Linear Transfer Function Model Research Articles

Linear modeling techniques for liquid height regulation in two tank - Two variable system

In this paper, two linear modeling techniques are presented for regulating the liquid height in two tank - two variable system (TT-TVS). Initially, the nonlinear dynamics of TT-TVS are linearized using the Taylor series linearization technique. However, this method reveals that some parameters of TT-TVS are inexact, necessitating the adoption of system identification techniques or mathematical approaches to accurately identify the linear dynamics. To address this, two new approaches are proposed: (i) a mathematical approach utilizing real-time input-output data, and (ii) a Linear Variable Parameter Transfer Function (LVPTF) model identification approach, which employs real-time data and MATLAB curve fitting tool. A comparative analysis between the proposed identification techniques and existing methods from the literature is also presented. The results indicate that the LVPTF modeling technique offers superior accuracy in identifying the linear dynamics of TT-TVS.

Research on Urban Architecture Design under the Concept of Smart City

After the digital city and smart city concepts, the latest proposed smart city concept is a general summary of the advanced form of urban information development, which plays an important role in the economic transformation of cities, social governance, improvement of residents' quality of life and energy conservation and environmental protection. The smart city puts forward new requirements for the architectural design of the city, and how to reasonably use the smart city concept in the architectural design is still a major issue for architects and professionals to think about. To this end, this paper proposes a state tracking based full working condition modeling method for nonlinear industrial systems. For the problem that the amount of historical data is too large and it is difficult to screen the modeling data, a sliding window is designed to screen the steady-state data, and a fast recursive algorithm of standard deviation in the window is derived; the influence mechanism of unknown disturbances on the system is analyzed, and the data modeling by dynamic regression to the steady state is selected, and a data-driven modeling algorithm that can eliminate the influence of disturbances is proposed; the model information contained in the process industrial big data is used to apply the higher order function to fit each A linear variable parameter transfer function model based on the characteristic parameters is proposed. The identification of an industrial process is shown to be effective. The main points of urban architectural design should be noted under the concept of smart city from four aspects: safety, diversity, environmental protection and emotionality.

An adaptive fractional order controller design: A realization for liquid level regulation in liquid level plant

In this paper, an adaptive FO − IλD1−λ controller design is proposed using a frequency domain approach. The proposed adaptive controller parameters are tuned based on the frequency domain specifications. To realize the velocity error constant for the proposed controller, Oustaloup Recursive Approximation (ORA) method is employed. The proposed controller is realized for liquid level regulation in the Liquid Level Plant (LLP). An identification technique is proposed to identify a linear adaptable parameter transfer function (LAPTF) model of LLP. The performance of the proposed controller is compared with the existing works. It is observed that the proposed controller outperforms the existing controllers in the literature.

Automated Data–Driven Model Extraction and Validation of Inverter Dynamics with Grid Support Function

This research focuses on the evolving dynamics of the power grid, where traditional synchronous generators are being replaced by non-synchronous power electronic converter (PEC)-interfaced renewable energy sources. The non-linear dynamics must be accurately modeled to ensure the stability of future converter-dominated power systems (CDPS). However, obtaining comprehensive dynamic models becomes more complex and computationally intensive as the system grows. This study proposes a scalable and automated data-driven partitioned modeling framework for CDPS dynamics. The method constructs reduced-ordered dynamic linear transfer function models using input-output measurements from a PEC switching model. Validation experiments were conducted on single-house and multi-house scenarios, demonstrating high accuracy (over 97%) and significant computational speed improvements (6.5 times faster) compared to comprehensive models. This framework and modeling approach offer valuable insights for efficient analysis of power system dynamics, aiding in planning, operation, and dispatch.

Uncertainty estimation in wave energy systems with applications in robust energy maximising control

Under control action, wave energy devices typically display nonlinear hydrodynamic behaviour, making the design of energy maximising control somewhat onerous. One solution to approach the optimal performance for nonlinear control problem under model mismatches is to employ a linear control strategy, which can be robust to linear model mismatches. However, accurate characterisation of the uncertainty in the linear model is vital, if the controller is to adequately capture the full extent of the uncertainty, while not being overly conservative due to overestimation of the uncertainty. This paper describes a procedure, employing CFD-based numerical tank experiments, to accurately produce a nominal linear empirical transfer function model, along with an accurate estimate of the uncertainty bounds in that linear model, due to hydrodynamic uncertainty. A robust control case study is provided, illustrating the nominal model estimation process, and its corresponding uncertainty set, including the complete procedure, required to generate the robust controller. Robust control results, on the fully nonlinear CFD model, are provided to demonstrate the efficacy of the modelling and control philosophy.

Software Reliability Analysis Using Nonlinear Transfer Function

In the progression of innovation, software plays a meaningful role in society. Hence, the need for reliable software increases day by day. But the development process of software has become very complex. In this paper, a nonlinear transfer function model has been developed to predict the remaining faults present in the software. A stepwise procedure is discussed for developing a nonlinear transfer function model. A comparison with the linear transfer function model has been carried out. Release time modeling has also been carried out. Some real data sets have been used for illustration.

Validation of a dynamic non-linear grinding circuit model for process control

A step-wise algebraic routine is used to fit a dynamic non-linear model, specifically developed for process control, to steady-state process data of an industrial single-stage grinding mill circuit. Step-test data from the industrial plant is used to validate the response of the non-linear model. The results indicate that the model provides a qualitatively accurate response of the main process variables. Because the non-linear model parameters can be calculated from steady-state data, it provides an advantage over classical system identification methods as it does not require an expensive and disruptive step-test campaign to develop linear transfer function models. The model is ideal for model-based predictive process control.

Modeling thermal systems with fractional models: human bronchus application

System thermal modeling allows heat and temperature simulations for many applications, such as refrigeration design, heat dissipation in power electronics, melting processes and bio-heat transfers. Sufficiently accurate models are especially needed in open-heart surgery where lung thermal modeling will prevent pulmonary cell dying. For simplicity purposes, simple RC circuits are often used, but such models are too simple and lack of precision in dynamical terms. A more complete description of conductive heat transfer can be obtained from the heat equation by means of a two-port network. The analytical expressions obtained from such circuit models are complex and nonlinear in the frequency $$\omega $$ . This complexity in Laplace domain is difficult to handle when it comes to control applications and more specifically during surgery, as heat transfer and temperature control of a tissue may help in reducing necrosis and preserving a greater amount of a given organ. Therefore, a frequency-domain analysis of the series and shunt impedances will be presented and different techniques of approximations will be explored in order to obtain simple but sufficiently precise linear fractional transfer function models. Several approximations are proposed to model heat transfers of a human middle bronchus and will be quantified by the absolute errors.

Estimation of Aircraft-Dependent Bumpiness Severity in Turbulent Flight

Atmospheric turbulence threatens flight safety of civil aviation aircraft by inducing aircraft bumpiness. A severity estimation method of aircraft bumpiness in turbulent flight is explored according to in-situ Eddy Dissipation Rate (EDR) indicator. With the turbulence intensity derived from EDR value, a time series of longitudinal and vertical turbulence was generated according to von Karman turbulence model. In order to obtain the vertical acceleration response of aircraft, the continuous change of aerodynamic force on the assembly of wing and horizontal tail was computed by Unsteady Vortex Lattice Method (UVLM). The computing accuracy was improved by using semi-circle division and assigning the vortex rings on the mean camber surface. Furthermore, the adverse effects of control surface deflections on bumpiness severity estimation can be effectively removed by separating turbulence-induced and aircraft maneuvers-induced aerodynamic force change. After that, the variance of vertical acceleration, as the severity indicator of aircraft bumpiness, was obtained by Welch spectrum estimation. With the refined grid level, the pitching moment change due to control surface deflections can be solved accurately by UVLM. The instantaneous acceleration change obtained by UVLM approximates recorded acceleration data with better accuracy than linear transfer function model. A further test with a set of flight data on the same airway shows that compared with in-situ EDR indicator, the proposed method gives an aircraft-dependent estimation of bumpiness severity, which can not only be used to estimate in-situ bumpiness but also be applied to forecast the bumpiness severity of other different aircrafts.

Dynamic analysis and decentralised control system design for diphenyl carbonate reactive distillation process

ABSTRACT Reactive distillation (RD), a process intensified technique, involves integrating reaction and separation in a single unit. High non-linearities associated with the RD process constrict the control degrees of freedom and set the key challenge in designing a robust control system. In the present work, the design is optimised for reactive distillation–diphenyl carbonate and a decentralised feedback control configuration is applied to carry out the control studies. A comparative decentralised control performance is studied for different transfer function models obtained by using analytical and optimisation-based process identification techniques. The controller parameters obtained from the simple internal model control tuning relations are applied to (i) the linear transfer function model and (ii) non-linear plant model. Set-point tracking and load rejection studies are carried out to compare the performance of different models and investigate the non-linear model’s controller performance.

Decadal Oscillation in the Predictability of Palmer Drought Severity Index in California

Severity of drought in California (U.S.) varies from year-to-year and is highly influenced by precipitation in winter months, causing billion-dollar events in single drought years. Improved understanding of the variability of drought on decadal and longer timescales is essential to support regional water resources planning and management. This paper presents a soft-computing approach to forecast the Palmer Drought Severity Index (PDSI) in California. A time-series of yearly data covering more than two centuries (1801–2014) was used for the design of ensemble projections to understand and quantify the uncertainty associated with interannual-to-interdecadal predictability. With a predictable structure elaborated by exponential smoothing, the projections indicate for the horizon 2015–2054 a weak increase of drought, followed by almost the same pace as in previous decades, presenting remarkable wavelike variations with durations of more than one year. Results were compared with a linear transfer function model approach where Pacific Decadal Oscillation and El Niño Southern Oscillation indices were both used as input time series. The forecasted pattern shows that variations attributed to such internal climate modes may not provide more reliable predictions than the one provided by purely internal variability of drought persistence cycles, as present in the PDSI time series.

Modeling of Mixed Artificially and Voluntary Induced Muscle Contractions for Controlled Functional Electrical Stimulation of Shoulder Abduction

Abstract This contribution investigates the modeling of shoulder abduction movements caused by simultaneous voluntary and artificially evoked muscle contractions. The latter are generated by feedback controlled functional electrical stimulation. To maintain a desired level of muscle activation (recruitment) by electrical stimulation also in presence of fatigue, we assess the recruitment in real-time from the M-wave, i.e., the electromyography (EMG) response caused by each applied stimulation pulse, and regulate it by a simple integral controller that adjusts the stimulation intensity. The reference of the FES-induced muscle recruitment serves as one input to the model. The voluntary muscle activity is also determined from EMG recordings by filtering and represents the second model input. A simple linear transfer function model of 2nd order captures the shoulder abduction angle in response to the estimated volitional and FES-induced muscle activity, while the two inputs are summed up after weighting. Least squares have been used to determine the model parameters from recorded input-output data obtained at a neurologically intact subject. The model describes the shoulder abduction movements well for the investigated angular range of 100◦ also under presence of muscular fatigue due to the applied feedback control of the FES-induced muscle activity. A root mean square error of 8◦ has been observed between the simulated and measured angle for validation data covering 5 minutes. The model can be used in future to design FES support systems for stroke patients with weak residual muscle activity. Due to the model’s simplicity, online identification via recursive least squares and adaptive control schemes are feasible.

Data-driven oxygen excess ratio control for proton exchange membrane fuel cell

Efficient oxygen excess ratio (OER) control is of great importance for proton exchange membrane fuel cell because it is closely associated with the economic efficiency and safety. As widely investigated, OER control is challenging due to the difficulties of system nonlinearity, parametric uncertainty and load disturbances. In this paper, an underlying difficulty for OER control is addressed by pointing out the overshoot response. To this end, this paper employs active disturbance rejection control which is able to handle the various difficulties in a data-driven manner. It treats the nonlinearity, uncertainty and disturbances as a lumped term, which is then estimated online via analyzing the real-time data. The estimated lumped term is canceled timely such that the remaining dynamics behaves like an integrator without overshoot term therein. The data-driven and conventional proportional-integral controllers are tuned and compared based on the linearized transfer function model, showing the potential superiority of the proposed method in terms of the uncertainty and disturbance rejection, anti-windup and overshoot reduction. The nonlinear simulation based on the nonlinear mechanism model further demonstrates it good flexibility under different operating conditions. Moreover, it requires less compressor movement efforts, leading to a dynamic energy-saving effect and thus prolonging the durability and lifetime of the compressor.

Black-box modelling of nonlinear railway vehicle dynamics for track geometry assessment using neural networks

ABSTRACTThe use of vehicle dynamics simulation for the track geometry assessment gives rise to new demands. In order to analyse the responses of the vehicles to the measured track geometry defects, the integration of the simulation process in the measurement chain of the track geometry recording car is envisaged. Fast and reliable simulation results are required. This work studies the use of black-box modelling approaches as an alternative to multi-body simulation. The performances of different linear and nonlinear black-box models for the simulation of the vertical and lateral bogie accelerations are compared. While linear transfer function models give good results for the simulation of the vertical responses, their use is not suitable for the highly nonlinear lateral vehicle dynamics. The lateral accelerations are best represented by recurrent neural networks. For the training and validation on high-speed lines using measured vehicle responses, the performance of the black-box simulation outperforms the multi-body simulation. Due to the larger variability of track design and track quality conditions on conventional lines, the model performance degrades and depends significantly on the analysed vehicle type and the track characteristics.

Time series analysis of covariance based on linear transfer function models

In this article, a time series analysis of covariance model is introduced when covariates time series have lead–lag relationship with response time series. Parameter estimation and hypothesis testing for this model are made in spectral domain. We provide an instruction for our approach using a real Hydrological time series data set.

A new modelling and identification scheme for time-delay systems with experimental investigation: a relay feedback approach

ABSTRACTIn this paper, the conventional relay feedback test has been modified for modelling and identification of a class of real-time dynamical systems in terms of linear transfer function models with time-delay. An ideal relay and unknown systems are connected through a negative feedback loop to bring the sustained oscillatory output around the non-zero setpoint. Thereafter, the obtained limit cycle information is substituted in the derived mathematical equations for accurate identification of unknown plants in terms of overdamped, underdamped, critically damped second-order plus dead time and stable first-order plus dead time transfer function models. Typical examples from the literature are included for the validation of the proposed identification scheme through computer simulations. Subsequently, the comparisons between estimated model and true system are drawn through integral absolute error criterion and frequency response plots. Finally, the obtained output responses through simulations are verified experimentally on real-time liquid level control system using Yokogawa Distributed Control System CENTUM CS3000 set up.

Forecasting Water Demand in Phoenix, Ariz.

Short‐term water demand forecasts support water utility planning efforts. This study applies a linear transfer function (LTF) approach to model and forecast water demand for single‐family residential, multi‐family residential, and nonresidential customer categories in Phoenix, Ariz. Among other things, nonresidential water usage is found to be somewhat more price‐responsive than residential usage. Variations in responses to weather and economic variables are also documented for the various customer categories. Out‐of‐sample demand simulations are generated for periods when actual demand is known. Descriptive accuracy metrics and two formal tests are used to analyze the accuracy of LTF projections against two random‐walk benchmarks. The descriptive accuracy results for per‐customer water usage forecasts in most cases favor the LTF model, but the improvements in accuracy with respect to the benchmarks are statistically insignificant in most cases. Mixed accuracy results are obtained from an analysis of the LTF customer base forecasts.

6軸油圧マニピュレータのモデリングと制御

This study is concerned with modeling and model-based controller design for hydraulic manipulator, aiming at dynamic and accurate position/force control. In general, hydraulically operated system is too complicated to be modeled by first principles. Based on a linear transfer function model obtained via system identification technique, we designed PID feedback control system and estimated efficiency of the model. We also examined accuracy of trajectory tracking control with respect to the end-effector position, under joint-wise PID feedback control.

Short‐Term Forecasting Analysis for Municipal Water Demand

Short‐term water demand forecasts inform decisions regarding budgeting, rate design, water supply system operations, and effective implementation of conservation policies. This study develops a linear transfer function (LTF) forecasting model for El Paso, Tex., a growing city located in the desert Southwest region of the United States. The model was used to generate monthly frequency out‐of‐sample simulations of water demand for periods when actual demand was known. To measure the accuracy of the LTF projections against viable alternatives, a set of benchmark forecasts was also developed. Both descriptive accuracy metrics and formal statistical tests were used to analyze predictive performance. The LTF model outperformed the alternatives in predicting demand per customer but fell a little short in projecting growth in the customer base. Changes in climatic and economic conditions were found to affect consumption per customer more rapidly than did changes in water rates.

Models and Techniques for Electric Load Forecasting in the Presence of Demand Response

Demand-side management has been recently recognized as a strategic concept in smart electricity grids. In this context, active demand (AD) represents a demand response scenario in which households and small commercial consumers participate in grid management through appropriate modifications of their consumption patterns during certain time periods in return of a monetary reward. The participation is mediated by a new player, called aggregator, who designs the consumption pattern modifications to make up standardized products to be sold on the energy market. The presence of this new input to consumers generated by aggregators modifies the load behavior, asking for load forecasting algorithms that explicitly consider the AD effect. In this paper, we propose an approach to load forecasting in the presence of AD, based on gray-box models where the seasonal component of the load is extracted by a suitable preprocessing and AD is considered as an exogenous input to a linear transfer function model. The approach is thought for a distribution system operator that performs technical validation of AD products, and therefore possesses full information about the AD schedule in the network. A comparison of the performance of the proposed approach with techniques not using the information on AD and with approaches based on nonlinear black-box models is performed on a real load time series recorded in an area of the Italian low voltage network.