Development of the propagation paths and deriving observer of feedforward active noise control system by using state-space formulation

This paper presents the derivation and simulation of the propagation paths of a feedforward active noise control (ANC) system in one dimensional free-field medium using state-space model (SSM) instead of Finite Impulse Response (FIR) model. Furthermore, a new observer namely State Space Least Mean Square (SSLMS) observer will be derived. This observer will be used to estimate the states along the propagation path which can not be estimated using LMS algorithm because LMS based on the FIR models. The system is simulated in MATLAB and the results of the pressure modes along the noise path are depicted and have shown that the level of the acoustic signal decreases gradually against the modes. The results of the novel observer to show the comparison of the tracking the pressures of three modes along the interfering region between the primary and secondary path are shown with the mode which is located at the observer achieving accurate estimation

Development of a State-Space Observer for Active Noise Control Systems

Active noise control (ANC) is a method of reducing the unwanted sound. This is realized by artificially generating canceling (secondary) source(s) of sound through detecting the unwanted (primary) noise and processing it by an electronic controller, so that when the secondary wave is superimposed on the primary wave the two destructively interfere and cancellation occurs at the observation point. ANC system is an active research area for its high demand especially in the acoustic noise and vibration control systems. A lot of work in modeling an ANC system involves the transfer function approach, but unfortunately this method allows observation at a single point or mode. It is of interest to measure the level of cancellation not only at the observer but also around it. Therefore, a state space approach would allow observation at multi modes simultaneously and became the subject of this research. This thesis is concerned with the study and development of a state-space model (SSM) for ANC system in on dimensional free-field medium instead of Finite Impulse Response (FIR) Models. In this work, the derivation of the SSM of each propagation path of ANC system is presented and hence the system is termed Feedforward state space control system with feedback inclusion single input single output (SISO) architecture. The criterions of success considered the evaluation process are the length of the propagation path, level of cancellation, convergence rate, number of modes of each path, and destructive interferences occur at the cancellation path. The secondary path of the ANC system is modeled by using the LMS algorithm to complete the design of the Filtered-X Least Mean Square (FXLMS) controller. Then the adaptive FXLMS controller is presented and incorporated with the proposed model for both Feedforward with / without the acoustic Feedback cases. As a result, the comparisons between the two cases are presented by mean of level of cancellation and convergence rate. The simulation results of the proposed model show that the level of the disturbance signal at ten modes along the primary path is decreasing as much as the modes go away from the source indicating that this model is suitable to build the mechanism of the ANC system which satisfies the relation between the wave dissipation against the number of modes which are distributed along the length of path. The derivation of the SSM gives the opportunity to extend the work furthermore to involve the derivation of a state-space optimal observer which is named State Space Least Mean Square (SSLMS) observer. This observer is employed to observe and monitor the pressure modes along the propagation path through simulating it in an offline structure i.e. without controller, or to observe the modes at the cancellation path through simulating the SSLMS in an on-line structure i.e. while the controller is converging. The comparison results between the real and observed modes of the secondary propagation show an accurate observing. Finally, the comparisons of the observed pressures of three modes along the cancellation path while the controller is converging (on-line structure) are shown with the mode which is located at the observer achieving the best cancellation

Estimation of parameters in a structured SIR model

[EN] In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model. We propose an iterative algorithm to study the identifiability of the system and a method to estimate the parameters which are identifiable. A least squares approach based on a finite set of observations helps us to estimate the initial values of the parameters. Finally, we test the proposed algorithms.The authors would like to thank the referees and the editor for their comments and useful suggestions for improvement of the manuscript. This work has been partially supported by Spanish Grant MTM2013-43678-P.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2017). Estimation of parameters in a structured SIR model. Advances in Difference Equations. 33:1-13. https://doi.org/10.1186/s13662-017-1078-5S11333Strogatz, S, Friedman, M, Mallinck-Rodt, AJ, McKay, S: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books, Washington (1994)De La Sen, M, Quesada, A: Some equilibrium, stability, instability and oscillatory results for an extended discrete epidemic model with evolution memory. Adv. Differ. Equ. 2013, 234 (2013)Han, Q, Wang, Z: On extinction of infectious diseases for multi-group SIRS models with satured incidence rate. Adv. Differ. Equ. 2015, 333 (2015)Cantó, B, Coll, C, Sánchez, E: Structural identifiability of a model of dialysis. Math. Comput. Model. 50, 733-737 (2009)Cantó, B, Coll, C, Sánchez, E: Identifiability of a class of discretized linear partial differential algebraic equations. Math. Probl. Eng., 1-12 (2011)Craciun, G, Pantea, C: Identifiability of chemical reaction networks. J. Math. Chem. 44, 244-259 (2008)Malik, MB, Salman, M: State-space least mean square. Digit. Signal Process. 18, 334-345 (2008)Ding, F, Liu, PX, Liu, G: Multiinnovatiovation least-squares identification for system modeling. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 18(3), 767-778 (2010)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, I. The generalized Markov parameter approach. Ind. Eng. Chem. Res. 42, 6607-6618 (2003)Boyadjiev, C, Dimitrova, E: An iterative method for model parameter identification. Comput. Chem. Eng. 29, 941-948 (2005)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, 2. The differential-algebraic approach. Ind. Eng. Chem. Res. 43, 1251-1259 (2004)Dion, JM, Commault, C, van der Woude, J: Generic properties and control of linear structured systems: a survey. Automatica 39, 1125-1144 (2003)Chou, IC, Voit, EO: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math. Biosci. 219, 57-83 (2009)Schmitz, OJ: Ecology and Ecosystems Conservation. Island Press, Washington (2013

Microgrid state estimation and control using Kalman filter and semidefinite programming technique

The design of environment-friendly microgrids at the smart distribution level requires a stable behaviour for multiple state operations. This paper develops a Kalman filter based optimal feedback control method for the microgrid state estimation and stabilization. First, the microgrid is modelled by a discrete-time state space equation. Then the cost-effective smart sensors are deployed in order to obtain the required system information. From the communication point of view, the recursive systematic convolution code is adopted to add the redundancy in the system. At the end, the soft output Viterbi decoder is used to recover the system information from the noisy measurements and transmission uncertainties. Thereafter, the Kalman filter is utilized to estimate the system states, which acts as a precursor for applying the control algorithm. Finally, this paper proposes an optimal feedback control method to stabilize the microgrid based on semidefinite programming. The performance of the proposed approach is demonstrated by extensive numerical simulations

Robust Least Squares Methods Under Bounded Data Uncertainties

Cataloged from PDF version of article.We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations

A Novel Blended State Estimated Adaptive Controller for Voltage and Current Control of Microgrid against Unknown Noise

© 2013 IEEE. In this study, a novel blended state estimated adaptive controller is designed for voltage and current control of microgrid against unknown noise. The core feature of the microgrid (MG) is its ability to integrate more than one distributed energy resource into the main grid. The state of a microgrid may deteriorate due to many reasons, for example malicious cyber-attacks, disturbances, packet losses, etc. Therefore, it is necessary to achieve the true state of the system to enhance the control requirement and automation of the microgrid. To achieve the true state of a microgrid, this study proposes the use of an algorithm based on the unscented kalman filter (UKF). The proposed state estimator technique is developed using an unscented-transformation and sigma-points measurement technique capable of minimizing the mean and covariance of a nonlinear cost function to estimate the true state of a single-phase, three-phase single-source and three-phase multi-source microgrid system. The advantage of the proposed estimator over using extended kalman filter (EKF) is investigated in simulations. The results demonstrate that the use of the UKF estimator produces a superior estimation of the system compared with the use of the EKF. An adaptive PID controller is also developed and used in system conjunction with the estimator to regulate its voltage and current against the number of loads. Deviation in load parameters hamper the function of the MG system. The performance of the developed controller is also evaluated against number of loads. Results indicate the controller provides a more stable and high-tracking performance with the inclusion of the UKF in the system

A Computationally Efficient Distributed Framework for a State Space Adaptive Filter for the Removal of PLI from Cardiac Signals

The proliferation of cardiac signals, such as high-resolution electrocardiograms (HRECGs), ultra-high-frequency ECGs (UHF–ECGs), and intracardiac electrograms (IEGMs) assist cardiologists in the prognosis of critical cardiac diseases. However, the accuracies of such diagnoses depend on the signal qualities, which are often corrupted by artifacts, such as the power line interference (PLI) and its harmonics. Therefore, state space adaptive filters are applied for the effective removal of PLI and its harmonics. Moreover, the state space adaptive filter does not require any reference signal for the extraction of desired cardiac signals from the observed noisy signal. Nevertheless, the state space adaptive filter inherits high computational complexity; therefore, filtration of the increased number of PLI harmonics bestows an adverse impact on the execution time of the algorithm. In this paper, a parallel distributed framework for the state space least mean square with adoptive memory (PD–SSLMSWAM) is introduced, which runs the computationally expensive SSLMSWAM adaptive filter parallelly. The proposed architecture efficiently removes the PLI along with its harmonics even if the time alignment among the contributing nodes is not the same. Furthermore, the proposed PD-SSLMSWAM scheme provides less computational costs as compared to the sequentially operated SSLMSWAM algorithm. A comparison was drawn among the proposed PD–SSLMSWAM, sequentially operated SSLMSWAM, and state space normalized least mean square (SSNLMS) adaptive filters in terms of qualitative and quantitative performances. The simulation results show that the proposed PD–SSLMSWAM architecture provides almost the same qualitative and quantitative performances as those of the sequentially operated SSLMSWAM algorithm with less computational costs. Moreover, the proposed PD–SSLMSWAM achieves better qualitative and quantitative performances as compared to the SSNLMS adaptive filter