Comprehending Complexity: Data-Rate Constraints in Large-Scale Networks

This paper is concerned with the rate at which a discrete-time, deterministic, and possibly large network of nonlinear systems generates information, and so with the minimum rate of data transfer under which the addressee can maintain the level of awareness about the current state of the network. While being aimed at development of tractable techniques for estimation of this rate, this paper advocates benefits from directly treating the dynamical system as a set of interacting subsystems. To this end, a novel estimation method is elaborated that is alike in flavor to the small gain theorem on input-to-output stability. The utility of this approach is demonstrated by rigorously justifying an experimentally discovered phenomenon. The topological entropy of nonlinear time-delay systems stays bounded as the delay grows without limits. This is extended on the studied observability rates and appended by constructive upper bounds independent of the delay. It is shown that these bounds are asymptotically tight for a time-delay analog of the bouncing ball dynamics

Time-delay systems : stability, sliding mode control and state estimation

University of Technology, Sydney. Faculty of Engineering and Information Technology.Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of instability or oscillation. This thesis is concerned with the stability, sliding mode control and state estimation problems of time-delay systems. Throughout the thesis, the Lyapunov-Krasovskii (L-K) method, in conjunction with the Linear Matrix Inequality (LMI) techniques is mainly used for analysis and design. Firstly, a brief survey on recent developments of the L-K method for stability analysis, discrete-time sliding mode control design and linear functional observer design of time-delay systems, is presented. Then, the problem of exponential stability is addressed for a class of linear discrete-time systems with interval time-varying delay. Some improved delay-dependent stability conditions of linear discrete-time systems with interval time-varying delay are derived in terms of linear matrix inequalities. Secondly, the problem of reachable set bounding, essential information for the control design, is tackled for linear systems with time-varying delay and bounded disturbances. Indeed, minimisation of the reachable set bound can generally result in a controller with a larger gain to achieve better performance for the uncertain dynamical system under control. Based on the L-K method, combined with the delay decomposition approach, sufficient conditions for the existence of ellipsoid-based bounds of reachable sets of a class of linear systems with interval time-varying delay and bounded disturbances, are derived in terms of matrix inequalities. To obtain a smaller bound, a new idea is proposed to minimise the projection distances of the ellipsoids on axes, with respect to various convergence rates, instead of minimising its radius with a single exponential rate. Therefore, the smallest possible bound can be obtained from the intersection of these ellipsoids. This study also addresses the problem of robust sliding mode control for a class of linear discrete-time systems with time-varying delay and unmatched external disturbances. By using the L-K method, in combination with the delay decomposition technique and the reciprocally convex approach, new LMI-based conditions for the existence of a stable sliding surface are derived. These conditions can deal with the effects of time-varying delay and unmatched external disturbances while guaranteeing that all the state trajectories of the reduced-order system are exponentially convergent to a ball with a minimised radius. Robust discrete-time quasi-sliding mode control scheme is then proposed to drive the state trajectories of the closed-loop system towards the prescribed sliding surface in a finite time and maintain it there after subsequent time. Finally, the state estimation problem is studied for the challenging case when both the system’s output and input are subject to time delays. By using the information of the multiple delayed output and delayed input, a new minimal order observer is first proposed to estimate a linear state functional of the system. The existence conditions for such an observer are given to guarantee that the estimated state converges exponentially within an Є-bound of the original state. Based on the L-K method, sufficient conditions for Є-convergence of the observer error, are derived in terms of matrix inequalities. Design algorithms are introduced to illustrate the merit of the proposed approach. From theoretical as well as practical perspectives, the obtained results in this thesis are beneficial to a broad range of applications in robotic manipulators, airport navigation, manufacturing, process control and in networked systems

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI

Fault localization on power cables using time delay estimation of partial discharge signals

Precise localization of partial discharge (PD) sources on power cables is vital to prevent power line failures that can lead to significant economic losses for electrical suppliers. This study proposes four methods to estimate the time delay of PD signals under electromagnetic interference, including white Gaussian noise (WGN) and discrete sinusoidal interference (DSI), using denoised PD signals with signal-to-noise ratios ranging from 10.6 to -7.02 dB. The maximum peak detection (MPD) and cross-correlation (CC) approaches, as well as two new techniques, interpolation cross-correlation (ICC) and envelope cross-correlation (ECC), are evaluated for their effectiveness in PD source localization. The researchers employ the time difference of arrival (TDoA) algorithm to compute PD location using the double-end PD location algorithm, where the PD location precision serves as an indicator of the accuracy of the time delay estimation methods. The study concludes that CC and ICC are the most suitable methods for estimating the time delay of PD signals in the PD location algorithm, as they exhibit the lowest error rates. These results suggest that CC and ICC can be used effectively for precise PD source localization under electromagnetic interference on power cables

Induction Machine Diagnosis using Stator Current Advanced Signal Processing

International audienceInduction machines are widely used in industrial applications. Safety, reliability, efficiency and performance are major concerns that direct the research activities in the field of electrical machines. Even though the induction machines are very reliable, many failures can occur such as bearing faults, air-gap eccentricity and broken rotor bars. Therefore, the challenge is to detect them at an early stage in order to prevent breakdowns. In particular, stator current-based condition monitoring is an extensively investigated field for cost and maintenance savings. In fact, several signal processing techniques for stator current-based induction machine faults detection have been studied. These techniques can be classified into: spectral analysis approaches, demodulation techniques and time-frequency representations. In addition, for diagnostic purposes, more sophisticated techniques are required in order to determine the faulty components. This paper intends to review the spectral analysis techniques and time-frequency representations. These techniques are demonstrated on experimental data issued from a test bed equipped with a 0.75 kW induction machine. Nomenclature O&M = Operation and Maintenance; WTG = Wind Turbine Generator; MMF = Magneto-Motive Force; MCSA = Motor Current signal Analysis; PSD = Power Spectral Density; FFT = Fast Fourier Transform; DFT = Discrete Fourier Transform; MUSIC = MUltiple SIgnal Characterization; ESPRIT = Estimation of Signal Parameters via Rotational Invariance Techniques; SNR = Signal to Noise Ratio; MLE = Maximum Likelihood Estimation; STFT = Short-Time Fourier Transform; CWT = Continuous Wavelet Transform; WVD = Wigner-Ville distribution; HHT = Hilbert-Huang Transform; DWT = Discrete Wavelet Transform; EMD = Empirical Mode Decomposition; IMF = Intrinsic Mode Function; AM = Amplitude Modulation; FM = Frequency Modulation; IA = Instantaneous Amplitude; IF = Instantaneous Frequency; í µí± ! = Supply frequency; í µí± ! = Rotational frequency; í µí± ! = Fault frequency introduced by the modified rotor MMF; í µí± ! = Characteristic vibration frequencies; í µí± !"# = Bearing defects characteristic frequency; í µí± !" = Bearing outer raceway defect characteristic frequency; í µí± !" = Bearing inner raceway defect characteristic frequency; í µí± !" = Bearing balls defect characteristic frequency; í µí± !"" = Eccentricity characteristic frequency; í µí± ! = Number of rotor bars or rotor slots; í µí± = Slip; í µí°¹ ! = Sampling frequency; í µí± = Number of samples; í µí±¤[. ] = Time-window (Hanning, Hamming, etc.); í µí¼ = Time-delay; í µí¼ ! = Variance; ℎ[. ] = Time-window

Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

The Estimation and Control of a Laboratory Heating and Ventilation System

This dissertation is concerned with the estimation and control of a laboratory heating and ventilation system (Instrutek VVS-400). The system is a 2x2 multi-input multi-output process (MIMO). It has been shown that simple techniques such as the ultimate cycle method do not provide adequate control of the process. The system was interfaced with a PC using Matlab/Simulink via a data acquisition package (Humusoft). Continuous time process identification techniques were applied to the flow and temperature processes. The alternative tangent and point method was used to model the processes, and their interaction, using a first order lag plus delay model. Models were obtained for a range of operating conditions. The accuracy of the flow and temperature measurement transducers were investigated ¾ some inaccuracies were determined. Tests revealed that both processes were continuously non-linear. This pointed toward adaptive control as appropriate. PI/PID controllers were used because both processes displayed a low time delay to time constant ratio. Tuning rules were selected on the basis of minimising the integral of absolute error. A strong interaction effect between the output temperature and input flow rate was reduced considerably using a static decoupler. A gain scheduler was designed, using look-up tables, to continuously interpolate for the most suitable controller settings and decoupler gain, as process operating conditions varied. The design was compared to an average model controller. Validation tests showed that the overall difference in performance was slim. It was concluded that discrete time identification methods would yield more appealing results for the gain scheduler, and that the design could be applied to other MIMO processes with relative ease

H2/H∞ controller design for input-delay and preview systems based on state decomposition approach

This thesis concentrates on the efficient solution methods of H2/H∞ optimal control problems for input-delay and preview systems. Although the problems can be reformulated to the ones for delay-free systems by augmenting the state space of the controlled systems, the numerical solution of the Riccati/KYP (Kalman-Yakubovich-Popov) equations for the augmented systems requires special efforts, and complicates controller tuning. On the other hand, it is known that the optimal control laws for certain classes of time-delay systems can be constructed without solving the augmented Riccati/KYP equations. Such design problems are called reduced-order construction problems in this thesis. The solutions of the reducedorder construction problems are still limited in theoretical and practical perspectives. The main purpose of the thesis is to propose a new approach for the reduced-order construction problems, which enables to derive the optimal output feedback controllers for input-delayed and preview systems in a unified manner. We focus on the internal dynamics of the overall systems, and decompose it toward the H^2 and H^∞ performance objectives. The fundamental idea of our approach is first introduced for the discrete-time inputdelayed H^2/H^∞ control problems. The state decomposition enables to solve the output feedback problem through the simpler ones, namely, the full information and output estimation problems. The discrete-time optimal controllers are obtained in the Smith predictor form. They are constructed from the Riccati/KYP equations for the delay-free systems. The solution procedure is further extended to the continuous-time preview H^2/H^∞ control problems in an output feedback setting. The optimal utilization of the preview information is exploited at the full information and output estimation problems. The clear structures of the optimal controllers are revealed as the combination of the finite-dimensional observers and preview-feedforward compensation. In the H^∞ control problems for the input-delayed and preview systems, the J-spectral factorization techniques in the literature are employed. Their interconnection to the augmented Riccati/KYP equations is clarified by reviewing the techniques from a view point of the internal state dynamics.首都大学東京, 2014-03-25, 博士(工学), 甲第440号首都大学東