P. Esquivel

Decentralized neural identifier and control for nonlinear systems based on extended Kalman filter

A time-varying learning algorithm for recurrent high order neural network in order to identify and control nonlinear systems which integrates the use of a statistical framework is proposed. The learning algorithm is based in the extended Kalman filter, where the associated state and measurement noises covariance matrices are composed by the coupled variance between the plant states. The formulation allows identification of interactions associate between plant state and the neural convergence. Furthermore, a sliding window-based method for dynamical modeling of nonstationary systems is presented to improve the neural identification in the proposed methodology. The efficiency and accuracy of the proposed method is assessed to a five degree of freedom (DOF) robot manipulator where based on the time-varying neural identifier model, the decentralized discrete-time block control and sliding mode techniques are used to design independent controllers and develop the trajectory tracking for each DOF.

Time-Dependent Statistical Analysis of Wide-Area Time-Synchronized Data

Characterization of spatial and temporal changes in the dynamic patterns of a nonstationary process is a problem of great theoretical and practical importance. On-line monitoring of large-scale power systems by means of time-synchronized Phasor Measurement Units (PMUs) provides the opportunity to analyze and characterize inter-system oscillations. Wide-area measurement sets, however, are often relatively large, and may contain phenomena with differing temporal scales. Extracting from these measurements the relevant dynamics is a difficult problem. As the number of observations of real events continues to increase, statistical techniques are needed to help identify relevant temporal dynamics from noise or random effects in measured data. In this paper, a statistically based, data-driven framework that integrates the use of wavelet-based EOF analysis and a sliding window-based method is proposed to identify and extract, in near-real-time, dynamically independent spatiotemporal patterns from time synchronized data. The method deals with the information in space and time simultaneously, and allows direct tracking and characterization of the nonstationary time-frequency dynamics of oscillatory processes. The efficiency and accuracy of the developed procedures for extracting localized information of power system behavior from time-synchronized phasor measurements of a real event in Mexico is assessed.

A Hilbert-Huang based approach for on-line extraction of modal behavior from PMU data

In this paper an efficient method for analyzing the local dynamics of transient oscillations using a local empirical mode decomposition (EMD) and the Hilbert transform is presented. Two novel approaches are investigated to characterize non-stationary issues. The first method is a local implementation of the EMD technique. The second technique is an algorithm to compute the Hilbert transform using variable window filters. By combining a sliding window of finite length with the sifting process by blocks, a local implementation of the empirical mode decomposition is proposed. Approaches to extending Hilbert-Huang analysis to analyze the local properties of general non-stationary signals are then explored based on finite-impulse-response (FIR) designed using Kaiser windows. This approach enables the Hilbert-Huang technique to be a truly online analysis technique for measured data. The application of these techniques is tested on time-synchronized phasor measurements collected by Phasor Measurement Units. Both, online analysis and off-line analysis are used in the study.

Direct current motor control based on high order neural networks using stochastic estimation

An adaptive discrete-time tracking controller for a direct current (DC) motor with controlled excitation flux is presented. A high order neural network in discrete-time is used to identify the plant model; this network is trained with an extended Kalman filter where the associated state and measurement noises discrete-time covariance matrices are calculated with stochastic estimation. Then, the discrete-time block control and sliding mode techniques are used to develop the trajectory tracking for the angular position of a DC motor with separate winding excitation. Numerical computation presented in this paper shows that the proposed method provides accurate estimation for the covariance matrices associated in the extended Kalman filter.

Complex Empirical Orthogonal Function analysis of wide-area system dynamics

A statistical approach to the dynamic characterization of system temporal behavior based on complex empirical orthogonal function (EOF) analysis is developed. This technique allows identification of the dominant spatial and temporal patterns in complex space-time data sets and is thus ideally suited for the study of propagating and standing features that can be associated with wide-area dynamics. A general technique for the computation of empirical orthogonal basis functions is suggested. In this procedure, measured data from multiple phasor measurement units (PMUs) are used to build an optimal set of orthonormal basis functions that best approximate the original data set. Complex EOF analysis is then used to extract information on dominant non- stationary spatial, temporal and frequency patterns of the observed oscillations. Algorithms are presented which provide accurate extraction and characterization of propagating features in the data using complex singular value analysis. Data obtained from GPS-based phasor measurement units from a real event in northern Mexico are used to study the practical applicability of the method. The results indicate that PMU data from geographically remote stations can be efficiently compressed and that the dominant modes of behavior can be identified and isolated. Comparison of extracted modal information to conventional spectral analysis indicates that the proposed algorithm produces near optimal approximations coupled with accurate modal properties.

Wide-area PMU data monitoring using spatio-temporal statistical models

In this paper, a statistically-based, data-driven framework that integrates the use of empirical orthogonal function (EOF) analysis and a time-frequency method is proposed to identify and extract, relevant dynamically independent spatio-temporal patterns from time synchronized data. Using time-frequency methods, the temporal signals at selected system locations are decomposed into modal approximations at different scales. Multi-scale EOF analysis is then used to extract cross-correlations across the measurement sites. The method allows for the extremely nonstationary behavior of interarea oscillations to be analyzed into separate frequency bands and is capable of detecting propagating features in non-stationary processes.

Complex Empirical Orthogonal Function Analysis of Power System Oscillatory Dynamics

Multivariate statistical data analysis techniques offer a powerful tool for analyzing power system response from measured data. In this chapter, a statistically based, data-driven framework that integrates the use of complex empirical orthogonal function analysis and the method of snapshots is proposed to identify and extract dynamically independent spatiotemporal patterns from time-synchronized data. The procedure allows identification of the dominant spatial and temporal patterns in a complex data set and is particularly well suited for the study of standing and propagating features that can be associated with electromechanical oscillations in power systems. It is shown that, in addition to providing spatial and temporal information, the method improves the ability of conventional correlation analysis to capture temporal events and gives a quantitative result for both the amplitude and phase of motions, which are essential in the interpretation and characterization of transient processes in power systems. The efficiency and accuracy of the developed procedures for capturing the temporal evolution of the modal content of data from time synchronized phasor measurements of a real event in Mexico is assessed. Results show that the proposed method can provide accurate estimation of nonstationary effects, modal frequency, time-varying mode shapes, and time instants of intermittent or irregular transient behavior associated with abrupt changes in system topology or operating conditions.

Recurrent Neural Identification on Xilinx system generator using V7 FPGA for a 2DOF robot manipulator

This paper describes an identification process for a class of discrete-time nonlinear systems, which includes the Xilinx system generator software and the process is implemented in a Virtex 7 (V7) field programmable gate array (FPGA). This procedure consists of programming a discrete-time nonlinear plant where the dynamics of this plant is reproduced by a discrete-time recurrent high order neural network (RHONN). The neural network is trained on-line with the extended Kalman filter algorithm where the associated state and measurement noises covariance matrices are composed by the coupled variance between the plant states. Additionally, a sliding window-based method for dynamical modeling of nonstationary systems is presented in order to improve the neural identification process. This identification process is implemented on a Virtex 7 (V7) FPGA using Xilinx system generator software where are programed in this FPGA: the discrete-time dynamics of the two degrees of freedom (2DOF) robot manipulator, the RHONN, the extended Kalman filter (EKF) training algorithm and the sliding window-based method. The obtained results from the FPGA are compared with the results obtained from Matlab/SImulink in order to validate the identification process for the present proposal.

Real-Time Control Based On High Order Neural Networks Using Stochastic Estimation

An adaptive discrete-time regulator system for a Furuta pendulum is presented. A high order neural network in discrete-time is used to identify the plant behavior; this network is trained with an extended Kalman filter where the associated state and measurement noises discrete-time covariance matrices are calculated with stochastic estimation. Then, the discretetime block control and sliding mode techniques are used to develop the regulation for the angular position of a Furuta pendulum. Real-time results presented in this paper shows that the proposed method provides accurate estimation for the covariance matrices associated in the extended Kalman filter.

Space-spectrum empirical model for unmasking modal components contained into space-time varying data measurements

This paper describes a space-spectrum empirical model for unmasking modal components contained into space-time varying data measurements obtained from interconnected dynamical systems using an empirical biorthogonal representation. The method incorporates frequency domain responses obtained from the application of the complex Fourier analysis to problems of spectral decomposition for space-time varying data sets. In addition, the model provides a frequency band based denoising procedure to effectively reduce the noise level in the data used. This is achieved by extending the empirical orthogonal function analysis of time series to the frequency domain where their fundamental properties are based on the interpretation of pre-selected frequencies contained into the eigenvectors of a cross-spectrum matrix. Without loss of generality, the method is applied to a synthetic example of a spring-mass mechanical system to demonstrate the performance of the decomposition method incorporating frequency domain responses where the details of its practical implementation are described.