of the comb-like band-stop filter amplitude as well as the stability condition of the closed-loop control system are derived to provide effective criteria for the parameter selection of the BSF-RC. The experimental validation of the developed BSF-RC scheme is conducted on a five-axis ultra-precision lathe equipped with a self-developed FTS via the diamond turning of three typical micro-structured functional surfaces. The experimental results show that good surface qualities with the maximal form error of a few hundred nanometers and the surface roughness of a several nanometers are achieved for all the obtained micro-structured surfaces by using the BSF-RC scheme under a high spindle speed.

Stress-Induced Transformations of Polarization Switching in CuInP2S6 Nanoparticles

Using the Landau-Ginzburg-Devonshire approach, we study stress-induced transformations of polarization switching in ferrielectric CuInP2S6 nanoparticles for three different shapes: a disk, a sphere, and a needle. Semiconducting properties of a nanoparticle are modeled by a surface charge layer, whose effective screening length can be rather small due to the field-effect. We reveal a very strong and unusual influence of hydrostatic pressure on the appearance of polarization switching in CuInP2S6 nanoparticles, hysteresis loops shape, magnitude of the remanent polarization, and coercive fields, and explain the effects by the anomalous temperature dependence and "inverted" signs of CuInP2S6 linear and nonlinear electrostriction coupling coefficients. In particular, by varying the sign of the applied pressure (from tension to compression) and its magnitude (from zero to several hundreds of MPa), quasi-static hysteresis-less paraelectric curves can transform into double, triple, pinched, or single hysteresis loops. Due to the sufficiently wide temperature and pressure ranges of double, triple, and pinched hysteresis loop stability (at least in comparison with many other ferroelectrics), CuInP2S6 nanodisks can be of particular interest for applications in energy storage (in the region of double loops), CuInP2S6 nanospheres maybe suitable for dynamic random access multibit memory, and CuInP2S6 nanoneedles are promising for non-volatile multibit memory cells (in the regions of triple and pinched loops). The stress control of the polarization switching scenario allows the creation of advanced piezo-sensors based on CuInP2S6 nanocomposites.

Shear capacity estimation of core steel tube reinforced PCCC column-beam interior joint under quasi-static load

In this study, the quasi-static tests were conducted on 13 core steel tube (CST) reinforced PVC-CFRP confined concrete (PCCC) column-beam interior joints. Distinct shear failure occurred in all joint specimens. The load-displacement hysteresis curves appeared pinching phenomenon, and the shape of hysteresis loops gradually deformed from shuttle to arch and finally changed to reverse S shape. The overall shape of hysteresis curves were relatively full, demonstrating that the joints had favorable seismic performances and energy dissipation capacity. The strain development law of materials in the joint area in the process of stress was clarified. The increment of joint stirrup ratio ([Formula: see text]), axial compression ratio ([Formula: see text]), column reinforcement ratio ([Formula: see text]) or beam reinforcement ratio ([Formula: see text]) improved the calculated shear capacity of the joints. The calculated shear capacity increased first and then decreased slightly as the diameter-thickness ratio of CST ([Formula: see text]) increased. In comparison, spacing of CFRP strip had little impact on the calculated shear capacity. Additionally, the concrete strength enhancement coefficient ([Formula: see text]) and joint stirrup utilization coefficient ([Formula: see text]) were introduced respectively to modify the shear capacity of concrete and joint stirrups, and a simplified formula for predicting the shear capacity of CST reinforced PCCC column-beam interior joints under quasi-static load was proposed. The predicted results agreed well with the test data.

A novel bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD)

The shape of hysteretic loops for a friction pendulum system transforms when excited by bi-directional motion, which exhibits unexpected dynamic behavior compared with unidirectional motion. Therefore, a novel bidirectional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) with two independent rails that satisfied the purpose of bidirectional structural response control and provided a full bidirectional friction force was proposed. The variable friction arrangement was applied to the rails so that the BRVFP-TMD could be accomplished with a linear hysteretic damping property that is contributed by the displacement-dependent variable friction force. Using unidirectional harmonic excitations with attack angle as bi-directional loading, illustrations were created to investigate the control effect of traditional pendulum friction TMDs with a spherical sliding surface. This demonstrated the collapse of hysteretic loops of traditional pendulum friction TMDs and superiority of BRVFP-TMD in terms of mechanism. For the BRVFP-TMD with a lightly damped structure, the optimizations of the fixed-point theory were accessed to obtain the closed-form solutions of the optimal parameters of the BRVFP-TMD. Numerical verifications based on bidirectional motions were conducted to evaluate the performance of the BRVFP-TMD. The bidirectional earthquake results indicated stable and excellent performance of the BRVFP-TMD in terms of either frequency response reduction or friction energy dissipation efficiency. Meanwhile, bidirectional wind-induced vibrations confirmed the correctness of the optimization and the stable robustness of the optimized BRVFP-TMD.

DYNAMICS NOISE BEHAVIORS ON MAGNETO-OPTICAL KERR EFFECT MEASUREMENT SYSTEM

Nowadays, computer and data processing industry are moving to nanomagnetic devices technology. One of the common measurement systems to observe nanomagnetic device are magneto optical Kerr effect and Faraday effects. The magneto-optical Kerr effect measurement system has been fabricated and precision noise measurement configuration was observed. A light intensity, which was reflected by thin film nanomagnetic surface, was measured accompany with its noise level. The lock-in amplifier was attached to pick up hysteresis signal and low noise level. Different frequency of lock-in amplifier was carried out to observe dynamics noise level behavior. Interestingly, we found butterfly shape noise corresponding to hysteresis loop shape. Furthermore, noise behavior with 0.94 scaling exponent, was found with respect to lock-in amplifier frequencies suggested that measuring in low frequency became more challenging.

Ripple Voltage Suppression of Dual Active Bridge Converter in Electric Locomotive Using H∞ Loop Shaping Control Method

The next-generation electric locomotive drive system has the problem of double grid frequency ripple voltage in the DC side of a single-phase PWM rectifier. In this paper, the intermediate stage dual-active-bridge DC-DC converter is studied, and an H∞ loop shaping ripple voltage suppression control strategy is proposed to restrain the harmonic voltage and optimize the dynamic and robust performance of the closed-loop system. Firstly, the mathematical model of the DAB closed-loop control system with fluctuating input voltage is established. Then, based on the H∞ loop shaping control theory, the dynamic performance, the ability of ripple voltage suppression, and the robust performance of the system are analyzed in the frequency domain. According to the results, a reasonable compensator is selected to reconstruct the magnitude frequency characteristic curve of the nominal system. After reconstruction, the solution of the robust stability margin of the corrected object is transformed into the H∞ robust control problem under the coprime factor uncertainty. The suboptimal H∞ robust controller is solved to obtain the best robustness boundary of the constructed system. Finally, the H∞ loop shaping ripple voltage suppression controller is obtained by combining the H∞ controller with the compensator. The experimental environment is set up in MATLAB-Simulink software. Compared with the traditional voltage loop control method and the input voltage feedforward control method, the dynamic performance of the proposed control strategy is slightly improved, and while within the allowable robust boundaries of the system, it has better ripple voltage suppression performance. When the system magnitude frequency curve is outside the tolerant robust stability margin, the ripple voltage suppression performance fails, but the harmonic content of output voltage is still far less than the other two control methods. The experiment results also prove the correctness of the theoretical analysis and that the proposed control method is effective and proper.