Filter Design Problem Research Articles

Robust Finite-Horizon Filtering for 2-D Systems With Randomly Varying Sensor Delays

This paper is concerned with the robust finite-horizon filter design problem for a class of two-dimensional (2-D) time-varying systems with norm-bounded parameter uncertainties and incomplete measurements. The incomplete measurements cover randomly occurring sensor delays and missing measurements that are presented in a unified form by resorting to a stochastic Kronecker delta function. The occurrences of the sensor delays and missing measurements are governed by stochastic variables with known probability distributions. The main aim of the addressed problem is to design a recursive filter with appropriate gain parameters that ensure the local minimum of certain upper bound on the estimation error variance at each time instant. With the aid of the inductive approach and the 2-D Riccati-like difference equations, one of the first few attempts is made to tackle the robust filter design problem for 2-D uncertain systems with random sensor delays over a finite horizon. Sufficient conditions are provided for the existence of an upper bound on the estimation error variance, an algorithm is then developed to derive such an upper bound, and finally the desired filter is designed to minimize the obtained upper bound. The filter design procedure is of a recursive form that facilitates the online calculation. A numerical simulation is carried out to show the effectiveness of the developed filtering scheme.

A Framework for Optimum Determination of LCL-Filter Parameters for N-Level Voltage Source Inverters Using Heuristic Approach

The use of voltage source multilevel inverters (VS-MLIs) has grown enormously over the last decade, and it is expected that these inverters will be deployed in future power grids (smart grids), especially for medium voltage–high power applications. This paper investigates the application of passive power filters (PPFs) for harmonic mitigation at the output of VS-MLIs for more efficient grid integration of renewable energy sources. It proposes a generic model, using a heuristic approach, for the optimum design of an LCL power filter at the output of VS-MLIs. The proposed model transforms the LCL filter design problem into an optimization problem and applies a genetic algorithm (GA) to solve it. The objective function to be optimized is a multi-objective function based on inverters’ total harmonic distortion and energy losses. The optimization problem is subject to applied design constraints. As a main optimization objective, a precise evaluation methodology for the inverter power losses is presented, which was built according to a practical switching device datasheet. The method is applicable to any VS-MLI topology and any number of levels (N). As a case study, the proposed design optimization approach was implemented to optimally design the LCL filter at the output of a grid connected 11 KV, 5 MVA 7-level cascaded H-bridge multilevel invert (CHB-MLI). The IGBT module Device IGBT of type FZ400R65KE3 by Infineon was used for simulation. MATLAB-SIMULINK is used for the modelling and simulation. We found that the proposed design approach is more generic, efficient, and simple to apply than conventional design approaches which requires more system detail, relies more on the designer’s experience, and normally does not results in optimum design. The proposed approach is generic and can be applied for different VS-MLIs topologies and for any number of levels (N).

Genetic Algorithm Based Prototype Filter Design for Oriented Side Lobe Energy Suppression in FBMC System

The prototype filter design problem is investigated for the filter bank multicarrier (FBMC) system of the fifth generation (5G) physical-layer wireless communications. In order to further suppress the side lobe energy within a certain frequency range, different constraint factors need to be introduced to meet the various side lobe energy suppression demands. In this paper, we formulate a dual-objective optimization problem which minimizes the stopband energy with constrained factors and subjects to the ISI/ICI constraints. Considering the uncertain constrained factors, a suboptimization problem is proposed by constraining the total stopband energy and the side lobe energy of the first segment to minimize the side lobe energy of the second or the third segments. Then, the nested sequential quadratic program-genetic algorithm (NSGA), one of the artificial intelligence (AI) aided algorithms, is introduced to obtain the optimal solution of the dual-objective problem, in which the genetic algorithm (GA) is applied to acquire the optimal constrained factors and the sequential quadratic program (SQP) is applied to acquire the optimal filter coefficients. Numerical results validate that the proposed method can achieve orientated side lobe energy suppression at specified segments for satisfying different side lobe energy suppression requirements with the confirmed algorithm convergence.

The design of a homotopy-based 1-D seismic FIR f − x wavefield extrapolation filters

This paper proposes a novel application of the homotopy method to design accurate non-causal complex-valued seismic FIR wavefield extrapolation digital filters for the purpose of seismic migration. The FIR filter design problem is solved using the scalar homotopy continuation method, since the filter design system of equations is overdetermined. In addition, the design approach was modified to satisfy the consistency conditions of the scalar homotopy method. Being a novel application to design FIR filters, the scalar homotopy method requires longer running design time compared to other existing methods such as the Weighted Least Squares (WLSQ) and the L1-norm methods. At the same time, the homotopy method is globally convergent and does not require the inversion of the Jacobian matrix, which is a significant advantage for practical purposes. Finally, the designed wavefield extrapolation digital filters were tested using the challenging Marmousi model data set, where prestack migration was performed successfully.

Robust Filtering of Discrete-Time Linear Systems With Correlated Process and Measurement Noises

The Gaussian noise assumption is only an approximation to reality and practical engineering systems are often subject to non-Gaussian disturbances, instrument failures and human errors, which all induce outliers. This paper deals with the problem of robust filter design for discrete-time linear systems with correlated process and measurement noises. In the presence of correlated noises, the impact of outliers may spread through correlations and even cause the breakdown of a robust estimator. To address this issue, the robust estimation problem is formulated as a regularized linear regression problem in which the outliers are explicitly modeled and regularized with $\ell _{1}$ -norm to promote sparse solutions. Because of the explicit modeling of outliers, their negative influences propagated through correlations can be estimated and reduced. Hence more accurate estimation results can be expected. By selecting an appropriate regularization parameter, the proposed filter reduces to the well-known Kalman filter and hence is capable of providing a good balance between robustness and optimality. Besides, the extra flexibility of assigning different weights to state and measurement outliers makes it possible to put more focus on outliers from a specific source. Examples using both simulated and experimental data demonstrate the effectiveness of the proposed robust filtering approach.

Resilient filtering for cyber‐physical systems under denial‐of‐service attacks

SummaryOwing to the deep integration of control, computation, and communication, cyber‐physical systems (CPSs) play an important role in wide real‐world applications. In this paper, we investigate the problem of resilient filter design of CPSs under malicious denial‐of‐service (DoS) attacks launched by adversaries. Firstly, based on two standard assumptions concerning with the frequency and duration of DoS attacks, we state the H∞ filtering problem for the CPSs under DoS attacks. Then, sufficient conditions are developed to ensure that, when there are DoS attacks, the filtering error dynamics of the underlying CPSs is mean square exponential stable with a prescribed H∞ disturbance attenuation performance. Furthermore, a switched filter is designed for CPSs under DoS attacks. Examples are given to illustrate the effectiveness and potential of the proposed new design techniques.

Decomposition and reconstruction of ore-caused anomalies information by airborne gamma-ray spectrum based on fractal singular value decomposition method

Identification method research on ore-caused anomalies information is one of the core technologies of airborne gamma-ray spectrum data post-processing. This paper proposed a decomposition and reconstruction method of anomaly information called fractal singular value decomposition (FSVD), aiming at the current ubiquitous truncation error and boundary effect problems in filter design in ore-caused anomaly information identification methods in airborne gamma-ray spectrum. Based on the multi-fractal theory, this method decomposes the singular value of the specific nucleus activity data of the airborne gamma-ray spectrum under time series, and quantitatively calculates the fractal singular value truncation parameter according to residual square sum minimum principle. According to the calculation result, the original data is partially reconstructed to rebuild the ore-caused anomalies information. This paper used the 1:50000 airborne gamma-ray spectrum trial production flight data of a certain area in Inner Mongolia (the surveying area contains proved metal ore occurrences) to verify the method. The results show that: after the original signals are decomposed by FSVD, the high, medium and low singular values can represent the background, anomaly, and noise signal, respectively. At the same time, the false anomaly signals caused by flight error exist in high singular values. After reconstructing the decomposed signals according to median singular values, background noises can be effectively separated, the ore-caused anomaly in the known ore-caused anomalies can be identified and band-like false anomalies caused by time domain batches can be removed.

Asynchronous H∞ filtering of continuous‐time Markov jump systems

SummaryThe paper investigates the asynchronous H∞ filtering design problem for continuous‐time linear systems with Markov jump. The hidden Markov jump principle is applied to represent the asynchronous situation between the target system and the designed filter. Via a Lyapunov technique, two sufficient conditions are developed to guarantee that the filtering error system is stochastically stable with a prescribed H∞ noise attenuation level. Furthermore, three filtering design approaches are developed in the form of linear matrix inequalities. Finally, one example is provided to show the effectiveness and feasibility of the developed methods.

Event-triggered mixed [formula omitted] and passive filtering for discrete-time networked singular Markovian jump systems

The mixed H∞ and passive filtering problem for a class of discrete-time networked singular Markovian jump systems (SMJSs) is investigated in this paper. To reduce transmission of signals in the limited bandwidth networks, a novel event-triggered scheme (ETS) is proposed. A networked singular Markovian jump filtering error system (FES) with time-delay is established by considering the network communication characteristic and the ETS. By utilizing Lyapunov–Kravoskii stability theory, some new criteria are derived in the form of linear matrix inequalities (LMIs) such that the FES is stochastically admissible (SA) and has a prescribed level of mixed H∞ and passive performance. The co-design method is given, which can realize the synchronous design for the filter and ETS parameters. The proposed method can deal with the mode-dependent or mode-independent filter design problems for SMJSs including H∞, passive and mixed filter (i.e., mixed H∞ and passive filter) in a unified form. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed method.

Model Predictive Current Control with a Fixed Switching Frequency for Power Factor Corrected Rectifiers in Microgrid

In this paper, a model predictive current control (MPCC) strategy with a fixed switching frequency to control the dual boost bridgeless power factor corrected (PFC) converter is proposed. The improved MPCC strategy solves the problem of filter design and the high electromagnetic interference (EMI) which caused by the traditional MPCC. With the consideration of a nonlinear inductor, a formula is fitted to represent the change of the inductance, and the improved strategy has strong robustness. The simulation and experiment shows that the quality of current and power factor of the system is improved by the proposed control strategy.

Robust L2-L∞ Filtering for LPV Systems with Distributed Delays

The linear parameter-varying(LPV) systems with distributed delays are studied by the robust filter design problem. Firstly, the parameter-dependent Lyapunov theory is used to propose the L2-L∞ performance criterion of time-delay correlation. Introducing the projection to understand the coupling between the Lyapunov parameter matrix and the system parameter matrix, and obtaining the L2-L∞ performance criterion which is easier to solve. Then the sufficient conditions for the existence of the filter are obtained. The parameterized linear matrix inequality(PLMIs) with infinite dimension is converted to LMIs with finite dimension by using approximate basis function and network technology. Finally, the feasibility of this method is verified by numerical simulation.

A New Filtering Scheme for HVDC Terminals Based on Damped High-Pass Filter

This paper presents the design and application of a recently developed damped high-pass (DHP) filter for the line-commuted converter HVDC terminals. The DHP filter can damp resonance at the noncharacteristic harmonic frequencies commonly encountered by multipulse HVDC links. A design method is developed to address two unique issues faced by HVDC filter design: a wide range of system impedances seen by a HVDC terminal and a variable reactive compensation configuration at the terminal. Both are challenging filter design problems even for traditional filter banks. Using realistic industry case and sensitivity studies, this paper has shown that the proposed filtering scheme and design method can result in saving in filter costs and space requirements without sacrificing performance in comparison with the common filtering schemes used at HVDC terminals. In addition, the proposed design concepts are also applicable to the design of other filters facing the same design issues.

Event-triggered fault detection for continuous-time networked polynomial-fuzzy-model-based systems

The paper deals with the event-triggered fault detection filter design problem for continuous-time networked polynomial-fuzzy-model-based (PFMB) systems. Unlike some existing results, a novel polynomial event-triggered mechanism (PETM) is introduced to reduce the network resource occupancy. Moreover, the resultant event-triggered conditions are checked only at each sampling instant. A polynomial fault detection filter (PFDF), whose membership functions (MFs) and fuzzy rules are different from the considered PFMB systems, is designed to ensure the augmented PFMB fault detection system is asymptotically stable with H∞ performance. The communication delay in communication network transmission is also considered. By adopting an appropriate Lyapunov–Krasovskii (L-K) functional, the sum of square (SOS)-based design conditions are less conservative and time-delay dependent. Two examples are used to demonstrate the effectiveness of the proposed method.

UDE-Based Robust Output Feedback Control With Applications to a Piezoelectric Stage

In this article, an uncertainty and disturbance estimator (UDE)-based robust output feedback control technique without using a state observer is proposed for a general class of nonlinear single-input single-output systems that are bounded-input bounded-output stable and subject to input and output disturbances. Instead of designing a controller for the original system directly, an equivalent system consisting of a first-order linear system plus a lumped uncertainty term is used to represent the input–output relationship. Then, a UDE-based robust controller is designed only using the system output feedback and the bandwidth of the open-loop system, making the design almost modeling-free. A prominent advantage of the proposed approach is that it has converted a challenging robust control problem into an intuitive filter design problem. The effectiveness of the proposed approach is validated on an experimental piezoelectric stage in the presence of hysteresis nonlinearity.

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.

Sparse FIR Filter Design via Partial 1-Norm Optimization

In this brief, we consider a sparse linear-phase FIR filter design problem. Recent methods assume that all the coefficients can be nullified and, thus, various 0 or 1-norm-based optimization techniques are applied on each of them. In contrast, the proposed algorithm is based on two important observations: 1) Given design specifications, some coefficients cannot be nullified, otherwise the specifications cannot be satisfied. 2) Impulse responses on neighboring positions of an FIR filter cannot vary dramatically so as to guarantee the smoothness of the corresponding magnitude responses over most of frequencies. In view of these facts, several rules are adopted in the proposed algorithm to select indices of potential zero coefficients to be used in 1-norm optimization. Simulation results have demonstrated the effectiveness of the proposed design algorithm.

New design approach of three-dimensional IIR notch filter using all-pass sections

ABSTRACTThis paper investigates the design problem of a multidimensional IIR notch filter. To address this issue, a 3-D recursive digital notch filter is considered. A closed-form analytical solution of the notch filter is firstly derived and used for its realisation. The latter is achieved through two types of filters: i) a 3-D IIR straight line filter and ii) 3-D IIR filter with order 111 based on all-pass sections. The straight-line filter is designed by frequency transformation of 3-D analogue prototype filter where a prescribed notch frequency is localised. The IIR filter is realised in proposed lattice structure as a cascade of all-pass sections where the 3-dB bandwidth of the notch filter can be adjusted by the lattice coefficient of the IIR filter independently.

Quantized L1 filtering for stochastic networked control systems based on T–S fuzzy model

This paper is concerned with the L1 filtering problem for a class of nonlinear Ito^ stochastic networked control systems (NCSs) described by Takagi–Sugeno (T–S) fuzzy model. Considering the disadvantages of network-induced delay and quantization error in information transmission, new results on stability and L1 performance are proposed for T–S fuzzy stochastic NCSs by exploiting a Lyapunov–Krasovskii function and by means of the Ito^ stochastic differential equations. Specially, attention is focused on the design of quantization filters of both the fuzzy-rule-independent and fuzzy-rule-dependent that guarantee a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbance input signals. Then, when fuzzy-rule-independent filter is employed, a sufficient condition is proposed to guarantee the mean-square asymptotic stability with an L1 performance for the T–S fuzzy filtering error system. The corresponding design problem of L1 filter is converted into a convex optimization problem by solving a set of linear matrix inequalities (LMIs). Further, the parallel results with the fuzzy-rule-dependent filtering case are obtained, which have less conservatism than the fuzzy-rule-independent one. Finally, two simulation examples are provided to illustrate the feasibility and effectiveness of the proposed method.

Optimal Design of IIR Filters via the Partial Fraction Decomposition Method

In this brief, we consider the minimax design of infinite impulse response (IIR) filter. First, we apply the partial fraction method to decompose the transfer function into a sum of low order fractions, as a result the minimax IIR filter design problem can be formulated with the stability condition as constraints. Second, among different possible decompositions of the transfer function, we prove that the second order decomposition can always achieve good approximation to the optimal solution. Based on the second order decomposition formulation, several numerical experiments have been conducted, and better IIR filters can be designed using the proposed method compared with existing methods in the literature.

Filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi–Sugeno (T–S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a known finite frequency (FF) domain. An FF performance is defined for 2D discrete-time systems, which generalises the standard one and makes use of the frequency-domain characteristics of practical signals. By virtue of the defined FF performance, sufficient conditions are proposed for analysing the disturbance attenuation performance of the filtering error system. Efficient conditions are obtained to guarantee the existence of a filter and such that the error system is asymptotically stable with an FF performance index. A systematic filter design scheme is developed by converting the corresponding fuzzy filter design into a convex optimisation problem. Finally, a gas absorption system is employed to illustrate the validity of the proposed methods.