Equivalent Transfer Function Research Articles

Design method of multivariable PI controller for turboprop engine based on equivalent transfer function

Traditional centralized Proportional Integral (PI) controller design methods based on Equivalent Transfer Functions (ETFs) have poor decoupling effect in turboprop engines. In this paper, a centralized PI design method based on dynamic imaginary matrix and equivalent transfer function is proposed. Firstly, a method for solving equivalent transfer functions based on the dynamic imaginary matrix is proposed, which adopts dynamic imaginary matrix to describe the dynamic characteristics of the system, and obtains the equivalent transfer function based on the dynamic imaginary matrix characteristics. Secondly, for the equivalent transfer function, a centralized PI control gain is designed using the Taylor expansion method. Meanwhile, this paper further proves that the centralized PI design method proposed in this paper has integral stability. Considering the impact of altitude and Mach number on turboprop engines, a linear feedforward control method based on the transfer function matrix is further proposed based on the centralized PI controller, and the stability of the entire comprehensive control method is proved. Finally, to ensure the safe and effective operation of the turboprop engine, a temperature and torque limiting protection controller is designed for the turboprop engine. Simulation results show that the centralized PI controller design method and linear feedforward control method proposed can effectively improve the control quality of turboprop engine control systems.

Internal Modal Resonance Analysis for Full Converter-Based Wind Generation Using Analytical Inertia Model

Full converter-based wind generation (FCWG) has become a prevailing choice in new wind farms. It is usually regarded that low short circuit ratio (SCR) or weak grid is a key condition to induce oscillations associated with wind farms. However, we have recently discovered a rare phenomenon that even in a strong grid with a large SCR, the internal modal resonance of FCWG can still lead to oscillations and threaten the converter-driven stability. To determine the internal modal resonance in FCWG, a novel analytical inertia model (AIM) is derived to elaborate all oscillation modes of FCWG (FOMs) for the first time. The derived model reviews the complex relations of all FOMs in a formulaic manner, which not only provides guidance on parameter resetting, but also illuminates how FOMs interact with each other. On this basis, an equivalent transfer function is integrated into the state space equation to characterize the interaction effect, and a universal torque model is proposed to yield insights into the mechanism of internal modal resonance owing to the variation of operating conditions. Furthermore, the effectiveness of AIM is substantiated as well as the analysis method, and the unusual event of internal modal resonance is also demonstrated.

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Assessing the collaborative quality value in nuclear power intelligent construction: A value chain analysis method based on double-layer GERT network

Due to the large number of participants and the multi-dimensional heterogeneity of economic activities, the value creation links are hidden and the value relationship is difficult to identify. Only paying attention to the effect and cost input of a single enterprise’s quality business cannot maximize the value of collaborative quality control, and cannot meet the requirements of nuclear power intelligent construction. Therefore, we propose to use collaborative quality value to characterize the value creation process and coordinate the interest relationship and value distribution among participants. On this basis, a collaborative quality value chain analysis method based on the double-layer GERT network is studied to quantitatively calculate the collaborative quality value. Specifically, the collaborative quality assurance mode is constructed and the interaction behavior among participants is analyzed. The value transfer and enhancement across participants is represented by the double-layer GERT network model, and the global and local values of the value chain are quantitatively measured based on the equivalent transfer function. Then, the key quality assurance business and activities that restrict the whole chain value-added are explored, and the collaborative quality value-added strategies are proposed. Finally, the effectiveness of this method is verified by a case study involving the fabrication of reactor pressure vessel (RPV) support inside a nuclear power project. This study provides a new method for realizing the value evaluation of collaborative quality control and maximizing the collaborative quality value of the whole value chain.

ETF dead-time compensation based multiloop control approach for multivariable processes

Due to significant interaction dynamics and time delays in multivariable processes, designing a well-tuned PI controller is always challenging. When tuning multi-loop PI controllers, effective open-loop transfer function should be used instead of the diagonal transfer function element. The complexity of the effective open-loop transfer function (EOTF) increase rapidly for high-dimensional multivariable processes. Therefore, in this manuscript, it is proposed to use equivalent transfer functions (ETFs) under perfect control approximation. Subsequently, a dead-time compensation (DTC) scheme is used for ETFs and PI controllers are tuned. DTC can facilitate eliminating the impact due to time delay from the multivariable process, making the task of tuning PI controllers relatively less complex. The proposed multi-loop control topology minimizes the controller effort, and a good controller design for a multivariable process can be achieved. The PI controller parameters for dead-time compensated ETFs are calculated using simple IMC PI tuning rules, where the filter factor is taken based on the paired element relative gain value. To examine the effectiveness of the proposed controller tuning approach, the proposed control strategy was applied to a wide range of multivariable processes. Compared to state-of-the-art control strategies, the proposed control strategy provides superior closed-loop performance indices, even when there is a significant plant-model mismatch.

Optimization Strategy for Output Voltage of CCM Flyback Converter Based on Linear Active Disturbance Rejection Control

To solve the problem of system output voltage fluctuation caused by interferences such as load fluctuation and internal inductor parameter perturbation in a flyback converter, a second-order linear active disturbance rejection control (LADRC) strategy based on output voltage is proposed in this paper. A small-signal model of a CCM flyback converter is established, and the equivalent transfer function of voltage control based on second-order LADRC is derived. A second-order LADRC is constructed, and a parameter design method for the controller is proposed. The response characteristics of the output voltage of the converter under five internal and external disturbances of different control strategies are compared and studied using MATLAB R2022b/Simulink simulation software, and a CCM flyback converter experimental platform based on dSPACE is built to verify the corresponding comparative experiments. The simulation and experimental results jointly verify the superiority of the control strategy for the anti-interference and robustness of the output voltage of the CCM flyback converter.

A Novel Data-Driven Self-Tuning SVC Additional Fractional-Order Sliding Mode Controller for Transient Voltage Stability With Wind Generations

This paper proposes a novel data-driven self-tuning additional sliding mode controller for power system transient voltage stability enhancement considering wind integration. We first develop a new additional fractional-order sliding mode controller (FOSMC) for the static var compensator (SVC). The tuning of FOSMC parameter settings is then reformulated as a Markov decision process (MDP) and solved by the deep reinforcement learning (DRL) algorithm. In addition, a data-driven estimation method is proposed for the identification of an equivalent transfer function that is further used to calculate reward during the training process, yielding the model-free training. After that, the well-trained agent allows us to tune the controller parameters considering system uncertainties and achieve robustness against various operating conditions. Comparative results with other state-of-art methods demonstrate that the proposed method can effectively suppress the chattering issue of the sliding mode controller and ensure transient voltage stability under different operating conditions.

An analytical method for phase noise evaluation in a microwave VCO stabilized by an interferometry structure

This study proposes a set of mathematical formulations to model a microwave interferometric structure to stabilize a free-running oscillator. The microwave interferometric structure employed a carrier suppression system to lock the voltage-controlled oscillator (VCO) frequency to a high-Q resonator and clean up the phase noise spectrum. Analytical relations were derived by modeling the system's stabilization loop components with an equivalent system transfer function. This model optimized the feedback loop circuits for a reliable frequency-locked structure with suitable spectral purity using well-known linear system methods. Thus, the phase noise of an oscillator's output signal locked to a high-Q cavity resonant frequency could be predicted and optimized. Furthermore, a prototype cavity-stabilized oscillator (CSO) system with commercial components wasimplemented to validate the proposed model. The results demonstrated that approximately 40 dB phase noise reduction at 10 kHz offset frequency was obtained at X-band, exhibiting good agreement with the proposed mathematical model. Moreover, the prototype structure's feedback circuits were designed, and their performance was validated using simulation and measurement data.

Rapid reconstruction algorithm for multifocal structured illumination microscopy

Multifocal structured illumination microscopy (MSIM) could surpass the diffraction limit by illuminating the sample with multiple-spot grid patterns. Developed as a parallel version of image scanning microscopy (ISM) to enhance data acquisition speed, MSIM can also be viewed as a variation of structured illumination microscopy (SIM) in which the conventional sinusoidal illumination is substituted with a lattice array of spots. This method outperforms regular SIM when imaging samples that are thick or highly scattered. In this study, we present a rapid reconstruction algorithm for MSIM in the spatial domain and demonstrate that the radius of its equivalent optical transfer function (OTF) support is twice that of a general wide-field microscopy in the epi-illumination geometry. Numerical simulations and experimental results have validated the effectiveness of the proposed algorithm.

Research on simplified modeling of large-scale wind farms based on equivalent transfer function and aggregate equivalent

Introduction: In grid-connected research of large-scale wind farms, the problem of long simulation time exists in the research based on detailed model. In order to realize the fast simulation and grid-connected transient research of wind farm, this paper presents a simplified equivalent model of wind farm based on equivalent transfer function and improved capacity weighting method.Methods: This paper analyzes the mathematical model of wind turbine, corresponding to the strategy of design simplification, and the simplified model is built according to the equivalent transfer function. In addition, this paper considers the equivalent line loss model of collector line, classifies and aggregates the simplified wind turbines, and calculates the equivalent value of the converged wind turbines by using the improved capacity weighting method, the grid-connected simplified modeling of large-scale wind farm is realized.Results: A model of wind farm-MMC-HVDC flexible grid-connected wind power system is built. The simulation results show that the simplified equivalent model improves the simulation speed greatly while guaranteeing the dynamic characteristics.Discussion: The simplified equivalent strategy of wind farm can keep the same dynamic performance with the detailed model, and improve the simulation speed, and realize the fast simulation and grid-connected transient research of wind farm.

Transfer Functions and Linear Distortions in Ultra-Wideband Channels Faded by Rain in GeoSurf Satellite Constellations

Because of rain attenuation, the equivalent baseband transfer function of large bandwidth radio-links will not be ideal. We report the results concerning radio links to/from satellites orbiting in GeoSurf satellite constellations located at Spino d’Adda, Prague, Madrid, and Tampa, which are all sites in different climatic regions. By calculating rain attenuation and phase delay with the Synthetic Storm Technique, we have found that in a 10-GHz bandwidth centered at 80 GHz (W-Band)—to which we refer to as “ultra-wideband-, both direct and orthogonal channels will introduce significant amplitude and phase distortions, which increase with rain attenuation. Only “narrow-band” channels (100~200 MHz) will not be affected. The ratio between the probability of bit error with rain attenuation and the probability of bit error with no rain attenuation increases with rain attenuation. The estimated loss in the signal-to-noise ratio can reach 3~4 dB. All results depend on the site, Tampa being the worst. To confirm these findings, future work will need a full Monte Carlo digital simulation.

SIMULATION OF THE SYSTEM OF MINERAL NUTRITION OF PLANTS IN CLOSED SOIL

One of the important factors in the high productivity of growing vegetable crops by the method of small volume of this system of vegetable production is the accurate and timely supply of mineral nutrition to their root system. During hydroponic cultivation, all mineral substances of plants are obtained from their aqueous solutions. In closed soil, the water regime should be regulated taking into account the biological characteristics of the culture, the growth phase and the intensity of light. To successfully implement the plant nutrition process, it is necessary to formulate a mathematical model of the process and equivalent transfer functions. This will make it possible to choose a rational way of management and determine the parameters of management systems. The analysis of the latest researches in the field of automation of processes of nutrition of plants grown in closed soil shows that for each specific case, a scheme of automation of this process was proposed, which led to different results of the implementation of the process of nutrition. To generalize the principles of regulating the supply of nutrient solutions to plants in closed soil, it is necessary to develop real mathematical models of processes and equivalent transfer functions that will allow choosing a rational method of management. The specificity of the object of research determines the need to use the analytical method of obtaining dynamic models as the main one. The mathematical description of the dynamics of mass transfer during drip irrigation includes the value of the evaporative capacity of plants. This value significantly depends on the parameters of the microclimate in the building. To determine the influence of these parameters on the dynamics of liquid transpiration, a mathematical model was obtained in the form of differential equations of heat and material balances. The obtained mathematical models and the structural schemes built on their basis will serve as the basis for creating a system of mineral nutrition of plants in closed soil.

Statistical linearization for random vibration energy harvesting with piezoelectric material nonlinearity

Due to piezoelectric softening and dissipative nonlinearities, the piezoelectric cantilever energy harvester exhibits nonlinear hysteresis when subjected to large excitation. These nonlinearities have brought significant challenges to the modeling and response prediction of randomly excited piezoelectric energy harvesting systems. In this study, the voltage responses of the nonlinear piezoelectric cantilever energy harvester under random excitation are initially assumed to follow the Gaussian distribution which is experimentally validated later. The equivalent linear transfer function are derived from the approximate linearization of the stiffness and damping using the statistical linearization (SL) technique. The mathematical expectations of the voltage responses are calculated from the multivariate normal distributions. Frequency sweep experiments are conducted to a cantilever energy harvester to identify the nonlinear piezoelectric material properties. The statistically linearized model was experimentally validated under random base acceleration excitation by comparing the probability density function of the predicted voltage responses and average power against the experimental measurements. The advantage of the SL technique lies in allowing one to use an iterative procedure to estimate the equivalent linear terms while the analytical expressions are unattainable because of the complex nonlinearity in the governing equations. The results show that the prediction of the SL model to the random base acceleration excitation agrees with experimental measurements with a broadband frequency range, although only the fundamental mode of the beam is considered.

Active Disturbance Rejection Control for Static Power Converters in Flexible AC Traction Power Supply Systems

Flexible traction power supply systems (FTPSSs) can solve problems in traditional systems and envision a promising future for rail transit power supply. The traction network voltage is determined by static power converters (SPCs), so the voltage control of SPCs is very important for the safe and stable operation of the system. The uncertainty of the train load, the power redistribution in the case of SPC disconnections from the network because of SPC internal faults, and the real-time cooperative control of multiple SPCs bring challenges to the voltage control of SPCs. Compared to classical error feedback control, active disturbance rejection control (ADRC) has better transient performance and immunity. An ADRC-based voltage-current dual-loop control strategy for SPCs is proposed in this paper. The equivalent block diagram and transfer function are deduced. The stability and immunity of the system are analyzed. Finally, the effectiveness and superiority of the proposed control strategy under different operating conditions are verified by simulation and experiment.

PS-G-GERT effectiveness evaluation model of link-based GEO satellite communication constellation under poor information background

The effectiveness evaluation of GEO satellite communication constellation not only characterizes the communication capability of the constellation but also provides a basis for optimizing the constellation structure. Whether due to information poverty or the complexity of the system, the impact of uncertain information on the effectiveness evaluation needs to be considered to ensure the accuracy of the evaluation results. To address this issue, this paper develops a model for evaluating the GEO satellite communication constellation's effectiveness in the context of poor information. Firstly, it analyses the GEO satellite communication constellation plus system based on communication links with an in-depth analysis of the constellation structure. Secondly, an equivalent transfer function algorithm based on the characteristic function and transfer probability is proposed with the help of graphical evaluation and review technique. Then, by analyzing the communication link importance connotation, the algorithm formula of communication link effectiveness and its importance is derived, and the constellation effectiveness and variance are found. Finally, the model constructed in this paper is used to evaluate the effectiveness of a GEO satellite communication constellation, further verifying the accuracy and validity of the model. Through comparative analysis, it is shown that the model can not only solving the effectiveness of the constellation but also analyzing the variation of its effectiveness. It lays a theoretical foundation for the analysis and optimization of the GEO satellite communication constellation effectiveness.

An Improved Down-Scale Evaluation System for Capacitors Utilized in High-Power Three-Phase Inverters under Balanced and Unbalanced Load Conditions

The DC-link capacitors in an electronic power system are the main constraint of the power density and lifespan of the power converters. Evaluating the load life of capacitors working in severely adverse circumstances plays an important role in the design stages of the next-generation power converters. In this article, an improved evaluation system for the capacitors utilized in high-power three-phase voltage source inverters is proposed. The purpose of this article is to reproduce the same encountered stresses when a DC-link capacitor is used in a high-power inverter with pulse-width modulation. Hence, an improved down-scale evaluation system for the DC-link capacitors used in high-power three-phase inverter systems under balanced and unbalanced load conditions is proposed. Moreover, AC and DC analyses in the proposed evaluation system are conducted. The equivalent circuit and transfer functions are derived to verify the proposed evaluation system. Finally, a prototype system is constructed to facilitate the theoretical results as the verification.

Determining the dynamic model of the charging resonant converter with inductive coupling by an experimental-analytical method

This paper reports the advanced experimental-analytical method for determining the dynamic model of resonant converters of electricity. The object of research is semiconductor resonance converters and methods for analyzing their dynamics. The well-known experimental-analytical method for determining a dynamic model implements the sequence «experiment – analytics – dynamic model» when the structure of the system may be unknown. Then it is necessary to determine the structures and parameters of many dynamic models, among which the optimal ones will be selected. This makes it difficult to establish usable patterns. Therefore, it is advisable to develop this method, according to which it is proposed to determine the parameters of the dynamic model according to the following sequence. First, carry out the analysis of the converter circuit and construct the dynamic models of sub-circuits. Next, an experiment is conducted with a simulation structural model of the converter, which is an input model of identification. After that, procedures are carried out for identifying and selecting optimal dynamic models among a set of initial identification models, as a result of which equivalent dynamics equations, gear ratios, and transfer functions of the selected converter models are obtained. In the proposed modification of the method, the converter model is determined in advance, and at the identification stage it is enough to determine only its parameters. More simply, patterns are identified, and the number of initial identification models is significantly reduced. The results of using the proposed method on the example of determining the dynamic model of the charging resonance converter with inductive coupling between the charger and the battery of an autonomous object are given. The results of the presented analysis can be used in the design of resonant contactless chargers.

Designing a Compact Microstrip Dual-Band Filter with Two T-Shaped Resonators and Suitable Frequency Selectivity

A miniaturized microstrip dual-band bandpass filter (DBPF) with two T-shaped resonators is proposed. The two T-shaped resonators lead to multiple transmission zeros in the stopband and higher filter selectivity. The filter is analyzed using LC and even/odd mode analyses to determine the transmission zeros. The LC equivalent circuit and transfer function are presented. The proposed filter is symmetrical, so the electrical length and impedance values are used for odd/even mode analysis. The designed DBPF is centered at 1.9/5.54[Formula: see text]GHz and is suitable for WLAN applications. The insertion loss of the filter is less than 0.5[Formula: see text]dB and its return loss is more than [Formula: see text][Formula: see text]dB in each band. Five transmission zeros are created with an attenuation greater than [Formula: see text][Formula: see text]dB. The total area of the proposed filter is [Formula: see text][Formula: see text]mm2. To validate the proper performance of the proposed filter, it is fabricated and measured.

Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

This paper deals with the design problem of multivariable Proportional-Integral-Derivative (PID) controllers for square and stable multivariable processes when a linear margin at the Nyquist plot is considered as robustness specification for each closed loop. A tuning method is developed based on the new concept of equivalent loop transfer function, which is proposed for centralized control and allows an independent design for each loop considering the interactions with the other loops through an iterative procedure. For the k-th loop, the PID parameters of the k-th column of the control matrix are calculated in each iteration by a linear programming optimization that maximizes the integral gains while fulfilling the robustness specification and achieving static decoupling. The method uses a frequency response array as representation of the process, which allows its applicability to systems with multiple time delays without requiring model reductions or approximations. The effectiveness of the method is illustrated by means of two simulation examples with dimensions <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3 \times 3$ </tex-math></inline-formula> . Comparisons with other centralized control methodologies show that the proposed approach achieves similar or greater performance and a remarkable better disturbance rejection response.

Steady-State Performance Analysis of the Distributed FxLMS Algorithm for Narrowband ANC System With Frequency Mismatch

Distributed narrowband active noise control (NANC) systems using diffusion filtered-x least mean square (FxLMS) algorithm can effectively suppress the low-frequency periodic noise generated by rotating machinery. The computational burden is dispersed among the nodes over the acoustic sensor networks. The frequency of the reference signal is usually identified by a non-acoustic sensor in a NANC system. However, the frequency of the reference signal will be different from the primary noise frequency due to inevitable aging and fatigue accumulation and the control performance of NANC degrades considerably. This phenomenon is referred to as frequency mismatch (FM). In this letter, we analyze the performance degradation of the diffusion FxLMS algorithm due to FM in an NANC system. A theoretical model of the diffusion FxLMS algorithm in the presence of FM is derived based on the equivalent transfer function approach. Extensive simulations are performed to confirm the validity of the theoretical analysis.