Phase Error Tracking Research Articles

Improved MSTOGI-PLL with enhanced control under non-ideal grid voltage conditions

Integration structure of second- and third-order generalized integrator phase-locking loop (MSTOGI-PLL) has received attention for the processing ability of harmonics and DC bias contained in grid voltage. However, due to that MSTOGI-PLL is sensitive to interharmonics and subharmonics, once low order harmonics dominate, the narrow bandwidth will result in slow response. Hence, based on the analysis on input and output frequency characteristics of existing MSTOGI, a frequency gain structure within the MSTOGI structure is added to improve the suppression ability, either to low-frequency or high-frequency harmonics. Secondly, in order to accelerate response and reduce overshoot of the output frequency of the phase-locked loop (PLL), a nonlinear PI dynamic regulator based on a hyperbolic threshold function is constructed. Furthermore, from the perspectives of voltage phase and frequency tracking error indicators, by comparing with three other types of PLL structures in weak grid application, the effectiveness of the proposed method is verified through simulation cases. Finally, a physical hardware platform based on dSPACE1104 is built to extract the grid voltage from the three-phase voltage regulating transformer, the theoretical derivation and simulation results are verified. The phase deviation is controlled within 0.44 rad s-1, and frequency deviation is controlled within 0.07 Hz.

A High Dynamic Velocity Locked Loop for the Carrier Tracking of a Wide-Band Hybrid Direct Sequence/Frequency Hopping Spread-Spectrum Signal

For hybrid direct sequence/frequency hopping (DS/FH) spread spectrum signals, even if the relative motion speed between the transmitter and receiver remains constant, the Doppler frequency will vary due to the continuous hopping of the carrier frequency. Under high dynamic conditions, the first-order and second-order change rates of the Doppler frequency attached to the received signal further increase the Doppler frequency agility, making it difficult for the carrier tracking loop to maintain steady-state tracking. To address these issues, a high dynamic velocity locked loop (HD-VLL) is proposed in this paper. Specifically, the accumulated phase tracking error caused by acceleration and jerk is first analyzed. Subsequently, to compensate for this phase tracking error with the system clock, the proposed loop adds an acceleration compensation module and a jerk compensation module. However, this results in the output of the high dynamic loop filter being updated with the system clock, which contradicts the multiplexing design of a traditional loop filter for parallel signal processing, making the hardware implementation of an HD-VLL impractical. Therefore, this contradiction leads us to design an HD-VLL-based multi-carrier NCO (HD-VLL-NCO). The HD-VLL and HD-VLL-NCO are simulated, revealing the HD-VLL’s superior dynamic adaptability and steady-state tracking, while the HD-VLL-NCO achieves comparable accuracy with the appropriate truncation bit width.

FPGA-Based Frequency Tracking Strategy with High-Accuracy for Wireless Power Transmission Systems

Aiming at the problem of the unavoidable phase-tracking error of the wireless power transfer (WPT) system caused by dead time, MOSFET drive and other factors, this paper proposes a frequency-tracking method with high accuracy based on a Field-Programmable Gate Array (FPGA) to track the current and voltage phase differences on the transmitting side. Compared with fixed-phase systems, the proposed method accurately controls the phase difference between voltage and current. It detects the phase difference in real time and adjusts the phase compensation angle dynamically to ensure that the system always operates under the optimal zero-voltage switching (ZVS) state, which reduces system loss. Experiments under operating conditions of varying transmission distances and load resistance values are carried out on a prototype. The experimental results show that the proposed method achieves a desired phase difference of 11.5° under the conditions of varying transmission distances and load resistance values, which meets the expectation of a phase difference between 10.5° and 13° to achieve ZVS. Within the range of over-coupling conditions, the output power and transmission efficiency of the WPT system are more significantly improved than those of the fixed-frequency system, which verifies the feasibility of the proposed method.

Code phase tracking error based autonomous integrity monitoring for GNSS/INS ultra-tightly integrated system

The ultra-tight integration of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) may suffer from faults in GNSS, INS and integration filter. Both the faults occurred at the current epoch and at previous epochs affect the position solution deviation of ultra-tight integration at the current epoch, and the effect is reflected in GNSS code phase tracking errors. In this paper, a new autonomous integrity monitoring algorithm is proposed for the federated GNSS/INS ultra-tight integrations in which the code phases of local GNSS signal replicas for GNSS signal tracking are completely derived from the integrated navigation solution. In the proposed algorithm, GNSS code phase tracking errors are employed to construct the test statistics for fault detection through a MHSS (Multiple Hypothesis Solution Separation) method improved from the classical MHSS used in ARAIM (Advanced Receiver Autonomous Integrity Monitoring). With the improved MHSS, the proposed algorithm can account for GNSS nominal biases, multiple GNSS faults and the faults in INS and integration filter. The protection levels under multiple hypothesis are also derived. A semi-physical simulation of the federated ultra-tight integration of GPS (Global Positioning System) and INS in airplane approaching case and a vehicle-based field test of the federated ultra-tight integration of GPS, Galileo and INS are conducted to validate the proposed algorithm. The experiments show that the designed fault detection can effectively detect the occurred faults and the derived protection levels can correctly bound the caused position solution error.

Interaction paths analysis and stability-enhancing methods for LCC-HVDC system with weak receiving-end grid

The stability problem becomes more prominent when line-commuted converter based high voltage direct current (LCC-HVDC) system is connected to weak receiving AC network. Although the impacts of controller parameters on the stability of LCC-HVDC system have been well studied, the interaction mechanism between LCC and weak AC network has not been totally understood and revealed. As a result, the proposal of corresponding solutions is restricted. To remedy such insufficiency, firstly, the sketchy interaction paths between LCC and AC network are extracted and analyzed in this paper based on the motion equation model. The results reveal that the phase interaction path provides negative damping and is the main contributor to the instability. Moreover, since the extinction angle (EA) is the critical node in phase path, the impacts of two coefficients of EA on the system stability are analyzed, namely phase tracking error (PTE)-EA coefficient kδγ and firing angle order (FAO)-EA coefficient kαoγ. The theoretical analysis shows that increasing kδγ or decreasing kαoγ will strengthen the system damping. Next, the comprehensive physical explanations for the above discoveries are presented. Then, two methods that have the same effects on modifying these coefficients are proposed to enhanced the system stability. Finally, the effectiveness of these two methods is verified by the simulations in PSCAD/EMTDC.

Benefits of Using Carrier Phase Tracking Errors for Ultratight GNSS/INS Integration: Precise Velocity Estimation and Fine IMU Calibration

We explore the benefits of using carrier phase tracking errors (CPTEs) as measurements for an ultratightly coupled (UTC) global navigation satellite system (GNSS)/inertial navigation system (INS) integration system. It is demonstrated that CPTEs and time-differenced carrier phases (TDCPs) are equivalent under the condition of zero initial phase error. Hence, for the UTC integration, precise velocity estimations at the millimeter/second level can be expected by using CPTEs as measurements. Furthermore, low-noise CPTE measurements benefit the fine online calibration of an inertial measurement unit (IMU). A high-accuracy IMU error model is included in the integration Kalman filter (IKF). The corresponding measurement model is derived in detail. A static field test and a dynamic road test are used to assess the performance. For the static test, standard deviations of velocity errors range from 2.29 to 3.17 mm/s. Standard deviations of velocity errors in the road test are found to be at the 6.01–6.07 mm/s level for horizontal components and 8.05 mm/s for vertical components. Again, for the dynamic test, the effect of IMU calibration is evaluated via inertial coast errors. The results show that the combination of CPTEs and the high-accuracy error model exhibits the smallest free-inertial coast errors, as compared with other considered methods.

Fractional order zero phase error tracking control of a novel decoupled 2-DOF compliant micro-positioning stage

This study focuses on a piezo-actuated two-degrees-of-freedom (2-DOF) decoupled compliant micro-positioning stage driven by a novel compound bridge-type amplification mechanism embedded with Scott-Russell mechanism. According to the system identification, the transfer functions of two working directions are obtained. Both of the measured dynamic cross couplings between them are also lower than −40 dB, demonstrating that the single-input-single-output control strategy can be adopted reasonably. Based on the identified frequency response, a fractional order proportional-integral (FOPI) controller is designed for the 2-DOF compliant micro-positioning stage. Compared with the integer order proportional-integral (IOPI) controller using same parameters, the amplitude error of the FOPI controller is 2% lower than that of IOPI controller. Additionally, a fractional order zero phase error controller (FOZPETC) is designed by obtaining the inverse of the fractional order closed-loop system in a large frequency range. And the gain of the corrected control system is 1 in a wide frequency band to eliminate the phase error in the close-loop control system. Finally, using the compound control strategy of FOZPETC+FOPI, a series of trajectory tracking tests are carried out on the proposed novel 2-DOF compliant micro-positioning stage. All the experimental results prove that the designed controller can achieve good positioning and tracking performance of the micro-positioning stage, and confirm the effectiveness of the compound control strategy of FOZPETC+FOPI.

Simplified Realization of Zero Phase Error Tracking

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output of a continuous time transfer function of relative order greater than or equal to two. In this paper, we will note that the sampling zeros of the zero-order hold equivalent of chain of integrators, 1/sn, are configured for natural realization of zero phase error tracking. This property is exploited to realize a simplified realization of zero phase error tracking control for chain of integrators. The property can also be utilized for general transfer functions when the sampling period for digital control is small. The effectiveness of the proposed approach for general transfer functions is demonstrated by simulations.

Low-complexity carrier phase estimation for M-ary quadrature amplitude modulation optical communication based on dichotomy.

In high-speed optical communication, the blind phase search (BPS) algorithm performs carrier phase estimation better but with higher computational complexity (CC), bringing a larger computational burden to the digital signal processing unit. In this paper, a new low-complexity CPE algorithm (DBPS) is proposed for M-ary quadrature amplitude modulation (M-QAM) formats. It uses the BPS algorithm to estimate the compensation phase interval, before using dichotomy to quickly and accurately determine the compensation phase value. Simulation results show the CC (multiplication / addition) of DBPS is reduced by 2.79 / 2.84 (16-QAM), 5.35 / 5.45 (64-QAM), and 2.98 / 3.01 (128-QAM) than that of BPS, and DBPS has a smaller phase tracking error variance. DBPS can relax the limitation of optical communication rate caused by high-speed data operations.

Loop Shaping by Single-Resonant Controllers for Prescribed Tracking of Sinusoidal References

It is well-known that in ac-grid-connected or motor-driving converters, current behavior directly sets the exchange of power between the two. Moreover, in corresponding current plants, most of the disturbance (formed by grid voltage or back EMF and the dc-link voltage) may be measured/estimated and appropriately canceled, reducing the current regulation problem to tracking challenge only. The latter is still of extreme importance since the amount of active/reactive power exchanged is proportional to current magnitude and phase. Recently, a method for deriving proportional-resonant controller structure and coefficients according to desired tracking behavior of ac signal amplitude, applied to typical power converter current loop, was proposed based on the fact that if ac signal envelope is perceived as dc signal, its transient behavior may be easily shaped utilizing well-known approaches employed in dc systems loop shaping while keeping zero phase tracking error at all time. This paper extends the proposed methodology by introducing in-depth analysis of the resulting loop gain shaping, applying practical issues, such as actuator delay, damping, and finite word length to the system, yielding a closed set of hands-on design guidelines. Experimental results are also given, providing a two-fold value: successfully validating the presented material and demonstrating that some of the previously reported outcomes (based on simulations) cannot be achieved in practice due to the above mentioned real world constraints.

Robust estimation of quantitative perfusion from multi-phase pseudo-continuous arterial spin labeling.

PurposeMulti‐phase PCASL has been proposed as a means to achieve accurate perfusion quantification that is robust to imperfect shim in the labeling plane. However, there exists a bias in the estimation process that is a function of noise in the data. In this work, this bias is characterized and then addressed in animal and human data.MethodsThe proposed algorithm to overcome bias uses the initial biased voxel‐wise estimate of phase tracking error to cluster regions with different off‐resonance phase shifts, from which a high‐SNR estimate of regional phase offset is derived. Simulations were used to predict the bias expected at typical SNR. Multi‐phase PCASL in 3 rat strains (n = 21) at 9.4 T was considered, along with 20 human subjects previously imaged using ASL at 3 T. The algorithm was extended to include estimation of arterial blood flow velocity.ResultsBased on simulations, a perfusion estimation bias of 6‐8% was expected using 8‐phase data at typical SNR. This bias was eliminated when a high‐precision estimate of phase error was available. In the preclinical data, the bias‐corrected measure of perfusion (107 ± 14 mL/100g/min) was lower than the standard analysis (116 ± 14 mL/100g/min), corresponding to a mean observed bias across strains of 8.0%. In the human data, bias correction resulted in a 15% decrease in the estimate of perfusion.ConclusionsUsing a retrospective algorithmic approach, it was possible to exploit common information found in multiple voxels within a whole region of the brain, offering superior SNR and thus overcoming the bias in perfusion quantification from multi‐phase PCASL.

Repetitive Control Meets Continuous Zero Phase Error Tracking Controller for Precise Tracking of B-Spline Trajectories

In this paper, a novel repetitive control scheme is presented and discussed, based on the so-called B-spline filters. These dynamic filters are able to generate a B-spline trajectory if they are fed with the sequence of control points defining the curve. Therefore, they are ideal tools for generating online reference signals with the prescribed level of smoothness for driving dynamic systems, possibly together with a feedforward compensator. In particular, a continuous zero phase error tracking controller (ZPETC) can be used for tracking control of nonminimum phase systems but because of its open-loop nature it cannot guarantee the robustness with respect to modeling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in nonideal conditions, provided that the desired reference trajectory and the disturbances are periodic. This paper is based on the results presented in the conference paper [L. Biagiotti, F. Califano, and C. Melchiorri, “Repetitive control of non-minimum phase systems along b-spline trajectories,” in Proc. IEEE 55th Conf. Decis. Control , 2016, pp. 5496–5501.], where asymptotic stability of the overall control scheme has been proved mathematically, but extends such results with an experimental validation based on a nonminimum phase system. Different models of the same physical system have been identified and used in the implementation of this model-based control scheme, allowing a real evaluation of the relationship between control system performance and model accuracy.

Wideband two dimensional interferometric direction finding algorithm using base-triangles and a proposed minimum planar array

In wideband interferometric direction finding ambiguity is inevitable due to practical antenna array dimensions. A new algorithm for wideband interferometer direction finding is developed to resolve the ambiguity problem with minimum number of antennas. The method is based on direction finding by three antennas arranged at the three vertices of a triangle named the base-triangle. A two dimensional matrix of ambiguous angles is generated. The ambiguity problem is resolved by an auxiliary base-triangle formed by a fourth antenna in the arrangement. The common angle between the two ambiguous directions derived from the two base-triangles, is the desired angle. As such a four antenna array is optimized with the proposed algorithm to minimize the direction finding error through the 6–18 GHz frequency band for different signal to noise ratios and in the presence of channel phase tracking error. The array performance is evaluated through Monte-Carlo simulations for a coverage of ±45° azimuth and ±45° elevation and a polynomial expression is fitted to the evaluated Root Mean Square errors. Finally, a comparison is made between the proposed method and various correlative interferometer methods. The method has an accuracy better or equal to the cosine function correlative interferometer with much less computation time.

Pulse-Width-Modulation with Zero Phase Error Tracking Controller System for Electrocardiogram Feature Extraction and Tracking from Virtual Patient

Pulse-Width-Modulation with Zero Phase Error Tracking Controller System for Electrocardiogram Feature Extraction and Tracking from Virtual Patient

Contour Error Control Based on Optimal Discrete Controller

An optimal discrete controller is presented in this paper for contour error control using the standard linear quadratic (LQ) method, upon which the offset loss function and the control loss function were considered to attain a relatively good compromise. The weight coefficient for the control loss and the optimal discrete sampling period are garnered, then a zero phase error tracking controller (ZPETC) is designed with the disturbance observer (DOB) to improve the anti-interference capability and the robustness of the system. The proposed methods are capable of enhancing the stability and rapidity of the discrete controller and reducing the contour error of the system. The results may be valuable for various trajectory tracking control applications.

Compact cross form antenna arrays intended for wideband two dimensional interferometric direction finding including the channel phase tracking error

The interferometer method as one of the most accurate schemes for wideband direction finding (DF) is used. The interferometer method has various algorithms which can be implemented depending on the required specifications. The advantages and disadvantages of these algorithms have been evaluated and the appropriate algorithm for a general practical case in view of the ambiguity resolution is proposed. The receivers’ channel phase tracking error is of significant concern in practice in interferometric DF systems. The induced error due to channels phase tracking error is estimated. Furthermore the use of physically realizable antennas, achievement of high accuracy, minimum number of antennas and consequently receivers and wideband DF is considered. The interferometric algorithms including Common Angle Search (CAS), Second Order Difference Array (SODA) and SODA-Based Inference (SBI) methods are compared for a linear array and the CAS method is selected as the appropriate algorithm. An optimized two dimensional cross form antenna array is devised by two orthogonal linear arrays. A cubic set for full coverage, has been proposed as the implementation of two dimensional wideband direction finding system with 360° azimuth and ±45° elevation coverage, and its resolution in presence of additive noise and the channel phase tracking error is evaluated.

Modeling and Quantitative Analysis of GNSS/INS Deep Integration Tracking Loops in High Dynamics.

To meet the requirements of global navigation satellite systems (GNSS) precision applications in high dynamics, this paper describes a study on the carrier phase tracking technology of the GNSS/inertial navigation system (INS) deep integration system. The error propagation models of INS-aided carrier tracking loops are modeled in detail in high dynamics. Additionally, quantitative analysis of carrier phase tracking errors caused by INS error sources is carried out under the uniform high dynamic linear acceleration motion of 100 g. Results show that the major INS error sources, affecting the carrier phase tracking accuracy in high dynamics, include initial attitude errors, accelerometer scale factors, gyro noise and gyro g-sensitivity errors. The initial attitude errors are usually combined with the receiver acceleration to impact the tracking loop performance, which can easily cause the failure of carrier phase tracking. The main INS error factors vary with the vehicle motion direction and the relative position of the receiver and the satellites. The analysis results also indicate that the low-cost micro-electro mechanical system (MEMS) inertial measurement units (IMU) has the ability to maintain GNSS carrier phase tracking in high dynamics.

Sine phase compensation combining an amplitude phase controller and a discrete feed-forward compensator for electro-hydraulic shaking tables

This article presents a novel control strategy on an electro-hydraulic shaking table under the acceleration control combining an amplitude phase controller and a zero phase error tracking controller with a discrete feed-forward compensator. Because of the electro-hydraulic system’s nonlinearity, phase delay and amplitude attenuation exist in the acceleration response signal inevitably when the electro-hydraulic shaking table system is excited by a sine vibration signal. Moreover, the phase delay of the electro-hydraulic shaking table is composed of phase deviation and actuator delay. For improving the acceleration tracking accuracy, an amplitude phase controller is employed to compensate the phase deviation and amplitude attenuation by introducing weights to adjust the reference signal. Meanwhile, the discrete feed-forward compensator is applied to compensate the actuator delay. As an offline compensator, the zero phase error tracking controller is employed to compensate the phase delay of the response signal and improve the convergence speed of the proposed controller. Overall, the proposed control strategy combines the merits of these three controllers with better tracking performance demonstrated by simulation and experimental results.

The high dynamics tracking capability for power descending in Chinese Chang’E-3 mission

As the exploration into the lunar and deep space becomes more diverse and profound, the flight process of the spacecraft is quite complex, which highly demands flight status monitoring and precise navigation. Accurate phase recovery in radio telecommunication is essential. This paper demonstrates the high dynamic tracking capability for power descending in Chinese Chang’E-3 mission, using open loop data recoding along with software phase lock loop tracking. Raw data recorded by Chinese Jiamusi and Kashi big antennas, as well as ESA’s New Norcia big antenna, have been used to recover the Doppler frequency for almost all the power descending phase. The standard deviation of phase tracking errors is around 5°. The phase tracking results and its variation characteristics are highly correlated with the flight events happening. The high dynamic phase tracking capability demonstrated in this paper have large flexibility and could be applied to flight operations in the future lunar and deep space missions.

Dual‐mode LQR‐feedforward optimal control for non‐minimum phase boost converter

A digital dual-mode linear quadratic regulator (LQR) with feedforward optimal controller is presented, which allows voltage control of a boost converter for wide-load-range condition, whether in continuous conduction mode (CCM) or in discontinuous conduction mode (DCM). Based on the conventional LQR method, the proposed controller is designed and makes the following two improvements. First, in order to eliminate the phase error caused by right-half-phase zero emerged in non-minimum phase boost converter, a feedforward controller is implemented by zero phase error tracking control technique because the inverse of non-minimum phase system is unstable. Second, since the models of DC-DC converter in CCM or DCM are different, the proposed control strategy allows boost converter to autonomously operate in CCM or DCM controller by utilising a mode detector. The proposed mode detector greatly enhances the control performance in both operating modes. Finally, the proposed controller has been implemented for voltage control of a boost converter. The simulation and experimental results show the proposed controller offers better performance in both transient response and frequency response than the conventional LQR controller.