LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

On switched control design of linear time-invariant systems with polytopic uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure. © 2013 Wallysonn A. de Souza et al.

Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or supercritical speeds. (C) 2012 Elsevier Ltd. All rights reserved.

Overview of analytical approaches

The general model The aim of this chapter is to introduce a structured overview of the different possibilities available to display and analyze brain electric scalp potentials. First, a general formal model of time-varying distributed EEG potentials is introduced. Based on this model, the most common analysis strategies used in EEG research are introduced and discussed as specific cases of this general model. Both the general model and particular methods are also expressed in mathematical terms. It is however not necessary to understand these terms to understand the chapter. The general model that we propose here is based on the statement made in Chapter 3, stating that the electric field produced by active neurons in the brain propagates in brain tissue without delay in time. Contrary to other imaging methods that are based on hemodynamic or metabolic processes, the EEG scalp potentials are thus “real-time,” not delayed and not a-priori frequency-filtered measurements. If only a single dipolar source in the brain were active, the temporal dynamics of the activity of that source would be exactly reproduced by the temporal dynamics observed in the scalp potentials produced by that source. This is illustrated in Figure 5.1, where the expected EEG signal of a single source with spindle-like dynamics in time has been computed. The dynamics of the scalp potentials exactly reproduce the dynamics of the source. The amplitude of the measured potentials depends on the relation between the location and orientation of the active source, its strength and the electrode position.

Accounting for baseline differences and measurement error in the analysis of change over time

If change over time is compared in several groups, it is important to take into account baseline values so that the comparison is carried out under the same preconditions. As the observed baseline measurements are distorted by measurement error, it may not be sufficient to include them as covariate. By fitting a longitudinal mixed-effects model to all data including the baseline observations and subsequently calculating the expected change conditional on the underlying baseline value, a solution to this problem has been provided recently so that groups with the same baseline characteristics can be compared. In this article, we present an extended approach where a broader set of models can be used. Specifically, it is possible to include any desired set of interactions between the time variable and the other covariates, and also, time-dependent covariates can be included. Additionally, we extend the method to adjust for baseline measurement error of other time-varying covariates. We apply the methodology to data from the Swiss HIV Cohort Study to address the question if a joint infection with HIV-1 and hepatitis C virus leads to a slower increase of CD4 lymphocyte counts over time after the start of antiretroviral therapy.

Time-frequency characterization of a sound propagation channel as an educational tool

This paper discusses the use of sound waves to illustrate multipath radio propagation concepts. Specifically, a procedure is presented to measure the time-varying frequency response of the channel. This helps demonstrate how a propagation channel can be characterized in time and frequency, and provides visualizations of the concepts of coherence time and coherence bandwidth. The measurements are very simple to carry out, and the required equipment is easily available. The proposed method can be useful for wireless or mobile communication courses.

Time-Frequency based Feature Selection for Discrimination of non stationary Biosignals.

This research proposes a generic methodology for dimensionality reduction upon time-frequency representations applied to the classification of different types of biosignals. The methodology directly deals with the highly redundant and irrelevant data contained in these representations, combining a first stage of irrelevant data removal by variable selection, with a second stage of redundancy reduction using methods based on linear transformations. The study addresses two techniques that provided a similar performance: the first one is based on the selection of a set of the most relevant time?frequency points, whereas the second one selects the most relevant frequency bands. The first methodology needs a lower quantity of components, leading to a lower feature space; but the second improves the capture of the time-varying dynamics of the signal, and therefore provides a more stable performance. In order to evaluate the generalization capabilities of the methodology proposed it has been applied to two types of biosignals with different kinds of non-stationary behaviors: electroencephalographic and phonocardiographic biosignals. Even when these two databases contain samples with different degrees of complexity and a wide variety of characterizing patterns, the results demonstrate a good accuracy for the detection of pathologies, over 98%.The results open the possibility to extrapolate the methodology to the study of other biosignals.

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Context-sensitive synaptic plasticity and temporal-to-spatial transformations in hippocampal slices

Hippocampal slices are used to show that, as a temporal input pattern of activity flows through a neuronal layer, a temporal-to-spatial transformation takes place. That is, neurons can respond selectively to the first or second of a pair of input pulses, thus transforming different temporal patterns of activity into the activity of different neurons. This is demonstrated using associative long-term potentiation of polysynaptic CA1 responses as an activity-dependent marker: by depolarizing a postsynaptic CA1 neuron exclusively with the first or second of a pair of pulses from the dentate gyrus, it is possible to “tag” different subpopulations of CA3 neurons. This technique allows sampling of a population of neurons without recording simultaneously from multiple neurons. Furthermore, it reflects a biologically plausible mechanism by which single neurons may develop selective responses to time-varying stimuli and permits the induction of context-sensitive synaptic plasticity. These experimental results support the view that networks of neurons are intrinsically able to process temporal information and that it is not necessary to invoke the existence of internal clocks or delay lines for temporal processing on the time scale of tens to hundreds of milliseconds.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Adaptive designs in the time to event setting: The potential for benefit and risk

Thesis (Ph.D.)--University of Washington, 2016-06

Heart rate variability characterization using a time-frequency based instantaneous frequency estimation technique

In this paper, a new method for characterizing the newborn heart rate variability (HRV) is proposed. The central of the method is the newly proposed technique for instantaneous frequency (IF) estimation specifically designed for nonstationary multicomponen signals such as HRV. The new method attempts to characterize the newborn HRV using features extracted from the time–frequency (TF) domain of the signal. These features comprise the IF, the instantaneous bandwidth (IB) and instantaneous energy (IE) of the different TF components of the HRV. Applied to the HRV of both normal and seizure suffering newborns, this method clearly reveals the locations of the spectral peaks and their time-varying nature. The total energy of HRV components, ET and ratio of energy concentrated in the low-frequency (LF) to that in high frequency (HF) components have been shown to be significant features in identifying the HRV of newborn with seizures.

Time series wind power forecasting based on variant Gaussian process and TLBO

Due to the variability and stochastic nature of wind power system, accurate wind power forecasting has an important role in developing reliable and economic power system operation and control strategies. As wind variability is stochastic, Gaussian Process regression has recently been introduced to capture the randomness of wind energy. However, the disadvantages of Gaussian Process regression include its computation complexity and incapability to adapt to time varying time-series systems. A variant Gaussian Process for time series forecasting is introduced in this study to address these issues. This new method is shown to be capable of reducing computational complexity and increasing prediction accuracy. It is further proved that the forecasting result converges as the number of available data approaches innite. Further, a teaching learning based optimization (TLBO) method is used to train the model and to accelerate
the learning rate. The proposed modelling and optimization method is applied to forecast both the wind power generation of Ireland and that from a single wind farm to show the eectiveness of the proposed method.

Improved Real-time State-of-Charge Estimation of LiFePO4 Battery Based on a Novel Thermoelectric Model

Li-ion batteries have been widely used in electric vehicles, and battery internal state estimation plays an important role in the battery management system. However, it is technically challenging, in particular, for the estimation of the battery internal temperature and state-ofcharge (SOC), which are two key state variables affecting the battery performance. In this paper, a novel method is proposed for realtime simultaneous estimation of these two internal states, thus leading to a significantly improved battery model for realtime SOC estimation. To achieve this, a simplified battery thermoelectric model is firstly built, which couples a thermal submodel and an electrical submodel. The interactions between the battery thermal and electrical behaviours are captured, thus offering a comprehensive description of the battery thermal and electrical behaviour. To achieve more accurate internal state estimations, the model is trained by the simulation error minimization method, and model parameters are optimized by a hybrid optimization method combining a meta-heuristic algorithm and the least square approach. Further, timevarying model parameters under different heat dissipation conditions are considered, and a joint extended Kalman filter is used to simultaneously estimate both the battery internal states and time-varying model parameters in realtime. Experimental results based on the testing data of LiFePO4 batteries confirm the efficacy of the proposed method.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.