Transfer Function Matrix Model Research Articles

Radiation Force Modeling for a Wave Energy Converter Array

The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, ν, of the radiation force transfer function matrix.

Sistema instrumental para estimar la relación de turbulencia del flujo de aire en una cuadrícula rígida, en función de su matriz de funciones de transferencia de orden dinámico reducido

En palabras de los expertos en tecnología de enfriamiento, existe al menos una brecha de 20 años entre la tecnología actual basada en la compresión de vapor para refrigeración, enfriamiento y HVAC, y lo que hemos definido como tecnologías alternativas. También hay una gran cantidad de esfuerzo científico para dotar a esta tecnología de compresión de vapor con más grados de libertad para implementar algoritmos de optimización de energía más precisos. De esta manera, como primer paso para obtener algoritmos de control más robustos en intercambiadores de calor de unidades de condensadores y evaporadores, los autores han desarrollado algunos sistemas de instrumentación para analizar el comportamiento del aire que fluye a través de las cuchillas rígidas de este tipo de dispositivos. Sin embargo, este esfuerzo anterior se informó anteriormente como un modelo modal vibracional completo para la grilla rígida en cuestión; Debido a sus 16 grados de libertad espacial y su 16 ° orden dinámico, su redisolución de modelo en línea mientras la unidad de intercambiador de calor está funcionando es casi imposible con una computadora normal. Por lo tanto, para obtener un algoritmo con menos consumo de recursos computacionales y con la misma precisión que el modelo modal completo, los autores han informado en este documento, la implementación de un modelo de matriz de función de transferencia de orden dinámico reducido. Reducción que, como se describe, se basa en el promedio de los polos y la selección de ceros, a partir de los gráficos experimentales establecidos de la magnitud espectral de frecuencia de un conjunto de pruebas de impacto (prueba modal experimental) realizadas en LaNITeF-CIDESI. La predicción numérica de la matriz de la función de transferencia del modelo dinámico de orden reducido se ha validado con el espectro experimental. Según la hipótesis, que debido al ángulo incidente, la vibración espectral de resonancia es excitada por el flujo de aire laminar, mientras que la turbulencia del flujo de aire no excita la espectral vibracional de resonancia, la relación de turbulencia del flujo de aire incidente se ha analizado desde un prueba de túnel de viento. Como conclusión principal, los autores han desarrollado y validado un nuevo sistema de instrumentación para analizar la relación de turbulencia del flujo de aire incidente en una red rígida, que puede ser parte de una unidad de condensador o evaporador de un sistema de enfriamiento convencional, mediante la implementación de la transferencia correspondiente. modelo matricial de funciones con orden dinámico reducido.

Experimental Study and Identification of Linear Model with Parameter Variation for Drum Type Laboratory Scale Boiler

Water-drum boilers (i.e., steam generators) are commonly used in power plants and other related industries. In the coming years, these boilers are expected to be operated over a broad range of operational scenarios, such as when the steam-to-boiler load changes due to variations in the electrical power as a result of renewable integration. The boiler system is multivariable in nature, and its behaviour changes considerably over a wide range of operational scenarios. However, exploring advanced control solutions to improve boiler operability is challenging due to the lack of experiments conducted on industrial boilers. Hence, a lab-scale experimental boiler is designed for control system research and education. This setup has a multivariable structure and exhibits a similar dynamic to the industrial boiler. Moreover, it is relatively simple to experiment on, in comparison with the real-world boiler. Thus, students and researchers are able to connect theory with practice and develop control solutions for practice. This paper presents the results of the experiments conducted on the lab boiler to develop a linear transfer function matrix model with parameter variations targeting robust control research.

Incremental multivariable predictive functional control and its application in a gas fractionation unit

The control of gas fractionation unit (GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay. PID controllers are still applied in most industry processes. However, the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process. In this work, an incremental multivariable predictive functional control (IMPFC) algorithm was proposed with less online computation, great precision and fast response. An incremental transfer function matrix model was set up through the step-response data, and predictive outputs were deduced with the theory of single-value optimization. The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm, and thereby making the control variable smoother. The predictive output error and future set-point were approximated by a polynomial, which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory. Then, the design of incremental multivariable predictive functional control was studied. Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.

Development and Analysis of Linear Model Representations of the Quad-Rotor System

A Quad-rotor, which is an airplane with four rotors, is considered a complex and challenging control problem. Analysis and design of its control systems is usually started by careful consideration of its mathematical models description. This paper presents a detailed mathematical model for a Vertical Takeoff and Landing (VTOL) type Unmanned Aerial Vehicle (UAV) known as the quad rotor. The presented paper focus on the nonlinear modeling of an experimental type quad-rotor. The first objective of this paper aims to develop a nonlinear dynamical model based on Newton-Euler approach. Then, a linear model is obtained around an optimized hovering point. The state space, transfer function matrix and matrix fraction description models are derived. Finally, a linear controller is designed to achieve a stable compensated system around a hovering point. The methodology applied in this paper takes the ST-450 experimental quad-rotor as a case study.

Modeling and Analysis of Interstand Tension Control in 6-high Tandem Cold Rolling Mill

The interstand tension control is one of the most important ways to meet tight tolerances for strip product quality during tandem cold rolling process. Using coordinate analysis and parabolic approximation for the mass flow balance principle, the strip velocities eliminating the use of forward slips and backward slips were calculated. In order to reduce the effect of roll eccentricity on the tension measurement, a filter based on bilinear transformation was designed. Applying a first-order Taylor series approximation, the transfer function matrix model of interstand tension stress was derived. The actual measurements on-site and the final calculation results showed that the established model had high calculation accuracy and was beneficial for interstand tension control of tandem cold rolling process.

Identification of active magnetic bearing system with a flexible rotor

Active magnetic bearings (AMBs) are widely applied in high-speed rotating machinery, especially in special environments. In designing and adjusting an AMB system, the mathematical model of the system plays an important role. Identification is a useful method to obtain the models of AMB systems. This paper concentrates on identification method for an AMB system with a flexible rotor. Based on the theoretical system model and the measured frequency–response model, the proposed method estimates the unknown parameters and establishes the transfer function matrix model of the AMB system. According to the theoretical model, this paper decomposes the identification procedure into a few steps and the model is sequentially reduced by these steps. In this procedure, the submodels are identified separately and finally combined together. The proposed method is validated by experiments on three AMB systems.

A P systems based hybrid optimization algorithm for parameter estimation of FCCU reactor–regenerator model

Fluid catalytic cracking unit (FCCU) reactor–regenerator is a complex multivariable system and suitable model is useful to understand and design FCCU reaction–regeneration processes. Inspired by the concepts of P systems (membrane computing) and quantum computing, a P systems based hybrid optimization algorithm (PHOA) is proposed to estimate the parameters of FCCU reactor–regenerator model. The expansion of the search space makes the novel algorithm realize exploration and the dynamic contraction of the search space makes it realize exploitation. The quantum update rules and adaptive mutation rule in combination with the new membrane structure contribute to the improvement of global searching performance. Studies on some benchmark functions indicate that the PHOA outperforms DNA based genetic algorithm (DNA-GA) and genetic algorithm (GA) both in search efficiency and accuracy. With the parameters obtained by PHOA, the transfer function matrix model of FCCU reactor–regenerator in an oil refinery is established. Experimental results reveal that model curves gained by this proposed method are in good agreement with the measured data with smaller sum of squared error. The effectiveness of the model is also validated by experiments.

Coupling Dynamic Model and Control of Chatter in Cold Rolling

The dynamic model of 4-h mill, which couples with the rolling process model, the mill roll stand structure model, and the hydraulic servo system model, is built by analyzing the vibration process of cold rolling. By linearization, the multiple input multiple output linear transfer function matrix model of single stand 4-h cold mill system is obtained. With the consideration of strip quality, the model of strip thickness control system is established in a simplified form. Meanwhile, the robust controller based on quantitative feedback theory is designed for the gauge control model. A comparison with PID controller shows that the controller has better disturbance attenuation performance for parameter uncertainty and external disturbance.

Transfer function matrix model of the bubbling fluidized bed boiler

Transfer function matrix model of the bubbling fluidized bed boiler The paper presents proposal of a model of the fluidized bed boiler adapted for use in model-based controllers e.g. predictive, adaptive or internal model control (IMC). The model has been derived in the form of transfer function matrix which allows its direct implementation in the controller structure. Formulated model takes into consideration the principal cross-coupling between process variables which enables the opportunity to search for feasibility of decoupling control. The results of the identification of the dynamics of the 2 MW industrial bubbling fluidized bed boiler using the proposed model form was presented. According to the experimental data it was found that despite of introduced simplifications presented model allows the boiler behavior prediction.

STUDY OF APPROXIMATE DISTRIBUTED DYNAMIC MODEL OF MULTISOURCE AND MULTI-SINK STEAM MANIFOLD SYSTEM ON THERMAL POWER PLANT

Due to the deficiencies of prior modeling methods of systems of boilers in parallel operation through a common manifold, in this article we use simplified approximate distributed modeling based on the compartmentalization and combination of the manifold. First, a principle is established to plot out the manifold into some basic pipe sections between each pair of source/sink points. Second, a simplified approximate distributed decoupled transfer function matrix model without steady errors is built for each pipe section. Finally, a smooth joint arithmetic is adopted to combine all the conterminous subsections of the pipe section with boilers/turbines at its ends into a whole system model. This method can decrease the size of the equipment and, therefore, makes it easier to model larger systems. The model presents more distributed characteristics and fits well in control system simulating. Some experiments have been done with favorable results to prove the validity of the method.

An Iterative Method to Stabilize a Transfer Function in the<tex>$s$</tex>- and<tex>$z$</tex>-Domains

Stability of the identified model is crucial in simulations and prediction applications. This paper proposes a two-step procedure that generates guaranteed stable transfer function (matrix) models from noisy data. It consists of an unconstrained optimal noise removal step followed by a stable approximation of the possible unstable estimate. The proposed method is applicable to continuous-time as well as discrete-time and multivariable systems

A Novel Linear Recurrent Neural Network for Multivariable System Identification

This paper proposes a novel linear recurrent neural network for multivariable system identification, namely a linerec neural network (LNN). Based on this network, the transfer function matrix model of a multivariable system can be identified directly according to its input and output data. In this way, LNNs differ from existing neural networks. An LNN is constructed based on the identification of prior knowledge in a system, and its weights have definite physical meaning. An LNN is equivalent to a linear equation set, and its training algorithm is based on Widrow-Hoff learning rules. In this paper, the theoretical foundation, structural algorithm and learning rules of LNNs are proposed and studied. To guarantee learning convergence, network training stability is analysed using discrete Lyapunov stability theory. Finally, simulation results show the feasibility of LNNs for multivariable system identification.

DATA–BASED MODELING OF THE SPATIOTEMPORAL TEMPERATURE DISTRIBUTION IN A REACH–IN PLANT GROWTH CHAMBER

The spatiotemporal temperature distribution in the imperfectly mixed airspace around plants has a considerableeffect on the physiological plant processes. In a fully instrumented climate chamber, eight identification experiments werecarried out to model the spatiodynamic temperature response around plants to variations in the supply air temperature andthe sensible heat, produced by the lamps (directly related to the light intensity), as control inputs. From the experimental data,a minimally parameterized, linear, discretetime transfer function matrix (TFM) model was identified, capturing thedominant model behavior of the dynamic process. Based on statistical considerations, a firstorder TFM model came out asthe best model structure. The firstorder model provided a good compromise between goodness of fit (minimum Rt2i of 0.91)and parametric efficiency (standard error), characterized the airflow behavior very well, and formed an adequate basis formodelbased process control.

The Prediction of Rain-Induced Attenuation in MM Wave Band by Rain Medium System Model

While the millimeter radio wave propagates through rainfall, it will be attenuated heavily due to assimilation and scattering of rain. It is imperative to establish a simple and effective model to predict the rain-induced attenuation. In this paper, the rainfall is taken as a random system that can attenuate the radio wave. The transfer function matrix model is selected to be the random system model. Using experiment rain attenuation data at different rain rate, the correlation entropy and residue error of the system is obtained by system identification method. On the basis of correlation entropy and residue error, we can determine the order of the predication system. At last, the predication model that can forecast heavy rain attenuation by small rain attenuation is gotten by applying the least square method. The comparison shows that the discrepancy between the predication result of the obtained model and the experiment rain attenuation data is relatively minor.

Dynamic Modeling and Adaptive Control of the Gas Metal Arc Welding Process

Control of the welding process is a very important step in welding automation. Since the welding process is complex and highly nonlinear, it is very difficult to accurately model the process for real-time control. In this research, a discrete-time transfer function matrix model for gas metal arc welding process is proposed. This empirical model takes the common dynamics for each output and inherent process and measurement delays into account. Although this linearized model is valid only around the operating point of interest, the adaptation mechanism employed in the control system render this model useful over a wide operating range. Since welding is inherently a nonlinear and multi-input, multi-output process, a multivariable adaptive control system is used for high performance. The process outputs considered are weld bead width and depth, and the process inputs are chosen as the travel speed of the torch and the heat input. A one-step-ahead (or deadbeat) adaptive control algorithm combined with a recursive least-squares methods for on-line parameter estimation is implemented in order to achieve the desired weld bead geometries. Control weighting factors are used to maintain the stability and reduce excessive control effort. Some guidelines for the control design are also suggested. Command following and disturbance rejection properties of the adaptive control system for both SISO and MIMO cases are investigated by simulation and experiment. Although a truly independent control of the outputs is difficult to implement because of a strong output coupling inherent in the process, a control system for simultaneous control of bead width and depth was successfully implemented.

The analytical modelling and dynamic behaviour of tray-type binary distillation columns

A completely original, parametric transfer-function matrix (TFM) model for a binary distillation column, is derived. From the ordinary differential equations describing the individual trays of a multitray column, a partial differential equation (PDE) representation is derived together with the necessary boundary conditions. Large-signal steady-state solutions are derived to provide parametric data for a small-signal PDE model obtained by linearization. The small-signal PDEs are solved analytically for sinusoidal inputs to produce the parametric TFM model for the system. The plant parameters and operating conditions are chosen to produce a physically symmetrical system which, in turn, yields a completely diagonal TFM choosing input and output vectors as the “sum and difference” of the circulating vapour and liquid flows within the column and the “difference and sum” of the top and bottom compositions, respectively. This deduction accords well with the findings of previous authors McMoran [1], Shinskey [2], and Stainthorp [3] based on part impirical, approximate analytical by Edwards and Jassim [4], or purely simulation methods [5]. Near first-order-lag behaviour is also a feature common to the findings of these earlier investigations and the precise derivation herein reported.

Irreducible model estimation for MIMO systems

Abstract Estimation of the parameters of a reducible (inflated common denominator) model for the transfer function matrix of MIMO systems is well known. However, the reduction of the model to the minimal form by pole-zero cancellation is possible only in the noise-free case. This paper presents an algorithm for the estimation of the minimal continuous-time transfer function matrix model. Monte Carlo simulation results are presented for discrete-time and continuous-time models. Least-squares and generalized least-squares methods have been used in both cases. An asymptotic analysis of convergence has also been provided for these models in the noise-free case. The computation times and space complexities of different variants of the algorithm are compared. The results show that in noisy situations, obtaining a discrete-time model by discretizing an estimated continuous-time model may be a viable proposition

Recursive parameter estimation of transfer function matrix models via Simpson's integrating rules

Recursive formulae for repeated integration of a continuous-time function with uniformly sampled data using Simpson's 1/3 and 3/8 integrating rules are derived. Combined with the recursive algorithm of the least-squares solution, a method for recursive parameter estimation of transfer function matrix models in multiple-input-multiple-output systems is proposed. It is demonstrated that the use of the popular integrating rules for parameter estimation can be as effective as sophisticated methods that use orthogonal functions and the associated operational properties reported in the literature. The proposed algorithm is suitable for on-line applications and computer programming. Three numerical examples are included to illustrate the applicability of the proposed method.

Linear Modelling of Ship Propulsion Plants

The extension of a non-linear digital simulation model of a marine propulsion plant, to include an approximate equation for the propeller shaft torque, is considered. It is then shown how linearized transfer-function matrix models can he developed from the non-linear system model. The evaluation of the first order partial derivatives, using the non-linear data in the simulation program, will then be described.