Model Of Phase-locked Loop Research Articles

Adaptive QSMO-Based Sensorless Drive for IPM Motor with NN-Based Transient Position Error Compensation

In commercial electrical equipment, the popular sensorless drive scheme for the interior permanent magnet synchronous motor, based on the quasi-sliding mode observer (QSMO) and phase-locked loop (PLL), still faces challenges such as position errors and limited applicability across a wide speed range. To address these problems, this paper analyzes the frequency domain model of the QSMO. A QSMO-based parameter adaptation method is proposed to adjust the boundary layer and widen the speed operating range, considering the QSMO bandwidth. A QSMO-based phase lag compensation method is proposed to mitigate steady-state position errors, considering the QSMO phase lag. Then, the PLL model is analyzed to select the estimated speed difference for transient position error compensation. Specifically, a transient position error compensator based on a feedback time delay neural network (FB-TDNN) is proposed. Based on the back propagation learning algorithm, the specific structure and optimal parameters of the FB-TDNN are determined during the offline training process. The proposed parameter adaptation method and two position error compensation methods were validated through simulations in simulated wide-speed operation scenarios, including sudden speed changes. Overall, the proposed scheme fully mitigates steady-state position errors, substantially mitigates transient position errors, and exhibits good stability across a wide speed range.

Subsynchronous oscillation suppression strategy of wind turbine’s phase-locked loop based on optimal damping ratio

The dynamic characteristics of the phase-locked loop (PLL) of the wind turbine are the key to the synchronous operation of these renewable energy sources with the power grid. In this paper, the coupled dynamic model of PLL of the permanent magnet synchronous generator (PMSG)-base wind turbine and power grid is established firstly. The complex torque method is used to calculate the synchronous and damping torque coefficients in the PLL oscillation mode. Secondly, the influence of the PLL parameter, voltage at the point of common coupling (PCC), wind turbine’s output power and electrical distance on the oscillation damping behavior of the PLL is analyzed. Further, a novel control strategy based on optimal damping ratio is proposed to suppress the subsynchronous oscillation of the system caused by wind turbine’s PLL in weak interconnected grids. Finally, a simulation model of regional power network with high penetration of wind power generation is built to demonstrate the effectiveness of the proposed control scheme in suppressing the system’s subsynchronous oscillation caused by the wind turbine’s PLL.

The Gardner Problem on the Lock-In Range of Second-Order Type 2 Phase-Locked Loops

Phase-locked loops (PLLs) are nonlinear automatic control circuits widely used in telecommunications, computer architecture, gyroscopes, and other applications. One of the key problems of nonlinear analysis of PLL systems has been stated by Floyd M. Gardner as being “to define exactly any unique lock-in frequency.” The lock-in range concept describes the ability of PLLs to reacquire a locked state without cycle slipping and its calculation requires nonlinear analysis. The present work analyzes a second-order type 2 phase-locked loop with a sinusoidal phase detector characteristic. Using the qualitative theory of dynamical systems and classical methods of control theory, we provide stability analysis and suggest analytical lower and upper estimates of the lock-in range based on the exact lock-in range formula for a second-order type 2 PLL with a triangular phase detector characteristic, obtained earlier. Applying phase plane analysis, an asymptotic formula for the lock-in range which refines the existing formula is obtained. The analytical formulas are compared with computer simulation and engineering estimates of the lock-in range. The comparison shows that engineering estimates can lead to cycle slipping in the corresponding PLL model and cannot provide a reliable solution for the Gardner problem, whereas the lower estimate presented in this article guarantees frequency reacquisition without cycle slipping for all parameters, which provides a solution to the Gardner problem.

The Influence of On-Orbit Micro-Vibration on Space Gravitational Wave Detection

Large-aperture space telescopes have played an important role in space gravitational wave detection missions. Overcoming the influence of the space environment on interstellar laser distance measurement and realistic high-concentration laser distance measurement is one of the topics that LISA and Taiji are working hard on. It includes solar temperature, spatial stress relief, pointing shake and tilt, etc. However, when considering the impact of vibration on the telescope, both LISA and Taiji only consider the resonance impact of vibration on structural parts, which greatly ignores the impact of high-frequency micro-vibration on space ranging. This paper first considers space gravitational wave detection. Then, we establish the heterodyne interference model and demodulation algorithm of the optical phase-locked loop, and then introduce the vibration component for theoretical analysis. The results show that, although the resonance effect of low-frequency vibration on the system structure is avoided in space gravitational wave detection, the influence of high-frequency micro-vibration on heterodyne interference cannot be ignored. At the same time, we quantitatively analyze the influence efficiency of amplitude and frequency; in the premise of small amplitudes, the influence of vibration frequency is related to the frequency of the heterodyne signal, which has important guiding significance in engineering.

Robust Subsynchronous Damping Control of PMSG-Based Wind Farm

This paper provides an H∞ robust control strategy for a permanent magnet synchronous generator (PMSG)-based wind farm to realize subsynchronous resonance suppression (SSR) subject to uncertain system distortions and parameter perturbation. Firstly, an eighth-order state space mathematical model of a PMSG-based wind farm is established, including the grid-side converter (GSC), GSC controller, and phase-locked loop (PLL) model. Secondly, the SSR characteristics of a PMSG-based wind farm are analyzed through eigenvalue analysis. Thirdly, a robust subsynchronous damping controller is designed based on eigenvalue analysis of SSR. Finally, the designed robust subsynchronous damping controller is validated with case studies of wind farms. The results show that the controller can increase the stability of PMSG-based wind farm systems and restrain SSR.

NSRR Microwave Sensor Based on PLL Technology for Glucose Detection

Microwave biosensor shows great potential in mediator-free glucose detection. However, most microwave biosensors are passive devices; therefore, the high-stability and SNR frequency spectrum are necessary for ensuring the detection precision. In this article, a nested split-ring resonator (NSRR) microwave sensor integrated with phase-locked loop (PLL) technology is proposed for building a portable glucose detection system. PLL drives the NSRR operating at the specific frequency, in which the insertion loss is utilized to characterize the glucose level. By establishing the noise contribution model of PLL to NSRR, the loop parameters of PLL are optimized for higher linearity and sensitivity. The results show that when the loop bandwidth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> is set to 20 kHz for a Type-II fourth-order PLL, −76.3 dBc of spur suppression is achieved in the noise-sensitive area (660–760 MHz). In this case, the operation frequency is set at 743 MHz to realize a sensitivity of 17.2 dB/mg mL−1 and linearity of 0.97 for glucose detection.

On the limit behavior of second-order analog phase-locked loops

The study of limit behavior of a dynamical system is necessary for nonlinear analysis and computation of the exact boundary of global stability in the parameters’ space. For phase-locked loops (PLLs), a problem of its global stability is equal to a problem of a pull-in range calculation, which is one of the key stability characteristics of a PLL. In this paper, we consider a model of a second-order analog PLL and show that it can exhibit a wide range of limit behavior, including cycles and polycycles of the first and second kind.

Modeling, Stability, and Design of the Single-Phase SOGI-Based Phase-Locked Loop Considering the Frequency Feedback Loop Effect

For single-phase grid-connected inverters, the second-order generalized integrator-based phase-locked loop (SOGI-PLL) is widely used for good harmonics attenuation and frequency adaptability. However, existing studies usually neglect the frequency feedback loop in the modeling and design process, and thus, the potential instability caused by the frequency feedback loop is not well explained. Besides, the improper design of SOGI-PLL can lead to the inverter instability both under ideal and weak grid conditions. Therefore, by fully considering the coupling of the frequency feedback loop, this article establishes an accurate model for SOGI-PLL. Furthermore, effects of different PLL parameters on behaviors of both the SOGI-PLL itself and the inverter are studied, based on which a graphical method for PLL parameters design is proposed. As proved, the frequency feedback loop can deteriorate the stability and performance of both SOGI-PLL itself and inverter system, especially if rapid transient is expected. The modeling method is also extended to the low-pass filter-SOGI-PLL and the improved parameters design is discussed. Experimental results verify the correctness of the proposed PLL model and the abovementioned analysis results. The proposed model is helpful to deeply reveal the instability mechanism and provides a reference for the PLL design under nonideal grid conditions.

Weak-light phase locking aided by frequency division phase meter for intersatellite laser interferometry

Weak light phase locking is an important part of intersatellite laser interference ranging. Phase-locked loop (PLL) is used to track the phase of heterodyne interference optical signal. Owing to shot noise, laser frequency and other kinds of noise, there is a phase difference between the internal PLL local oscillator and the heterodyne signal, while the phase detection range of the PLL is only one period. If the phase difference exceeds the phase detection range at a certain time, the local oscillator may enter the wrong operating point under feedback regulation, resulting in cycle clip, which leads to subsequent phase reconstruction errors. In this paper, a cycle clip diagnosis method based on the detection background of gravitational waves is proposed. Based on the original PLL, an auxiliary frequency phase divider with larger phase detection range is introduced, which can provide a basis for judging whether the cycle clip occurs in the PLL. In this paper, a digital weak-light PLL model is established to evaluate the influence of various noise. The theoretical spectral density of the error phase is given according to the two main kinds of noise (laser phase noise and particle noise). Considering the limited detection range of PLL, large error phase may lead to cycle clip, making the PLL work at the wrong locking point. A phase meter with smaller frequency division phase range can be used to solve this problem. First, the input heterodyne sine signal is converted into in-phase square wave N frequency division. Then the phase difference is determined by comparing the output signal with output signal reduced by 1/&lt;i&gt;N&lt;/i&gt; through the time-to-degital converter (TDC) Based on the theory of PLL and noise, the theoretical model of frequency division phase meter is established. The simulation results show that the frequency division phase meter can realize a wide range of phase detection under the current theoretical framework and has the ability to judge the cycle clip of weak light phase locking. It can be used in the weak- light phase locking task represented by LISA.

RESEARCH OF SYNCHRONIZATION CIRCUITS FOR DIGITAL COMMUNICATION SYSTEMS

In a digital communication system, the transmitter and receiver have several generators for modulation and demodulation; increasing and decreasing the sampling frequency; synchronization of symbols and bit streams. The causes of phase and carrier frequency errors are the instability of the frequency of the local generators of the transmitter and receiver; presence of Doppler frequency shift; signal propagation delay from the transmitter to the receiver. Synchronization circuits of modern digital communication systems are built on the basis of phase-locked loop (PLL). The purpose of the work is: research of various characteristics of the digital PLL (locking time; established error; transient behavior) for various types of input action; study of the bit error rate of a coherent digital communication system. The PLL consists of the following components: a phase detector that generates a signal that varies in proportion to the phase difference between the input signal and a locally generated sinusoid; controlled generator that generates an output signal whose phase and frequency depends on the input signal; loop filter, which removes unwanted high-frequency components in the output signal of the phase detector and forms a signal that controls the NCO. During adaptation, the PLL has some transient process that depends, in particular, on three factors: the presence of a zero-phase error is determined by the PLL contour filter; the determined bandwidth of the circuit and the initial deviation between the input and reference frequencies affect the PLL adaptation time; the attenuation coefficient of the PLL affects the adaptation behavior: the speed and magnitude of emissions. The study of the output signal of the linear PLL model for damping factor , and , and we will use an input signal of the step function type, linear voltage changes and hyperbola. type 1, type 2, and type 3 PLLs can adapt to a zero-error step input. If the input signal is a linearly varying voltage, PLL types 2 and 3 can adapt with zero phase error, while type 1 adapts with a residual phase error. For hyperbola input, only type 3 PLL can fully adapt: type 2 adapts with residual error, while type 1 cannot adapt. The damping factor should be in the range of . When changing the input signal frequency from 3.55 MHz to 3.72 MHz, the capture time of the type 2 PLL changes from about 150 μs to about 600 μs, that is, when the frequency increases by 170 kHz, the capture time increases almost four times. The error that has occurred is affected by the choice of the contour filter and the features of the synchronization.

A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> and 2 °/h, respectively.

A Multivariable Controller in Synchronous Frame Integrating Phase-Locked Loop to Enhance Performance of Three-Phase Grid-Connected Inverters in Weak Grids

This article presents a new current controller in the synchronous reference frame and its associated design for enhancing the performance of three-phase grid-connected inverters, especially against weak-grid conditions. The existing controllers do not perform strongly during high-impedance grid conditions and lead to oscillations and instability issues due to the interactions between the synchronization and control units. The proposed controller addresses this issue by 1) deriving a linear model of the three-phase phase-locked loop (PLL), 2) integrating the PLL model into the current controller design, 3) using a multivariable control design for multi-input multi-output systems, and 4) designing the controller gains using optimal linear quadratic theory. The proposed controller has superior performance over a substantially wider range of weak-grid conditions compared to conventional controllers. Extensive simulation and experimental results are presented in order to validate and reveal the desirable performance of the proposed controller.

Adaptive Neural Network for a Stabilizing Shunt Active Power Filter in Distorted Weak Grids

Harmonics destructively impact the performance and stability of power systems. This paper proposes the development of a stable shunt active power filter (SAPF) for harmonics mitigation. The proper and stable operation of the SAPF control system requires the determination of the current reference, phase angle synchronization, and DC-link voltage regulation. This paper uses an artificial neural network (ANN) and one of its sub-methods, the adaptive linear neuron (ADALINE), to determine the current reference. However, determining the current reference requires providing a stable phase angle, which is a fundamental challenge in distorted grids because harmonics created in the grid cause phase angle synchronization problems, due to malfunction of the conventional phase-locked loop (PLL). These things considered, the weak grid connection imposes an instability issue due to the poor performance of the conventional PLL when the grid impedance is high. In this paper, a robust synchronous filter (RSF) is adopted, which separates the harmonic from the main component to provide harmonics-free signals for the PLL. Using RSF, a robust synchronizer quasi-static filter (RSQSF) PLL model is designed, which is effective in dealing with harmonics in weak-grid conditions. MATLAB Simulink was used to check the validation and effectiveness of the proposed control structure. The results show a reduction in harmonics generated in the grid by 86.7% for nonlinear load with a balanced source, 84% for nonlinear load with an unbalanced source under grid impedance, and 80.46% for the nonlinear load with an unbalanced source under weak-grid conditions.

Accurate LTP Model and Stability Analysis of the Second-Order Generalized Integrator-Based Single-Phase Phase-Locked Loop

This article focuses on the modeling and stability analysis of the typical single-phase phase-locked loop (PLL) based on second-order generalized integrator (SOGI). Traditionally, SOGI-based PLL (SOGI-PLL) is linearized as the linear time-invariant (LTI) model for the stability analysis and parameter design. Yet, the PLL has periodical nature due to the periodical variation of the grid voltage. The traditional LTI model for PLL thereby reduces the precision of stability analysis. For addressing this problem, an accurate linear time-periodic (LTP) model of the single-phase SOGI-PLL is proposed in this article. The proposed model can precisely characterize the coupling nature of phase, frequency, and amplitude estimated by SOGI-PLL. A precise stability region of SOGI-PLL, thereby, can be derived from the proposed LTP model. The effectiveness of the proposed LTP model for SOGI-PLL is verified by simulation and experimental tests.

Time-domain modelling and performance research of millimeter-wave all-digital phase-locked loop

In this paper, a modified time-domain model of millimeter-wave all-digital phase-locked loop (ADPLL) is implemented. In order to reflect the true behaviour of ADPLL, a quantified output digitally controlled-oscillator (DCO) with time domain jitter is proposed. In this ADPLL time-domain model, the DCO model can only output discrete frequency points to imitate the quantization effect of true DCO, and the overlap of different level tuning band is added into this model to imitate the true situation. In addition, the DCO time domain jitter and wander are also added into this model by using the Box-Muller method. Finally, a period estimation method is used to calculate the phase power spectrum density of the output signal, and then the phase noise is obtained through subsequent processing.

Improved MIMO Modeling and Enhanced Transient Performance of Phase-Locked Loop During Grid Fault

A phase-locked loop (PLL) is commonly used in grid-connected power converter for synchronization. A single input single output (SISO) linear model of PLL with the phase angle of the point of common coupling (PCC) voltage as input and the estimated phase angle as the output is generally used in the PLL analysis and design. However, an undesirable coupling between the magnitude and phase of the input voltage is present when a filtering stage is incorporated before the control loop, which a SISO model cannot capture, and could result in a significant disturbance in the PLL estimated phase during grid faults. This paper proposes a generalized multi-input multi-output (MIMO) linear model that captures the complete PLL dynamics during symmetrical faults for a PLL equipped with any prefilter. Furthermore, a compensation method that decouples the magnitude dynamics of the input voltage from the phase dynamics is proposed in this paper. The proposed compensation improves the PLL's phase tracking performance by ensuring that the prefiltered PLL acts only on the PCC voltage phase changes. A vital application of the proposed compensation method for PLL is during a grid fault case, wherein the converters are expected to contribute to the fault current, which requires an accurate measurement of the PCC voltage phase. The compensation method's effectiveness is demonstrated using power hardware in the loop simulation of a hardware voltage source converter interfaced to a distribution system simulated in real-time.

Identification of Phase-Locked Loop System From Its Experimental Time Series

Phase-locked loops (PLLs) are now widely used in communication systems and have been a classic system for more than 60 years. Well-known mathematical models of such systems are constructed in a number of approximations, so questions about how they describe the experimental dynamics qualitatively and quantitatively, and how the accuracy of the model description depends on the dynamic mode, remain open. One of the most direct approaches to the verification of any model is its reconstruction from the time series obtained in experiment. If it is possible to fit the model to experimental data and the resulting parameter values are close to the expected values (calculated from the first principles), the quantitative correspondence is nearly proved. In this brief, for the first time, the equations of the PLL model with a bandpass filter are reconstructed from experimental signals of the generator in various modes. The reconstruction shows that the model known from literature generally describes the experimental dynamics in regular and chaotic regimes. The relative error of parameter estimation is between 2% and 50%. The reconstructed nonlinear function of phase is not harmonic and highly asymmetric in contrast to model one.

A Class of Nonlinear Active Disturbance Rejection Loop Filters for Phase-Locked Loop

It is well-known that a phase-locked loop (PLL) technique is widely used in engineering scenarios, recovering and synthesizing the phase and frequency values. The loop filter is the core part of the PLL. This article proposes a class of nonlinear active disturbance rejection loop filters for the PLL. First, we present the detailed nonlinear mathematical model of PLL in consideration of the phase unbalancing, the voltage harmonics, and the voltage offset. Next, based on the model, a class of nonlinear active disturbance rejection loop filters with different nonlinearity degree-of-freedom are proposed in the synchronous reference frame, which can make the PLL in possession of better performance in comparison with that of PLL designed by traditional methods. Moreover, the parameter tuning rules of the nonlinear loop filters are given. Furthermore, hardware-in-the-loop experiments are finished in the dSPACE platform so as to check the real-time performance of the loop filters in more electronic aircraft power grid system scenario. At last, we conclude that the loop filter with the nonlinear generalized integrator extended state observer type2 possesses the best performance among the three loop filters for PLL in this article.

Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control* *Project supported by the Center for Nonlinear Systems, Chennai Institute of Technology, India (Grant No. CIT/CNS/2020/RD/061).

A fractional-order difference equation model of a third-order discrete phase-locked loop (FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.

Chaos and bifurcation in time delayed third order phase-locked loop

In this paper, the modern nonlinear theory is applied to a third order phase locked loop (PLL) with a feedback time delay. Due to this delay, different behaviors that are not accounted for in a conventional PLL model are identified, namely, oscillatory instability, periodic doubling and chaos. Firstly, a Pade approximation is used to model the time delay where it is utilized in deriving the state space representation of the PLL under investigation. The PLL under consideration is simulated with and without time delay. It is shown that for certain loop gain (control parameter) and time delay values, the system changes its stability and becomes chaotic. Simulations show that the PLL with time delay becomes chaotic for control parameter value less than the one without time delay, i.e, the stable region becomes narrower. Moreover, the chaotic region becomes wider as time delay increases.