Phase-lead Compensator Research Articles

Fractional-Order Phase Lead Compensation Multirate Repetitive Control for Grid-Tied Inverters

To reduce computational load and memory consumption, multirate repetitive control (MRC) with downsampling rates provides a flexible and efficient design for proportional-integral multi-resonant repetitive control (PIMR-RC) systems for grid-tied inverters. However, in MRC systems, repetitive controllers with low sampling rates produce low delay periods, and integer-order phase lead compensation may cause undercompensation or overcompensation. These imprecise linear phase lead compensations may result in deteriorated control performance. To address these problems, based on an infinite impulse response (IIR) filter, a fractional-order phase lead proportional-integral multi-resonant multirate repetitive control (FPL-PIMR-MRC) is proposed for grid-tied inverters in this paper. The proposed method can provide a suitable fractional phase lead step to achieve a wide stability region, minor tracking errors, and low hardware costs. The IIR fractional-order lead filter design, stability analysis, and the step-by-step parameter tuning of the FPL-PIMR-MRC system are derived in detail. Finally, simulation performed confirms the feasibility and effectiveness of the proposed scheme.

Using IIR Filter in Fractional Order Phase Lead Compensation PIMR-RC for Grid-Tied Inverters

Phase lead compensation precision dramatically affects the performance of repetitive controller (RC). Integer order phase lead compensation of proportional integral multi-resonant type RC (PIMR-RC) with low sampling frequency cannot meet the need of fine phase compensation. In addition, the digital control delay affects the actual modeling of the system, and then influences the precision phase compensation. To finely compensate the phase lag of the PIMR-RC system, this paper proposes a fine fractional order phase lead compensation PIMR-RC (FL-PIMR-RC) scheme based on a novel phase lead infinite impulse response (IIR) filter. Its comprehensive synthesis is systematically detailed, including actual modeling considering 1.5-period digital control delay, IIR fractional lead filter design, stability analysis, and parameter optimization. Finally, experiments on a 2 kW prototype grid-tied inverter are successfully carried out to verify the solution.

An enhanced phase-locked loop for non-ideal grids combining linear active disturbance controller with moving average filter

Aiming at the accuracy deterioration of the synchronous reference frame phase-locked loop (SRF-PLL) caused by the non-ideal grid conditions and the limitation of phase-locked loop based on the linear active disturbance rejection controller (LADRC-PLL), this paper proposes an enhanced three-phase phase-locked loop combining the improved moving average filter and linear active disturbance rejection controller (IMAF-LADRC-PLL). First, a linear extended state observer (LESO) is presented to estimate all uncertainties and disturbances of SRF-PLL. On this basis, an improved moving average filter (IMAF) with phase-lead compensator is used to further enhance the harmonic suppression property. By combining the LESO and IMAF in a specific control structure, the proposed IMAF-LADRC-PLL has satisfactory steady-state accuracy without sacrificing the dynamic performance. To ensure the phase-locked accuracy against frequency fluctuation, a frequency-adaptive implementation is suggested. Furthermore, the parameter tuning and performance analysis of IMAF-LADRC-PLL are also presented in this paper. Experimental results show that the proposed IMAF-LADRC-PLL can achieve better dynamic performance on frequency step response and maintain the phase-locked accuracy in the presence of grid harmonics, voltage unbalances and direct current offsets, compared with the traditional LADRC-PLL or PID-type IMAF-PLL strategy.

Research and experiment on control loop system of Source Measure Unit

Aiming at the problem that the capacitive load of the source measure unit (SMU) system affects the stability of the loop control, this paper makes an in-depth theoretical analysis of the loop control system based on the SMU. A theoretical and circuit model is established after the analysis. In the control loop structure, an integrator with proportional amplification serves as an error amplifier for the control loop system to obtain sufficient phase margin at the optimal bandwidth. A phase-lead compensation capacitor scheme is studied and proposed to achieve the maximum tolerance range to achieve the loop stability. The results show that the simulation and experimental results are basically consistent. The results verify the theoretical correctness and practical value of this SMU control loop system, and provide a theoretical basis for the research of the SMU control loop structure of the subsequent SIP process.

A Control Strategy of LCL-Type Grid-Connected Inverters for Improving the Stability and Harmonic Suppression Capability

The conventional inverter-side current single-loop feedback control scheme is weak in suppressing the grid-side current harmonics, posing a challenge for an inverter to inject high-quality current under distorted grid voltage. With capacitor current compensation added, the control scheme achieves controllability of the grid-side current harmonics so that it can effectively suppress some specific harmonic components. However, due to the stability requirements, only a few low-order harmonic resonance controllers can be applied, which limits the mitigation of high-order harmonics. To tackle this problem, the grid-side current feedback control with inductor–capacitor–inductor (LCL) resonance damping is proposed in this paper. In this case, a higher LCL resonance frequency can be set compared to the inverter-side current single-loop feedback control scheme. Thereby, more resonance controllers can be applied to suppress high-order grid-side current harmonics. The active damping method of capacitor current proportional feedback plus capacitor voltage proportional feedback is adopted because of its high robustness to grid impedance variations. Furthermore, this paper reveals that the applied active damping method has a limitation in that it only considers a single inverter under inductive grid impedance, which cannot eliminate the risk of resonance caused by the interaction of multiple inverters and the grid. To address this issue, a phase lead compensator (PLC) is proposed, eliminating the resonance risk by removing the non-passive region of the inverter output admittance. To retain the advantage of the inverter-side current single-loop feedback control scheme, i.e., only a few measuring devices are required, a digital differentiator is used to calculate the capacitor current from the capacitor voltage. The difference between the measured inverter-side current and the calculated capacitor current is taken to approximate the grid-side current for the feedback control. The control performance is comparable to using the grid-side current for feedback. Simulation and experimental results demonstrate that the proposed control scheme endows the inverter with good stability and current quality without extra measurement devices.

Extended State-Based OSG Configurations for SOGI PLL With an Enhanced Disturbance Rejection Capability

Changes in the orthogonal signal generator (OSG) configuration of the standard second-order generalized integrator-based phase-locked loop (S-SOGI PLL) have shown to offer an improved low-voltage ride-through capability. However, the resulting PLLs: highpass SOGI (H-SOGI) and lowpass SOGI (L-SOGI) PLLs have no dc-offset estimation capability and lack robustness to disturbances. Therefore, this article focuses on maximizing the merits of H-SOGI and L-SOGI PLLs for grid and industrial applications by incorporating dc-offset estimation and enhancing their disturbance rejection capability. Accordingly, two varieties of SOGI PLLs, namely: extended state highpass SOGI (ES-H-SOGI) and extended state lowpass SOGI (ES-L-SOGI) PLLs are proposed. In the proposed PLLs, states of the OSGs are extended to achieve dc-offset estimation and rejection, while frequency-adaptive implementation of the moving average filter (MAF) is developed to achieve complete harmonic rejection at off-nominal frequencies of the input voltage. To alleviate the undesirable effect of the MAF in terms of the PLL's slow transient response, frequency-adaptive implementation of a phase-lead compensator is introduced. In this article, design guideline that achieves an optimal tradeoff between disturbance rejection and dynamic performance in the ES-H-SOGI and ES-L-SOGI PLLs is presented. Finally, experimental comparison between the proposed ES-H-SOGI and ES-L-SOGI PLLs and their ES-S-SOGI PLL counterpart is carried to show that the proposed PLLs outperform the ES-S-SOGI PLL in terms of dynamic performance while achieving enhanced disturbance rejection capability.

Learning-Based Repetitive Control of a Bowden-Cable-Actuated Exoskeleton with Frictional Hysteresis.

Bowden-cable-actuated soft exoskeleton robots are known for their light weight and flexibility of power transmission during rehabilitation training or movement assistance for humans. However, friction-induced nonlinearity of the Bowden transmission cable and gearbox backlash pose great challenges forprecise tracking control of the exoskeleton robot. In this paper, we proposed the design of a learning-based repetitive controller which could compensate for the non-linearcable friction and gearbox backlash in an iterative manner. Unlike most of the previous control schemes, the presented controller does not require apriori knowledge or intensive modeling of the friction and backlash inside the exoskeleton transmission system. Instead, it uses the iterative learning control (ILC)to adaptively update the reference trajectory so that the output hysteresis caused by friction and backlashis minimized. In particular, a digital phase-lead compensator was designed and integrated with the ILC to address the issue of backlash delay and improve the stability and tracking performance. Experimental results showed an average of seven iterations for the convergence of learning and a 91.1% reduction in the RMS tracking error (~1.37 deg) compared with the conventional PD control. The proposed controller design offers promising options for the realization of lightweight, wearable exoskeletons with high tracking accuracies.

Reduced-Order Generalized Integrator-Based Phase-Locked Loop: Performance Improvement for Grid Synchronization of Single-Phase Inverters

Generalized integrator-based orthogonal signal generator phase-locked loops (GI-OSG PLLs) are very popular in single-phase grid synchronization. Generally speaking, the OSG of this PLL is realized from a second-order integrator perspective. As a result, the OSG implementation impacts the PLL dynamics. Improving the PLL performance by employing a reduced-order OSG implementation is the main motivation for this paper. Therefore, a reduced order-OSG PLL is proposed. In the proposed PLL, a single state and two output equations are employed to obtain a pair of orthogonal signals. This results in the loss of orthogonality between the OSG outputs and the single-phase supply voltage. Also, harmonic filtering capability provided by SOGI-OSG becomes non-existent. These issues are resolved by incorporating steady-state phase angle-offset error compensation at the PLL output and a moving average filter (MAF) within the PLL loop. To counteract the influence of MAF on the PLL’s stability and dynamics performance, a phase-lead compensator is designed. Through experimental studies, it is shown that the proposed reduced order-OSG PLL offers excellent dynamic performance. Also, the proposed PLL achieves minimal fluctuation of PV power when employed for grid synchronization of a PV system.

Prediction and Compensation Model of Longitudinal and Lateral Deck Motion for Automatic Landing Guidance System

This paper mainly studies the longitudinal and lateral deck motion compensation technology. In order to ensure the safe landing of the carrier-based aircrafts on the flight decks of carriers during the landing process, it is necessary to introduce deck motion information into the guidance law information of the automatic landing guidance system when the aircraft is about to land so that the aircraft can track the deck motion. To compensate the influence of the height change in the ideal landing point on the landing process, the compensation effects of the deck motion compensators with different design parameters are verified by simulation. For further phase-lead compensation for the longitudinal automatic landing guidance system, a deck motion predictor is designed based on the particle filter optimal prediction theory and the AR model time series analysis method. Because the influence of up and down motions on the vertical motion of the ideal landing point is the largest, the compensation effects of the designed predictor and compensator are simulated and verified based on the up and down motion of the power spectrum. For the compensation for the lateral motion, a tracking strategy of the horizontal measurement axis of the inertial stability coordinate system to the horizontal axis of the hull coordinate system (center line of the deck) is proposed. The tracking effects of the horizontal measurement axis of the designed integral and inertial tracking strategies are simulated and compared. Secondly, the lateral deck motion compensation commands are designed, and the compensation effects of different forms of compensation commands are verified by simulations. Finally, the compensation effects for the lateral deck motion under integral and inertial tracking strategies are simulated and analyzed.

Design Method of the Wheel Slip Speed Feedback Controller and Phase Lead Compensator in Locomotives

Design Method of the Wheel Slip Speed Feedback Controller and Phase Lead Compensator in Locomotives

A control system for MR damper-based suspension of front-loaded washing machines featuring magnetic induction coils and phase-lead compensator

This paper studies a semi-active control system for magneto-rheological (MR) damper-based suspension of front-loaded washing machines. In this system, a permanent magnet is fastened to the shaft end of a shear-mode MR damper and an induction coil is wound directly on the slots of damper housing. Vibration of the washing machine tube leads to the relative reciprocal movement between the magnet and induction coil, which results in an induction voltage. The induced voltage is then served as an input signal to control the damping force of the MR damper. Because of the MR fluid hysteresis, a phase-lead compensator and an amplifier are employed in the controller of the MR damper. After the controller design, simulations and experiments are performed to evaluate the control system effectiveness. From the experimental results, performance characteristics of the proposed control system are discussed and compared with those of constant current and uncontrolled states.

Combining the wavelet transform with a phase-lead compensator to a respiratory motion compensation system with an ultrasound tracking technique in radiation therapy

This study evaluated the feasibility of applying the wavelet transform (WT) combined with a phase-lead compensator (PLC) to our previously developed two-dimensional respiratory motion compensation system (RMCS). This system automatically and instantaneously adjusts PLC parameters according to different respiration signals to reduce influences of the system delay time, improving the compensation effect of the RMCS during respiratory motion compensation. This study performed respiratory movement compensation experiments with a two-dimensional respiratory motion simulation system (RMSS) and the RMCS. Human respiratory signals were captured using our previously developed ultrasound image tracking algorithm (UITA). In this study, a displacement compensation RMCS algorithm based on the combination of WT and PLC was developed by LabVIEW, which allows an automatic adjustment of the PLC parameters according to various respiratory waveforms, achieving a better compensation effect. The experiment results indicated that the compensation rate (CR) of right-left and superior-inferior directions had both improved 67.96–88.05% and 70.38–91.43%, respectively. In this study, the proposed method combined with WT and PLC applied in respiratory movement compensation experiments; the UITA was used for tracking diaphragm motion which substitutes for tumor motion. This noninvasive monitoring method also helps reduce side effects after treatment. The experimental results indicated that the effect of using the WT combined with the PLC to compensate for various respiratory signals was improved over our previously developed compensation algorithm.

High-Performance Fractional Order PIMR-Type Repetitive Control for a Grid-Tied Inverter

Low switching frequency is usually used in high-power wind grid-tied inverter systems to reduce power loss caused by on–off switching activity. Proportional integral multi-resonant type repetitive control (PIMR-type RC) can track reference grid current signals and suppress harmonic signals of grid-tied inverter system. A low switching frequency will result in a low sampling rate of control system. However, integer-order phase-lead compensation will lead to a poor compensation accuracy of PIMR-type RC with a low sampling rate, leading to poor tracking and suppressing performance of PIMR-type RC, and even result in system instability. To solve these problems, a high-performance fractional-order phase-lead compensation PIMR-type RC (FO-PIMR-RC) scheme is proposed in this paper. Fractional-order phase-lead compensation is adopted to compensate accurately the phase lag caused by controlled plant and PIMR-type RC and approximately realized by a finite impulse response (FIR) filter. Stability analysis and harmonic suppression performance are provided, and the parameter optimization design is implemented. Simulation and experimental results prove the desirable performance of the proposed control scheme.

Down-Sampled Repetitive Controller for Grid-Connected Ćuk CCM Inverter

The Ćuk inverter operating in the continuous conduction mode (CCM) is susceptible to grid disturbances, and its transfer function has two right-half-plane zeros (RHPZs), which causes a large phase lag. To improve the output-tracking precision in the grid-connected environment, a repetitive controller (RC) with linear phase-lead compensation has been developed for the Ćuk inverter. However, this controller requires a heavy computational burden and memory space; these problems become more severe as the converter operates at a higher switching frequency. This article proposes to use a down-sampled repetitive controller (DRC) for the Ćuk CCM inverter to alleviate these problems. The down-sampling technique itself can significantly reduce the computational burden and memory space of RC. On the contrary, its control accuracy becomes very low, particularly for the Ćuk CCM inverter. Unlike conventional module integrated inverters (MIIs), the Ćuk CCM inverter must adopt a fractional-order phase-lead compensation algorithm to compensate for the effect of the large phase lag in the down-sampled environment. To clarify the inevitable usage of DRC with a fractional-order phase-lead compensation for Ćuk CCM inverter, the DRC is classified into four types; this article provides its detailed design guideline based on stability analysis of the overall control system and also presents design examples for representative MIIs. Experiments using a 300-W prototype Ćuk inverter validate that the proposed control approach achieves acceptable output-tracking accuracy. The total computation time and memory space with the DRC decrease by 76.0% and 80.0% compared to those with the conventional RC, while the output-tracking accuracy with the DRC decreases by 0.42%.

Robustness Investigation of Multi-Inverter Paralleled Grid-Connected System With LCL-Filter Based on the Grid-Impedance Allocation Mechanism

Due to the existence of grid impedance, there is coupling resonance problem which may cause the multi-inverter grid-connected system to become unstable. This article focuses on universal mechanism for multimodule grid-connected system composed of LCL-type inverters. By establishing the multi-input multi-output matrix of the multi-inverter system, the system stability is divided into two parts, i.e., the self-stability and the interactive-stability. Then, based on elaborate deduction for the interactive-stability, the equivalent allocation mechanism of grid impedance is raised and a stability criterion for multimodule inverters system is proposed. In addition, on the basis of exploring the effect of the digital-control delay on the stability of the multi-inverter system in the weak grid, the phase-lead compensator combining with the optimal capacitor-current-feedback coefficient is adopted to improve the system robustness against grid impedance variation. Finally, the effectiveness of the theoretical analysis is verified by experimental results.

A Type-3 Modified SOGI-PLL With Grid Disturbance Rejection Capability for Single-Phase Grid-Tied Converters

This article presents a type-3 second-order generalized integrator phase-locked loop (SOGI-PLL) algorithm for single-phase system. Disturbances, such as dc offset and harmonics, are present in the practical grid voltages, due to occurrence of faults, sensors, and analog-to-digital converters. The type-3 SOGI-PLL exhibits fast dynamic performance with gain and phase-lead compensation. However, the general type-3 SOGI-PLL introduces fundamental frequency oscillations in the estimated quantities at the output, when grid voltage contains disturbances. The incorporation of filters for suppression of frequency oscillations, due to dc offset, reduces the bandwidth of PLL, which affects the dynamic response of PLL by introducing phase delay. Thus, a modified notch-filter SOGI (MNF-SOGI) based type-3 SOGI-PLL is proposed with frequency adaptive control to eliminate the phase error, without affecting the dynamic performance. A detailed analysis is presented on the effect of dc offset and scaling error. To enhance dynamic response, filtering, and stability designed guideline based on settling time is also discussed. The proposed type-3 MNF-SOGI-PLL has better grid parameter estimation and fast response with inherent dc offset rejection capability. The effectiveness of the proposed type-3 MNF-SOGI-PLL is evaluated under various grid disturbance conditions and experimentally verified.

Tuning of Proportional-Resonant Controllers Combined with Phase-Lead Compensators Based on the Frequency Response

In this research article, the proportional-resonant controllers (PR) are introduced to fulfil the increased demand for controllers aiming at the tracking and/or rejection of periodic signals with superior performance than conventional PID ones. The main characteristic of these controllers is the infinite gain in the frequency of interest, which can lead to stability problems and makes their design and tuning more complex. More precisely, this paper presents a systematic approach for the computation of PR controllers parameters based on a frequency response method, using stability margins and sensitivity functions as indicators of performance and stability for the controlled system. In addition, a combination with a phase-lead compensator is proposed to allow better performance in an augmented bandwidth. Finally, the effectiveness of the proposed method is demonstrated for different classes of processes found in typical control problems.

Capacitor Current Feedback With Phase-Lead Compensator to Eliminate Resonant Frequency Forbidden Region for LCL-Type Grid-Connected Inverter in Weak Grid

Digital-controlled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type grid-connected inverter, with capacitor-current-feedback active damping, is widely adopted in the mediate-to-high power application because of low output harmonics and high power quality. Owing to the digital control delay, however, the inverter robustness might be weakened against the grid-impedance variation. In this article, a simple phase-lead compensator is proposed to insert into the capacitor-current feedback-path for compensating the digital control delay. In doing so, the boundary frequency of the virtual-positive-resistance-region (VPRR) can be increased from one-sixth to almost one-fourth of the sampling frequency. In addition, the resonant frequency forbidden region for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter can be eliminated, such that the inverter robustness can be significantly improved against the grid-impedance variation. To ensure the system stability and attain a good control performance, a design procedure is further presented for the phase-lead compensator as well as the closed-loop parameters. Finally, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type grid-connected inverter is built and tested in the lab, and experimental results are presented to verify the effectiveness of the proposed control scheme and parameter design procedure.

Improved Odd-Harmonic Repetitive Control Scheme for Cuk-derived Inverter

This paper proposes an improved odd-harmonic repetitive control (IORC) scheme for a uk-derived inverter. The IORC is composed of a modified odd-harmonic repetitive controller (RC) combined with a proportional-integral (PI) controller plus a feedforward controller to achieve a zero steady-state error in the uk-derived inverter. The IORC features larger gains at odd-harmonic frequencies by modification of the conventional odd-harmonic RC. And, it also adopts a linear phase-lead compensator to compensate for the phase lag of the uk-derived inverter. Hence, the IORC can effectively eliminate the odd-harmonic components in the output current of the grid-connected uk-derived inverter. In addition, it requires less memory space and provides faster transient response compared to conventional RC schemes. However, the distinctive structure of the IORC makes it difficult to guarantee the stability of the overall control system. Thus, in this paper, a new stability analysis method for the IORC system are given, and then a practical design guideline is also provided to obtain the optimal control parameters. Experimental results are presented to validate the proposed controller in the 300-W uk-derived inverter prototype.

Bridgeless Hybrid-Mode Zeta-Based Inverter: Dynamic Modeling and Control

In this article, we present a bridgeless hybrid-mode Zeta inverter for distributed energy systems. We integrate the secondary diode of the conventional unfolding-type Zeta inverter into one of diagonal pairs of the secondary-side switches in a bridgeless Zeta inverter. This structure decreases the number of active power components and provides naturally well distributed loss at the body diodes of the secondary-side switches over one cycle of grid voltage, and as a result, increases both output power transfer and reliability. To attain medium-high power capacity with appropriate size of magnetic components, the bridgeless Zeta inverter operates in both discontinuous conduction mode (DCM) and continuous conduction mode (CCM). However, control of the proposed inverter is difficult because of the distinct system dynamics caused by the operations in DCM and CCM. To deal with this control problem, we first identify the mode boundaries and, corresponding to each mode, develop a dynamic model to design a controller. Then, we propose to use a feedback controller plus a feedforward controller supplemented with a repetitive controller that uses a phase-lead compensator. Experimental results using a 300-W prototype demonstrate the feasibility and effectiveness of the proposed modeling and control approach.