Showing papers on "Transfer function published in 2018"
TL;DR: In this article, the authors investigated the usefulness of the Bode diagram in calculus including classical and fractional derivatives and proved that fractional derivative with continous kernel are best to model real world problems, as they do not inforce a nonsingular model to become singular due to the singularity of the kernel.
Abstract: The paper is devoted to investigate three different points including the importance, usefulness of the Bode diagram in calculus including classical and fractional on one hand. On the other hand to answer and disprove the statements made about fractional derivatives with continuous kernels. And finally to show researchers what we see and we do not see in a commutative world. To achieve this, we considered first the Caputo–Fabrizio derivative and used its Laplace transform to obtain a transfer function. We represented the Bode, Nichols, and the Nyquist diagrams of the corresponding transfer function. We in order to assess the effect of exponential decay filter used in Caputo–Fabrizio derivative, compare the transfer function associate to the Laplace transform of the classical derivative and that of Caputo–Fabrizio, we obtained surprisingly a great revelation, the Caputo–Fabrizio kernel provide better information than first derivative according to the diagram. In this case, we concluded that, it was not appropriate to study the Bode diagram of transfer function of Caputo–Fabrizio derivative rather, it is mathematically and practically correct to see the effect of the kernel on the first derivative as it is well-established mathematical operators. The Caputo–Fabrizio kernel Bode diagram shows that, the kernel is low past filter which is very good in signal point of view. We consider the Mittag–Leffler kernel and its corresponding Laplace transform and find out that due to the fractional order, the corresponding transfer function does not exist therefore the Bode diagram cannot be presented as there is no so far a mathematical formula that help to find transfer function of such nature. It is therefore an opened problem, how can we construct exactly a transfer function with the following term ( i w ) α ( i w ) α + b for instance? We proved that fractional derivative with continous kernel are best to model real world problems, as they do not inforce a non-singular model to become singular due to the singularity of the kernel. We show that, by considering initial time to be slightly above the origin then the Riemann–Liouville and Caputo-power derivatives are fractional derivatives with continuous kernel. We considered some interesting chaotic models and presented their numerical solutions in different ways to show what we see or do not see if a commutative world. To end, we presented the terms to be followed to provide a new fractional derivative.
128 citations
TL;DR: In this article, a convolutional neural network (CNN) was used to recover the complex object information in a network training process for Fourier ptychography forward imaging.
Abstract: Fourier ptychography is a recently developed imaging approach for large field-of-view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolutional neural network (CNN) and recover the complex object information in a network training process. In this approach, the input of the network is the point spread function in the spatial domain or the coherent transfer function in the Fourier domain. The object is treated as 2D learnable weights of a convolutional or a multiplication layer. The output of the network is modeled as the loss function we aim to minimize. The batch size of the network corresponds to the number of captured low-resolution images in one forward/backward pass. We use a popular open-source machine learning library, TensorFlow, for setting up the network and conducting the optimization process. We analyze the performance of different learning rates, different solvers, and different batch sizes. It is shown that a large batch size with the Adam optimizer achieves the best performance in general. To accelerate the phase retrieval process, we also discuss a strategy to implement Fourier-magnitude projection using a multiplication neural network model. Since convolution and multiplication are the two most-common operations in imaging modeling, the reported approach may provide a new perspective to examine many coherent and incoherent systems. As a demonstration, we discuss the extensions of the reported networks for modeling single-pixel imaging and structured illumination microscopy (SIM). 4-frame resolution doubling is demonstrated using a neural network for SIM. The link between imaging systems and neural network modeling may enable the use of machine-learning hardware such as neural engine and tensor processing unit for accelerating the image reconstruction process. We have made our implementation code open-source for researchers.
79 citations
TL;DR: In this article, it was shown that canceling the reflection at the actuated boundary will yield zero delay robustness for systems with strong reflections, and that the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop.
Abstract: We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff between convergence rate and delay robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay robustness. Indeed, for such systems, using a backstepping controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.
69 citations
TL;DR: The harmonic transfer matrix (HTM) is used to model the frequency shift existing in the sequence-domain impedance model and, by unifying positive sequence and negative sequence components, the complexity of impedance model derivation can be reduced.
Abstract: The sequence-domain impedance using harmonic linearization technique can well describe the harmonic behavior of the interconnected system consisting of the grid and converter. However, fast phase-locked loop (PLL) design, unbalanced current controller structure will cause the unneglectable off-diagonal components in impedance matrix of converter. Due to the frequency coupling and sequence coupling effect in the sequence domain, the traditional single input single output transfer function lacks the capability to accurately express this frequency shift relationship. Therefore, in this paper, the harmonic transfer matrix (HTM) is used to model the frequency shift existing in the sequence-domain impedance model. By unifying positive sequence and negative sequence components, the complexity of impedance model derivation can be reduced. The linear time-periodic system is transformed to a linear time-invariant system in harmonic domain. And then, Nyquist criteria is applied to analyze the stability of the interconnected system. Finally, simulation results verify the proposed HTM-based sequence-domain impedance modeling method.
54 citations
TL;DR: In this article, the authors derive compact equations describing the modification of amplified spontaneous emission signal beat noise arising from optical and electrical filtering in optically preamplified direct detection receivers.
Abstract: We derive compact equations describing the modification of amplified spontaneous emission signal beat noise arising from optical and electrical filtering in optically preamplified direct detection receivers. In particular, we show that this modification typically results in a further decrease of the signal quality factor. This is particularly pronounced in the presence of electrical filters with steep transfer functions such as, e.g., occurring when feeding the signal through an antialiasing filter prior to analog-to-digital conversion or in a real-time oscilloscope, in the latter case leading to counter-intuitive dependencies of the measured signal quality on the characteristics of the test setup. Predictions are exemplified in concrete system models and verified with experiments. While the modeling assumptions and the accuracy of the predictions are in line with models previously reported in the literature, derived expressions allow straightforwardly tying the modification of the level dependent noise to signal levels, baud rate, signal spectrum, and filter transfer functions.
53 citations
TL;DR: In this paper, a two-degree-of-freedom (2DOF) control scheme for voltage compensation in a dynamic voltage restorer (DVR) power circuit is presented.
Abstract: This paper presents a two degrees of freedom (2DOF) control scheme for voltage compensation in a dynamic voltage restorer (DVR). It commences with the model of the DVR power circuit, which is the starting point for the control design procedure. The control scheme is based on a 2DOF structure implemented in a stationary reference frame ( $\alpha \text{--}\beta$ ), with two nested controllers used to obtain a passband behavior of the closed-loop transfer function, and is capable of achieving both a balanced and an unbalanced voltage-sag compensation. The 2DOF control has certain advantages with regard to traditional control methods, such as the possibility of ensuring that all the poles of the closed-loop transfer function are chosen without the need for observers and reducing the number of variables to be measured. The use of the well-known double control-loop schemes that employ feedback current controllers to reduce the resonance of the plant is, therefore, unnecessary. A simple control methodology permits the dynamic behavior of the system to be controlled and completely defines the location of the poles. Furthermore, extensive simulations and experimental results obtained using a 5-kW DVR laboratory prototype show the good performance of the proposed control strategy.
53 citations
TL;DR: The reduction methodology is developed based on separately clustering the generators and loads according to their behavior dissimilarities and the characteristic matrix of the resulting clustering is adopted for the Galerkin projection to derive explicit reduced-order power models and controllers.
Abstract: This paper considers the network structure preserving model reduction of power networks with distributed controllers. The studied system and controller are modeled as second-order and first-order ordinary differential equations, which are coupled to a closed-loop model for analyzing the dissimilarities of the power units. By transfer functions, we characterize the behavior of each node (generator or load) in the power network and define a novel notion of dissimilarity between two nodes by the $\mathcal {H}_{2}$
-norm of the transfer function deviation. Then, the reduction methodology is developed based on separately clustering the generators and loads according to their behavior dissimilarities. The characteristic matrix of the resulting clustering is adopted for the Galerkin projection to derive explicit reduced-order power models and controllers. Finally, we illustrate the proposed method by the IEEE 30-bus system example.
41 citations
TL;DR: A thorough robustness analysis on a typical kind of fractional-order delay system has been made, and a kind of robust FO proportional and derivative controller is proposed based on phase and gain margins, which can achieve both robustness and satisfactory dynamic performance.
Abstract: Most of the existing controller tuning methods are based on accurate system model and sensitive to some inevitable uncertainties and unmeasurable disturbance. Aiming at this problem, a thorough robustness analysis on a typical kind of fractional-order (FO) delay system has been made in this study. A kind of robust FO proportional and derivative controller is proposed based on phase and gain margins. The tuning methods are demonstrated under different circumstances, namely there is gain variation, time constant variation, order variation or even multiple parameters variations in system transfer function. Simulation results show that the closed-loop control system with the proposed controller can achieve both robustness and satisfactory dynamic performance, and outperform the conventional proportional-integral-derivative controller in all cases.
40 citations
TL;DR: Examination of the performance of both offline and online secondary path modeling algorithms that are used in narrowband active noise control (NANC) systems reveals that disturbances that are sensed by error sensors reduce the convergence rate and accuracy of adaptive system identification.
39 citations
TL;DR: In this article, the coefficients of three fractional-order low-pass transfer functions are presented to aid in the design of these filters based on their arbitrary quality factors, and the results are verified by PSpice simulation of a conveyor-based lowpass filter with fractional order of 1.5 and quality factor Q ǫ = 5.
Abstract: The coefficients of three fractional-order low-pass transfer functions are presented to aid in the design of these filters based on their arbitrary quality factors. These coefficients are found by minimizing the error between these fractional-order transfer functions and the second-order transfer function using numerical least squares optimization. Coefficients and design equations are presented for fractional-orders between one and two. Stability of the transfer functions with the presented coefficients is examined and possibilities of characteristic frequency shifting are shown. The results are verified by PSpice simulation of a conveyor-based low-pass filter with fractional order of 1.5 and quality factor Q = 5.
38 citations
TL;DR: Combining periodic signals with the advanced methods presented in this article provides access to highquality FRF measurements, while the measurement time is reduced by eliminating disturbing transient effects.
Abstract: The aim of this article is to give a tutorial overview of frequency response function (FRF) or impulse response (IR) function measurements of linear dynamic systems. These nonparametric system identification methods provide a first view on the dynamics of a system. As discussed in "Summary," the article discusses three main points. The first replaces classic FRF measurement techniques based on spectral analysis methods with more advanced, recently developed algorithms. User guidelines will be given to select the best among these methods according to four specific user situations: 1) measurements with a high or low signal-to-noise ratio (SNR), 2) systems with smooth or fast-varying transfer functions as a function of the frequency, 3) batch or realtime processing, and 4) low or high computational cost. The second main point is to store the reference signal together with the data. This will be very useful whenever there are closed loops in the system to be tested, including interactions between the generator and the setup. The final point is to use periodic excitations whenever possible. Periodic excitations provide access to a full nonparametric noise model, even under closed-loop experimental conditions. Combining periodic signals with the advanced methods presented in this article provides access to highquality FRF measurements, while the measurement time is reduced by eliminating disturbing transient effects.
TL;DR: A novel approach to low-order SFR modelling of a future power system with a high share of frequency-support-capable VSWTGs has been presented and the developed model facilitates studying power system frequency dynamics by avoiding the need for modelling complex VSWTG systems, while retaining a satisfying level of accuracy.
Abstract: Wind power generation has reached a significant share in power systems worldwide and will continue to increase. As the converter-connected generation reduces the grid inertia, more and more interest has been given to exploiting the kinetic energy and controllability of variable-speed wind turbine generators (VSWTGs) for frequency support. Consequently, the grid frequency dynamics are changing. Thus, it is necessary to include the frequency response of wind power plants in the system frequency response (SFR) model. A novel approach to low-order SFR modelling of a future power system with a high share of frequency-support-capable VSWTGs has been presented. Low-order model of VSWTGs with primary frequency response and natural inertial response has been developed considering different wind turbine operating regimes and compared to the non-linear model for validation. Low-order model has been presented in a symbolic transfer function form. Model accuracy has been discussed and the impact of VSWTG parameters on frequency response has been analysed. The developed model facilitates studying power system frequency dynamics by avoiding the need for modelling complex VSWTG systems, while retaining a satisfying level of accuracy.
TL;DR: In this paper, a variable time step controller for six-step operation is proposed to eliminate the low-frequency oscillation in the phase current in permanent magnet machine drives in a flux weakening region by updating output voltage, sampling phase currents and executing the digital controller synchronized with the variable sampling time.
Abstract: The six-step operation of surface-mounted permanent magnet machine drives in a flux weakening region has many advantages compared to the pulse width modulation mode, such as the reduced switching loss and fully utilized inverter output voltage. However, if the ratio of the sampling frequency to the fundamental frequency is low in fixed sampling system, the low-frequency oscillation in the current can be incurred in the six-step operation. The low-frequency current causes a system stability problem and reduces system efficiency due to an excessive heat and high power loss. Therefore, this paper proposes the variable time step controller for six-step operation. By updating an output voltage, sampling phase currents, and executing the digital controller synchronized with the variable sampling time, the turn on and off switch signals for six-step operation can be generated at the exact moment. As a result, the low-frequency oscillation in the phase current can be eliminated. In addition, the system transfer function of the proposed control method is discussed for the system stability and system dynamic analysis. The effectiveness of the proposed method is verified by the comparative simulation and experimental results.
TL;DR: The Loewner framework for model reduction is extended to the class of linear switched systems and through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system.
Abstract: The Loewner framework for model reduction is extended to the class of linear switched systems. One advantage of this framework is that it introduces a trade-off between accuracy and complexity. Moreover, through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system. Hence, another advantage of the framework is that it does not require the initial system matrices. More exactly, the data used in this framework consists in frequency domain samples of input-output mappings of the original system. The definition of generalized transfer functions for linear switched systems resembles the one for bilinear systems. A key role is played by the coupling matrices, which ensure the transition from one active mode to another.
TL;DR: A novel design of dead-time compensator (DTC) is introduced, which can be used to predict the undelayed output response of any process such that the control design may be focused on the delay-free part of the process for performance optimization.
Abstract: To address the difficulty of controlling industrial processes with long time delay, a novel design of dead-time compensator (DTC) is introduced, which can be used to predict the undelayed output response of any process (no matter stable or unstable) such that the control design may be focused on the delay-free part of the process for performance optimization. Based on the undelayed output estimation, a two-degree-of-freedom (2DOF) control scheme is analytically developed for optimizing the set-point tracking and disturbance rejection, respectively. By proposing the desired transfer functions, the corresponding controllers are analytically derived based on commonly used low-order process models. A notable advantage is that there is a single adjustable parameter in the proposed DTC, as well as in each controller, which can be monotonically tuned to meet a good tradeoff between the prediction (or control) performance and its robustness. Illustrative examples from the literature and a practical application to a temperature control system of a jacketed reactor are used to demonstrate the effectiveness of the proposed predictor-based control scheme.
TL;DR: This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method.
TL;DR: In order to ensure the swiftness of the transient response of the WPT system, a novel control strategy combining one cycle control and proportional differential control (OCC- PD) is proposed and the superiorities of the OCC-PD are proved through the analytic expressions of dynamic characteristic parameters.
Abstract: This paper proposes a novel dynamic analysis and a switching converter control strategy for primary-side voltage controlled wireless power transfer (WPT) system. First, the modeling of the high-order double-sided LCC resonant converter is carried out. By dividing the resonant circuit into three equivalent parts and analyzing their transfer functions, respectively, the approximated boundary of the start-up transient time of the WPT stage is solved analytically. Furthermore, in order to ensure the swiftness of the transient response of the WPT system, a novel control strategy combining one cycle control and proportional differential control (OCC-PD) is proposed. By using switching flow-graph technique, the transfer functions of the buck converter applying the OCC, proportional integral differential, and OCC-PD control are obtained. The superiorities of the OCC-PD are proved through the analytic expressions of dynamic characteristic parameters. The input impedance of the WPT stage cascaded to the buck converter is also derived to evaluate the performance of the whole WPT system. Finally, simulations and experiments are carried out through a 6.6-kW two-stage primary-controlled WPT prototype. The results are in accordance with the theoretical analysis and validate the superiorities of the proposed OCC-PD strategy in the aspects of the transient response and the robustness.
TL;DR: A new and simple method for the identification of a single transfer function that is embedded in a dynamical network that requires knowledge of the local topology only.
TL;DR: The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition.
Abstract: In this paper, fractional-order time delay system modeling is presented using Haar wavelet operational matrix of integration. Therefore, it does not require any prior knowledge of transfer function structure or partial information about fractional differentiation order. It allows the estimation of the implicit time delay parameter together with other model parameters by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition. The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. The efficacy of the approach is verified on various integer and non-integer (fractional) order systems in simulation. For realistic condition, proposed method is verified in the presence of noise in simulation and also demonstrated on the real-time process control temperature system.
TL;DR: In this article, the parabolized stability equations (PSE) are used to build reduced-order models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control.
Abstract: In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.
TL;DR: An acoustic reflective computational metasurface that can independently manipulate the reflection phase and amplitude of an incident acoustic signal and can be used to realize a unique linear spatially invariant transfer function is conceptually realized.
Abstract: The use of metasurfaces has allowed the provision of a variety of functionalities by ultrathin structures, paving the way toward novel highly compact analog computing devices. Here, we conceptually realize analog computing using an acoustic reflective computational metasurface (RCM) that can independently manipulate the reflection phase and amplitude of an incident acoustic signal. This RCM is composed of coating unit cells and perforated panels, where the first can tune the transmission phase within the full range of 2π and the second can adjust the reflection amplitude in the range of 0–1. We show that this RCM can achieve arbitrary reflection phase and amplitude and can be used to realize a unique linear spatially invariant transfer function. Using the spatial Fourier transform (FT), an acoustic analog computing (AAC) system is proposed based on the RCM together with a focusing lens. Based on numerical simulations, we demonstrate that this AAC system can perform mathematical operations such as spatial ...
TL;DR: It is shown that the fractional approach becomes ill-conditioned for some configurations of the poles and zeros of the linear dynamic parts, causing identifiability issues, and a lifted formulation of the estimation problem is proposed, which improves the algorithmic performance in the framework of Newton-based methods.
TL;DR: In this paper, the evolution of the decorrelation bandwidth of intercore crosstalk (IC-XT) based on the modified mode-coupled equations (MCEs) in homogeneous weakly coupled multicore fibers (WC-MCFs) is investigated.
Abstract: We investigate the evolution of the decorrelation bandwidth of intercore crosstalk (IC-XT) based on the modified mode-coupled equations (MCEs) in homogeneous weakly coupled multicore fibers (WC-MCFs). The modified MCEs are numerically solved by combining the fourth order Runge-Kutta method with the compound Simpson integral method. It can be theoretically and numerically observed that the decorrelation bandwidth of IC-XT decreases with transmission distance by fractional linear function. The evolution rule of IC-XT’s decorrelation bandwidth is further confirmed by experiments, which can be used as an evaluation criterion for the channel model. Finally, we propose a new channel model with the coupling matrix of IC-XT generated directly from the phase transfer function (PTF), which is in good agreement with the above evaluation criterion. We believe the proposed channel model can provide a good simulation platform for homogeneous WC-MCF based communication systems.
TL;DR: An online adaptation-gain update method that can extend the inductance robust limit is proposed and the design consideration for the two additional parameters of the proposed method is made by full-digital simulation.
Abstract: For high-velocity/high-precision linear motion systems, one of the most important factors that influence their dynamic performance is the characteristic of the inner current loop. The proportional–integral controller is the most practical strategy used for current control. However, its linear structure and imperfect decoupling capability make it difficult to obtain satisfying transient response under multiple operation conditions. The predictive current control (PCC) is designed as the current controller contributes to its superior performance. The main drawback of the PCC lies in its sensitivity against the unavoidable disturbances due to the parameters mismatch and the unmodeled dynamics. In this paper, an online adaptation-gain update method that can extend the inductance robust limit is proposed. First, by analyzing the closed-loop transfer function of the PCC system in the discrete domain, the effect of disturbances is discussed. Then, to eliminate the static current errors and improve the transient response, an adaptive disturbance observer is introduced. However, the direct dependence of the equivalent integral gain of the observer on the inductance in the controller leads to the deteriorative current response as the larger inductance mismatch exists. Therefore, an improved variable-gain method utilizing the current estimation errors is developed to reduce the current overshoot and the oscillation. Meanwhile, the design consideration for the two additional parameters of the proposed method is made by full-digital simulation. Finally, the effectiveness of the proposed method is uniformly verified with both simulation and experimental results.
TL;DR: A matrix description has been proposed to describe the configurations of frequency compensating multistage amplifiers with feedback networks and according to simulations, the proposed configurations in both voltage and current states show excellence performance versus previous works.
TL;DR: It is mathematically proved that, for a passive and reciprocal network, loss is the necessary condition to realize a negative group delay and the optimum strategy is to place zeros and poles of the transfer function on the left complex plane.
Abstract: In this paper, a systematic synthesis approach is proposed for achieving negative group delay responses using lossy coupling matrix. It is mathematically proved that, for a passive and reciprocal network, loss is the necessary condition to realize a negative group delay. Also, the optimum strategy is to place zeros and poles of the transfer function on the left complex plane. A closed-form relation between the group delay and magnitude is then derived based on this strategy, and followed by a complete synthesis approach using coupling matrix. Two numerical and one experimental examples are finally given to illustrate the proposed synthesis method.
TL;DR: The full PSIJ transfer function model is significantly simplified, which provides physical insights of PSIJ at inverter chains and is successfully validated by SPICE simulations with 130 nm CMOS technology.
Abstract: Precise analytical models of power supply noise induced jitter (PSIJ) at inverter chains are proposed. Based on the piecewise linear approximated I–V curve model, analytical models of local PSIJ transfer functions at local rising and falling edges are derived. The total PSIJ transfer function of an inverter chain output is then estimated by alternately accumulating the local PSIJ transfer function at local rising and falling edges. Based on several assumptions, the full PSIJ transfer function model is significantly simplified, which provides physical insights of PSIJ at inverter chains. Accuracy of the proposed analytical model is successfully validated by SPICE simulations with 130 nm CMOS technology. In addition, properties of the PSIJ transfer function at inverter chains are analyzed based on the proposed model.
TL;DR: In this article, a novel approach for estimation of the thermal impulse response (TIR) functions and determination of the dynamic thermal characteristics of a multilayer facade wall with unknown thermal properties, structure, and dimensions is proposed.
TL;DR: In this paper, a new lumped parameter model is proposed to describe the inertial nature of pipelines with inlet/outlet pressure and flow rate as outer variables in the state space.
Abstract: Many algorithms and numerical methods, such as implicit and explicit finite differences and the method of characteristics, have been applied for transient flow in gas pipelines. From a computational point of view, the state space model is an effective method for solving complex transient problems in pipelines. However, the impulse output of the existing models is not the actual behavior of the pipeline. In this paper, a new lumped parameter model is proposed to describe the inertial nature of pipelines with inlet/outlet pressure and flow rate as outer variables in the state space. Starting from the basic mechanistic partial differential equations of the general one-dimensional compressible gas flow dynamics under isothermal conditions, the transfer functions are first acquired as the fundamental work. With Taylor-expansion and a transformation procedure, the inertia state space models are derived with proper simplification. Finally, three examples are used to illustrate the effectiveness of the proposed model. With the model, a real-time automatic scheduling scheme of the natural gas pipeline could be possible in the future.
TL;DR: Simulation results demonstrate that the estimations can be as accurate as those obtained with relay identification methods for time-driven control systems based on other approaches (state-space, curve fitting, Laplace transform, etc.).
Abstract: This paper presents a method to estimate the parameters of first and second order systems with time delays with different accuracy levels for autotuning of event-based PI control loops. In particular, the event-based sampling condition applied in this work is based on the sampling strategy known as symmetric-send-on-delta (SSOD). The method is based on forcing the system to enter into a limit cycle and on using the information achieved from the oscillation to estimate the transfer function parameters. By manipulating the PI controller, the system can reach different limit cycles as a consequence of the intersections of the Nyquist map of the process with the describing function reciprocal of the event-based sampler. The frequency and amplitude of the limit cycle selected to apply the method define the quality of the estimations, avoiding the inaccuracy that relay identification methods based on describing function produce. Simulation results demonstrate that the estimations can be as accurate as those obtained with relay identification methods for time-driven control systems based on other approaches (state-space, curve fitting, Laplace transform, etc.)