Control-Relevant System Identification using Nonlinear Volterra and Volterra-Laguerre Models

One of the key impediments to the wide-spread use of nonlinear control in industry is the availability of suitable nonlinear models. Empirical models, which are obtained from only the process input-output data, present a convenient alternative to the more involved fundamental models. An important advantage of the empirical models is that their structure can be chosen so as to facilitate the controller design problem. Many of the widely used empirical model structures are linear, and in some cases this basic model formulation may not be able to adequately capture the nonlinear process dynamics. One of the commonly used nonlinear dynamic empirical model structures is the Volterra model, and this work develops a systematic approach to the identification of third-order Volterra and Volterra-Laguerre models from process input-output data.First, plant-friendly input sequences are designed that exploit the Volterra model structure and use the prediction error variance (PEV) expression as a metric of model fidelity. Second, explicit estimator equations are derived for the linear, nonlinear diagonal, and higher-order sub-diagonal kernels using the tailored input sequences. Improvements in the sequence design are also presented which lead to a significant reduction in the amount of data required for identification. Finally, the third-order off-diagonal kernels are estimated using a cross-correlation approach. As an application of this technique, an isothermal polymerization reactor case study is considered.In order to overcome the noise sensitivity and highly parameterized nature of Volterra models, they are projected onto an orthonormal Laguerre basis. Two important variables that need to be selected for the projection are the Laguerre pole and the number of Laguerre filters. The Akaike Information Criterion (AIC) is used as a criterion to determine projected model quality. AIC includes contributions from both model size and model quality, with the latter characterized by the sum-squared error between the Volterra and the Volterra-Laguerre model outputs. Reduced Volterra-Laguerre models were also identified, and the control-relevance of identified Volterra-Laguerre models was evaluated in closed-loop using the model predictive control framework. Thus, this work presents a complete treatment of the problem of identifying nonlinear control-relevant Volterra and Volterra-Laguerre models from input-output data

MODELLING OF NONLINEAR SYSTEMS USING INTEGRATED OBFARX PLUS NEURAL NETWORK MODELS

The objective of this project is to develop a new model, which is by combining OBFARX linear model with nonlinear NN model. The results obtained will be compared with the previous models to show performance improvement by the new model. The new model development is based on the model developed by (Zabiri et al 2011) which is OBF linear model combination with nonlinear NN model. The OBF-NN model cannot work efficiently on some problems due to the limitations of the OBF part of the equation. So it is important to analyze the new model which is OBFARX-NN with OBF-NN model. The scope for this project will be the development of the parallel OBFARX-NN model, methods for estimating the model parameter, simulation analysis using MATLAB and evaluation on OBFARX-NN model performance. The method for completing the project will be firstly, make sure all the necessary information about the individual model is available. Then develop a theoretically working OBFARX-NN model. After that, analysis of the performance of the created model is done and also alterations here and there for better clarification. All in all, the result are the improve performance of process control by OBFARX-NN model compared to OBF-NN model.The most important aspect of the model development is the extrapolation capabilities of the model itself. When a model is forced to perform prediction in regions beyond the space of original training, then it can be said that the model can function well even when the process parameter is changed. This aspect is very important because in practical plant, the process conditions are continually changing making extrapolation inevitable. Thus, by testing the extrapolation capabilities of the OBFARX-NN model, the project had come up with the subsequent RMSE value and compared with previous model. The RMSE value indicates superior performance in the extrapolation region

Virtual reference feedback tuning of controllers parameterized using orthonormal basis functions

Supervisor : Dr. Gustavo Henrique da Costa OliveiraCo-supervisor : Dr. Prof. Gideon Villar LeandroDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa: Curitiba, 08/06/2015Inclui referênciasÁrea de concentração: Sistemas eletrônicosResumo: Projetar e determinar com exatidão controladores para sistemas dinâmicos sempre foi um desafio para a engenharia e no intuito de ampliar a aplicação de plantas controladas em sistema reais, muitas técnicas foram desenvolvidas para generalizar o método de projetar controladores e tornar essa tarefa mais fácil e assertiva. Dessa maneira, desde os primeiros estudos a respeito da teoria e prática de projeto de controladores PID, muitas outras ferramentas surgiram, dentre elas a área de controle baseado em dados, que tem por objetivo conseguir um controlador cujo sistema se comporte próximo a uma referência. Para tanto, utiliza-se um único dado de experimento com entradas e saídas coletados da planta a fim de determinar a dinâmica do sistema em malha fechada. A técnica de controle baseada em dados possui duas principais vertentes. A primeira é um processo iterativo bem representado pela técnica do Iterative Feedback Tuning (IFT). A segunda, conhecida como VRFT, ou Virtual Reference Feedback Tuning, é uma técnica não iterativa que tem por objetivo relacionar uma referência virtual a um sistema realimentado cujo controlador deseja-se determinar. Tal técnica tem a principal vantagem e característica de transformar o problema de determinação do controlador em um problema de identificação de sistemas com dados de entrada e saída virtuais calculados utilizando dados de uma planta de referência. Para tanto, é comum encontrar na literatura trabalhos que utilizar uma estrutura fixa e pré-determinada do controlador, normalmente estruturas PID. Porém, a aproximação de tal controlador apresenta falhas de identificação e de desempenho do sistema realimentado, pois nem sempre a estrutura escolhida contém a estrutura ideal, aquela cuja identificação aproxima o erro a zero ou muito próximo disso. Dentre diversos métodos de identificação de sistemas, as séries de base de função ortonormal (OBF) possuem a grande vantagem de poder generalizar tal estrutura de controlador e depender unicamente da quantidade de funções escolhidas para representar o sistema e de um polo ou um par de polos conjugado. Por fim, este trabalho apresenta a aplicação do método de base de funções ortonormais na identificação do controlador cujos dados são obtidos através da técnica de referência virtual (VRFT). A teoria foi aplicada em sistemas dinâmicos lineares e não lineares incluindo um reator químico do tipo CSTR em presença (ou não) de ruído de medição. A técnica foi testada em ambos os sistemas e sobre diversos níveis de ruído, apresentou resultados notáveis na etapa de identificação de sistemas e consequentemente produziu uma solução para o problema de determinar com precisão e facilidade o controlador para um sistema em malha fechada. A escolha da classe de controladores é então generalizada, o que permite ao sistema e à técnica do VRFT, grande aplicabilidade na solução de problemas complexos de sistemas dinâmicos reais. Palavras-chave: Bases de Funções Ortonormais. Identificação em malha fechada. Referencia Virtual. Controle Baseado em dados.Abstract: To design and determine with accuracy controllers for dynamical systems has always been a challenge for engineering. In order to extend the application of controlled plants in real system many techniques have been developed, most of them with the objective of generalizing methods and permit controller design in an easier and assertive way. Therefore, since the first studies about the theory and practice on designing of PID controllers, a new control area based on data aims to get a controller whose system behaves as close as possible to a pre-defined reference. To this end, a single set of input and output data is collected from the plant in order to finally identify the dynamics of such closed-loop system. Data-based control techniques have two main strands. The first, an iterative technique known as Iterative Feedback Tuning (IFT) and the second one, a noniterative model called Virtual Reference Feedback Tuning (VRFT) which aims to relate a virtual reference to a feedback system whose controller would be determined. The VRFT technique has the main advantage and characteristic of turning the task of the controller determination into a problem of system identification with a set of input and output data plus a virtual reference. To this end, it is common to find in literature studies that assume a fixed and pre-determined controller structures on VRFT, mainly related with the PID control structure. Still, the solution may fail to present a good performance because not always the chosen structure contains the ideal one whose identification brings the error with regards to the desired performance close to zero. Beyond several model structures used by systems identification methods, the orthonormal basis functions (OBF) models have been receiving much attention in the literature since the past decade. In the VRFT context, it has the great advantage of being able to generalize the controller structure and improve accuracy and applicability of the method. This is the main contribution of this work, which applies and analyses OBF-models to design controllers using the VRFT technique. The VRFT approach is better explained and its methodology, advantages and limitations are compared between similar procedures. In addition, it presents a potential alternative to enhance the VRFT technique and its results by using a generalized class of modeling structures described using orthonormal basis functions The theory is applied on linear and nonlinear dynamical systems including a CSTR reactor in presence (or not) of noise measurements. After all, the presented modeling technique delivered notable results on both identification and closed loop evaluations. Consequently, the problem of determining a feasible VRFT controller for expected closed-loop system behavior is solved, making wider the applicability of solving complex problems of real dynamical systems by the VRFT technique. Key-words: Orthonormal Basis Functions. Closed-loop Identification. Virtual Reference Feedback Tuning. Data-Base Controller Tuning

Optimising the assessment of cerebral autoregulation from black box models

Cerebral autoregulation (CA) mechanisms maintain blood flow approximately stable despite changes in arterial blood pressure. Mathematical models that characterise this system have been used extensively in the quantitative assessment of function/impairment of CA. Using spontaneous fluctuations in arterial blood pressure (ABP) as input and cerebral blood flow velocity (CBFV) as output, the autoregulatory mechanism can be modelled using linear and non-linear approaches, from which indexes can be extracted to provide an overall assessment of CA. Previous studies have considered a single – or at most a couple of measures, making it difficult to compare the performance of different CA parameters. We compare the performance of established autoregulatory parameters and propose novel measures. The key objective is to identify which model and index can best distinguish between normal and impaired CA. To this end 26 recordings of ABP and CBFV from normocapnia and hypercapnia (which temporarily impairs CA) in 13 healthy adults were analysed. In the absence of a ‘gold’ standard for the study of dynamic CA, lower inter- and intra-subject variability of the parameters in relation to the difference between normo- and hypercapnia were considered as criteria for identifying improved measures of CA. Significantly improved performance compared to some conventional approaches was achieved, with the simplest method emerging as probably the most promising for future studies

Intelligent Control via Wireless Sensor Networks for Advanced Coal Combustion Systems

Numerical Modeling of Solid Gas Flow, System Identification for purposes of modeling and control, and Wireless Sensor and Actor Network design were pursued as part of this project. Time series input-output data was obtained from NETL's Morgantown CFB facility courtesy of Dr. Lawrence Shadle. It was run through a nonlinear kernel estimator and nonparametric models were obtained for the system. Linear and first-order nonlinear kernels were then utilized to obtain a state-space description of the system. Neural networks were trained that performed better at capturing the plant dynamics. It is possible to use these networks to find a plant model and the inversion of this model can be used to control the system. These models allow one to compare with physics based models whose parameters can then be determined by comparing them against the available data based model. On a parallel track, Dr. Kumar designed an energy-efficient and reliable transport protocol for wireless sensor and actor networks, where the sensors could be different types of wireless sensors used in CFB based coal combustion systems and actors are more powerful wireless nodes to set up a communication network while avoiding the data congestion. Dr. Ahmadi's group studied gas solid flow in a duct. It was seen that particle concentration clearly shows a preferential distribution. The particles strongly interact with the turbulence eddies and are concentrated in narrow bands that are evolving with time. It is believed that observed preferential concentration is due to the fact that these particles are flung out of eddies by centrifugal force

An Improved Global Harmony Search Algorithm for the Identification of Nonlinear Discrete-Time Systems Based on Volterra Filter Modeling

This paper describes an improved global harmony search (IGHS) algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS) algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL) is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes

Modelling and Analysis of Drosophila Early Visual System A Systems Engineering Approach

Over the past century or so Drosophila has been established as an ideal model organism to study, among other things, neural computation and in particular sensory processing. In this respect there are many features that make Drosophila an ideal model organism, especially the fact that it offers a vast amount of genetic and experimental tools for manipulating and interrogating neural circuits. Whilst comprehensive models of sensory processing in Drosophila are not yet available, considerable progress has been made in recent years in modelling the early stages of sensory processing. When it comes to visual processing, accurate empirical and biophysical models of the R1-R6 photoreceptors were developed and used to characterize nonlinear processing at photoreceptor level and to demonstrate that R1-R6 photoreceptors encode phase congruency. A limitation of the latest photoreceptor models is that these do not account explicitly for the modulation of photoreceptor responses by the network of interneurones hosted in the lamina. As a consequence, these models cannot describe in a unifying way the photoreceptor response in the absence of the feedback from the downstream neurons and thus cannot be used to elucidate the role of interneurones in photoreceptor adaptation. In this thesis, electrophysiological photoreceptor recordings acquired in-vivo from wild- type and histamine defficient mutant fruit flies are used to develop and validate new com- prehensive models of R1-R6 photoreceptors, which not only predict the response of these photoreceptors in wild-type and mutant fruit flies, over the entire environmental range of light intensities but also characterize explicitly the contribution of lamina neurons to photore- ceptor adaptation. As a consequence, the new models provide suitable building blocks for assembling a complete model of the retina which takes into account the true connectivity between photoreceptors and downstream interneurones. A recent study has demonstrated that R1-R6 photoreceptors employ nonlinear processing to selectively encode and enhance temporal phase congruency. It has been suggested that this processing strategy achieves an optimal trade-off between the two competing goals of minimizing distortion in decoding behaviourally relevant stimuli features and minimizing the information rate, which ultimately enables more efficient downstream processing of spatio-temporal visual stimuli for edge and motion detection.Using rigorous information theoretic tools, this thesis derives and analyzes the rate-distortion characteristics associated with the linear and nonlinear transformations performed by photoreceptors on a stimulus generated by a signal source with a well defined distribution

MODELLING OF NONLINEAR SYSTEMS USING INTEGRATED OBFARX PLUS NEURAL NETWORK MODELS

The objective of this project is to develop a new model, which is by combining OBFARX linear model with nonlinear NN model. The results obtained will be compared with the previous models to show performance improvement by the new model. The new model development is based on the model developed by (Zabiri et al 2011) which is OBF linear model combination with nonlinear NN model. The OBF-NN model cannot work efficiently on some problems due to the limitations of the OBF part of the equation. So it is important to analyze the new model which is OBFARX-NN with OBF-NN model. The scope for this project will be the development of the parallel OBFARX-NN model, methods for estimating the model parameter, simulation analysis using MATLAB and evaluation on OBFARX-NN model performance. The method for completing the project will be firstly, make sure all the necessary information about the individual model is available. Then develop a theoretically working OBFARX-NN model. After that, analysis of the performance of the created model is done and also alterations here and there for better clarification. All in all, the result are the improve performance of process control by OBFARX-NN model compared to OBF-NN model.The most important aspect of the model development is the extrapolation capabilities of the model itself. When a model is forced to perform prediction in regions beyond the space of original training, then it can be said that the model can function well even when the process parameter is changed. This aspect is very important because in practical plant, the process conditions are continually changing making extrapolation inevitable. Thus, by testing the extrapolation capabilities of the OBFARX-NN model, the project had come up with the subsequent RMSE value and compared with previous model. The RMSE value indicates superior performance in the extrapolation region