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In this paper, an all-fiber optical second-order temporal differentiator (OTD) scheme using an optical Sagnac loop is proposed firstly. The optical Sagnac loop is based on a single length of polarization-maintaining fiber (PMF). Feasibility of the proposed method is verified through theory and simulation. Research results shows that, the PMF-based optical Sagnac loop can provide the second-order temporal differential processing with the bandwidth up to 6.625THz for the input optical Gaussian pulse, under the condition that only one port of the Sagnac loop has optical signal input. The performance of the proposed second-order differentiator was measured from three aspects, differential error factor D, energy efficiency E and 3dB bandwidth of the differentiator. When the input Gaussian pulse has an attenuation factor of 0.5ps, the differential error factor is only about 0.0055 and the energy efficiency is as high as 0.7534. On this basis, an even-order optical temporal differentiator based on cascaded optical Sagnac loops was proposed. The feasibilities of realizing fourth-order and sixth-order optical temporal differentiators were verified. Moreover, the performance of the proposed evenorder differentiators based on cascaded optical Sagnac loops were analyzed comprehensively. It can be concluded from the research results that, the optical temporal differentiator based on cascaded Sagnac loops could achieve good even-order differential function. [ABSTRACT FROM AUTHOR]

Summary: A novel switching differentiator with a considerably simplified form is proposed. Under the assumption that the time‐derivative of a time‐varying signal has a Lipschitz constant, it is shown that estimation error is asymptotically convergent to zero. The estimated derivative shows neither chattering nor peaking phenomenon. A differentiator that estimates the first‐order derivative of a signal is first proposed, and, by connecting this differentiator in series, higher‐order derivatives also become available. Simulation results show that the proposed differentiator shows extreme performance improvements compared to the previously established widely used differentiators such as high‐gain observer or higher‐order sliding mode differentiator. [ABSTRACT FROM AUTHOR]

Abstract The online calculation of fractional derivative is an important technique used in the control engineering area. To achieve satisfactory computing performance, this paper proposes a useful and effective tool named fractional order tracking differentiator (FOTD), which is easy to be implemented. A constructive method for designing the FOTD is developed using a class of asymptotically stable fractional order systems. It is shown that FOTD is the pioneering one to achieve it with simple structure, convenient construction and predominant performance. Finally, several examples are conducted to illustrate the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In recent years, Open Street Map (OSM) has evolved into a highly popular geospatial system. The key of success of OSM is that OSM is open to absolutely everyone. OSM is not dependent on any one government, company, university or international organization. OSM is based on crowdsourcing, in which users collaborate to collect spatial data of urban and rural areas on the earth. With the arising of Linked Open Data (LOD) initiative, and more concretely with Linked Geo Open Data (LGOD), many Web resources have been made available to everyone, providing geo-located datasets. In this paper, a framework, called XOSM (XQuery for OpenStreetMap), for integrating and querying OSM and LGOD resources, is presented. The framework is equipped with a Web tool and a rich XQuery-based library, enabling the definition of queries combining OSM layers and layers created from LGOD resources (KML, GeoJSON, CSV and RDF (and also XML)). The framework also provides an API to execute XQuery queries using the library. [ABSTRACT FROM AUTHOR]

Abstract A novel topology for implementing fractional-order differentiator and integrator transfer functions is presented in this paper. This topology is based on the employment of a second generation Current Conveyor with EXtra inputs (EX-CCII), passive resistors, and fractional-order capacitors. The main benefit offered by this implementation is that both fractional-order differentiator and integrator transfer functions are simultaneously available at different output terminals, and that their frequency characteristics can be orthogonally adjusted without disturbing each other. With only one EX-CCII device needed, the proposed design is attractive from the active component count point of view. As an application example, a fractional-order controller is designed in order to control the velocity of a small scale submersible equipped with one propeller. Evaluation of the performance of the presented topology is performed using Cadence and the Design Kit provided by the Austria Mikro Systeme (AMS) 0.35 μ m CMOS process, as well as through experimental results. [ABSTRACT FROM AUTHOR]

Abstract A fractional-order active disturbance rejection control strategy is presented to realize precise trajectory tracking and point-to-point positioning performances of a newly designed linear motor. Structure characteristics and working mechanism of the new linear motor are analyzed. Reference acceleration feedforward, extended state observer, tracking differentiator, and fractional-order proportional derivative algorithm are combined to achieve high-precision trajectory tracking and point-to-point positioning performances. Different simulations and experiments are compared, and results illustrate that the proposed method performs well in spite of parameter variations and external disturbances. Consequently, precision trajectory tracking and point-to-point positioning performances of the novel linear motor have been obtained. Highlights • A novel linear motor. • A new fractional-order active disturbance rejection controller. • Precision trajectory tracking and point-to-point positioning performances. [ABSTRACT FROM AUTHOR]

Fractional-order differentiator is a principal component of the fractional-order controller. Discretization of fractional-order differentiator is essential to implement the fractional-order controller digitally. Discretization methods generally include indirect approach and direct approach to find the discrete-time approximation of fractional-order differentiator in the Z -domain as evident from the existing literature. In this paper, a direct approach is proposed for discretization of fractional-order differentiator in delta-domain instead of the conventional Z -domain as the delta operator unifies both analog system and digital system together at a high sampling frequency. The discretization of fractional-order differentiator is accomplished in two stages. In the first stage, the generating function is framed by reformulating delta operator using trapezoidal rule or Tustin approximation and in the next stage, the fractional-order differentiator has been approximated by expanding the generating function using continued fraction expansion method. The proposed method has been compared with two well-known direct discretization methods taken from the existing literature. Two examples are presented in this context to show the efficacy of the proposed discretization method using simulation results obtained from MATLAB. [ABSTRACT FROM AUTHOR]

To damp the LCL-filter resonance in a grid-connected inverter, the feedback of capacitor current is usually adopted, and it can be replaced by the feedback of capacitor voltage as a low-cost solution, if an accurate digital differentiator can be made. The best way for realizing such a differentiator has so far proved to be an indirect nonideal generalized integrator (GI). As a simple alternative, this paper proposes two digital differentiators, which are directly developed in the discrete domain. They are a first-order differentiator based on backward Euler plus digital lead compensator and a second-order differentiator based on Tustin plus digital notch filter. The basic idea of the proposed methods is to correct their frequency responses to match the ideal differentiator with embedded digital filters. It is shown that the proposed differentiators exhibit the same derivative performance as the nonideal-GI differentiator, and they are more attractive for digital implementations due to their direct discrete natures, compact expressions, and easy algebraic manipulations. In particular, the proposed first-order differentiator is most competitive for its general representation and simplest implementation. Finally, a 12-kW prototype is built, and experiments are performed to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

To deal with the operation performance degradation of permanent magnet synchronous machine (PMSM) drives with uncertainties and unmodeled dynamics, this paper presents a finite-time nonlinear disturbance observer (FTNDO) based discretized integral sliding mode (DISM) composite control scheme. Based on the reaching-law approach, a DISM speed controller featuring a superior dynamic quality and global robustness against disturbances is constructed. This controller can avoid the reaching phase and overlarge control action. In addition, a sliding mode differentiator based FTNDO is devised and extended to the discrete-time domain for disturbance estimation. The attractive features of the FTNDO are that it can provide a finite-time converging estimation and alleviate the chattering effect in conventional sliding mode observers, while retaining robustness to parameter variations. By feeding the estimate forward to the pre-stage DISM controller, both disturbances and chattering can be significantly suppressed. Moreover, considering the estimation error of a FTNDO caused by discrete sampling, a stability analysis of the composite controller is discussed. Experimental results validate the superiority of the presented scheme. [ABSTRACT FROM AUTHOR]

A fractional-order capacitor and inductor emulator, implemented using MOS transistors, instead of passive capacitors, is introduced in this paper. This is achieved using current mirrors as active elements, without passive resistors, and therefore reducing the circuit complexity and resulting in both a resistorless and capacitorless topology. The emulator has been designed by combining fractional-order differentiator or integrator topologies with a voltage-to-current converter. An important benefit from the design flexibility point of view is that the same topology could be used for emulating a fractional-order capacitor or inductor through an appropriate selection of the time constants and gain factors. Considering that the MOS transistors operate in the strong inversion region, it is feasible for this emulator to operate at high frequencies. The evaluation of the proposed topology has been performed using Cadence IC design suite and the Design Kit provided by the Austrian Micro Systems 0.35 μm CMOS process. [ABSTRACT FROM AUTHOR]

The new design of a fractional-order microwave differentiator is proposed. It is first of its kind and uses short-circuited stub and transmission line sections to emulate the behaviour of an ideal fractional-order differentiator. Least mean square errorbased objective function is formulated to obtain the transfer function of the proposed design, using the chain scattering parameters of line elements in the Z-domain. During the optimisation process, impedance values of equal-electrical-length line elements are considered in the range 10-150 Ω, such that they are practically realisable on the microstrip format. The structure is implemented on the FR4 substrate with permittivity of 4.4 having 1.6 mm thickness. The measured result for the magnitude response of the transmission coefficient is found to be in good agreement with ideal one in the operating frequency range from 0.8 to 6.6 GHz. [ABSTRACT FROM AUTHOR]

In this paper, a robust back-stepping output feedback trajectory tracking controller is proposed for quadrotors subject to parametric uncertainties and external disturbances. Based on the hierarchical control principle, the quadrotor dynamics is decomposed into translational and rotational subsystems to facilitate the back-stepping control design. With given model information incorporated into observer design, a high-order extended state observer (ESO) that relies only on position measurements is developed to estimate the remaining unmeasurable states and the lumped disturbances in rotational subsystem simultaneously. To overcome the problem of “explosion of complexity” in the back-stepping design, the sigmoid tracking differentiator (STD) is introduced to compute the derivative of virtual control laws. The advantage is that the proposed controller via output-feedback scheme not only can ensure good tracking performance using very limited information of quadrotors, but also has the ability of handling the undesired uncertainties. The stability analysis is established using the Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed control scheme in achieving a guaranteed tracking performance with respect to an 8-shaped reference trajectory. [ABSTRACT FROM AUTHOR]

A new approach to perform analog optical differentiation is presented using half-wavelength slabs. First, a half-wavelength dielectric slab is used to design a first order differentiator. The latter works properly for both major polarizations, in contrast to our previously design based on Brewster effect (Youssefi et al., 2016). Inspired by the proposed dielectric differentiator, and by exploiting the unique features of graphene, we further design and demonstrate a reconfigurable and highly miniaturized differentiator using a half-wavelength plasmonic graphene film. To the best of our knowledge, our proposed graphene-based differentiator is even smaller than the most compact differentiator presented so far. [ABSTRACT FROM AUTHOR]

In modern rotating machinery, rotary encoders have been widely used for the purpose of positioning and dynamic control. The study in this paper indicates that, the encoder signal, after proper processing, can be also effectively used for the health monitoring of rotating machines. In this work, a Kurtosis-guided local polynomial differentiator (KLPD) is proposed to estimate the instantaneous angular speed (IAS) of rotating machines based on the encoder signal. Compared with the central difference method, the KLPD is more robust to noise and it is able to precisely capture the weak speed jitters introduced by mechanical defects. The fault diagnosis of planetary gearbox has proven to be a challenging issue in both industry and academia. Based on the proposed KLPD, a systematic method for the fault diagnosis of planetary gearbox is proposed. In this method, residual time synchronous time averaging (RTSA) is first employed to remove the operation-related IAS components that come from normal gear meshing and non-stationary load variations, KLPD is then utilized to detect and enhance the speed jitter from the IAS residual in a data-driven manner. The effectiveness of proposed method has been validated by both simulated data and experimental data. The results demonstrate that the proposed KLPD-RTSA could not only detect fault signatures but also identify defective components, thus providing a promising tool for the health monitoring of planetary gearbox. [ABSTRACT FROM AUTHOR]

We propose and experimentally demonstrate a microwave photonic intensity differentiator based on a Kerr optical comb generated by a compact integrated micro-ring resonator (MRR). The on-chip Kerr optical comb, containing a large number of comb lines, serves as a high-performance multi-wavelength source for implementing a transversal filter, which will greatly reduce the cost, size, and complexity of the system. Moreover, owing to the compactness of the integrated MRR, frequency spacings of up to 200-GHz can be achieved, enabling a potential operation bandwidth of over 100 GHz. By programming and shaping individual comb lines according to calculated tap weights, a reconfigurable intensity differentiator with variable differentiation orders can be realized. The operation principle is theoretically analyzed, and experimental demonstrations of the first-, second-, and third-order differentiation functions based on this principle are presented. The radio frequency amplitude and phase responses of multi-order intensity differentiations are characterized, and system demonstrations of real-time differentiations for a Gaussian input signal are also performed. The experimental results show good agreement with theory, confirming the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

In this paper a new, operational transresistance amplifier (OTRA) based, third order quadrature oscillator (QO) is presented. The proposed structure forms a closed loop using a high pass filter and differentiator. All the resistors employed in the circuit can be implemented using matched transistors operating in linear region thereby making the proposed structure fully integrated and electronically tunable. The effect of non-idealities of OTRA has been analyzed which suggests that for high frequency applications self-compensation can be used. Workability of the proposed QO is verified through SPICE simulations using 0.18µm AGILENT CMOS process parameters. Total harmonic distortion (THD) for the proposed QO is found to be less than 2.5%. The sensitivity, phasenoise analysis is also discussed for the proposed structure. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a robust control for linear systems with external disturbances using a homogeneous differentiator-based observer based on a implicit Lyapunov function approach. Sufficient conditions for stability of the closed-loop system in the presence of external disturbances are obtained and represented by linear matrix inequalities. The parameter tuning for both controller and observer is formulated as a semi-definite programming problem with linear matrix inequalities constraints. Simulation results illustrate the feasibility of the proposed approach and some improvements with respect to the classic linear observer approach. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Parametric uncertainty associated with unmodeled disturbance always exist in physical hydraulic systems, and complicate the advanced nonlinear controller design. In this paper, an adaptive compensation with a robust integral of the sign of the error (RISE) feedback is developed for high precise tracking control of hydraulic motion system. To handle both payload and hydraulic unknown parameters in one controller, a chain of integrator nonlinear system model is first derived, and an adaptive RISE controller is then proposed, in which adaptive law is synthesized to handle parametric uncertainty and RISE robust term to attenuate unmodeled disturbance. The major feature of the proposed controller is that it can theoretically guarantee asymptotic tracking performance with a continuous control input, in the presence of various parametric uncertainties and unmodeled disturbances such as unconsidered dynamics as well as external disturbances via Lyapunov analysis. However, the proposed controller takes the acceleration as a system state, which usually suffers heavy noise pollution and thus cannot be utilized directly in actual control. To solve this practical issue, in this paper, a tracking differentiator is employed to extract high-quality acceleration signal and to make the proposed controller feasible execution. The effectiveness of the proposed nonlinear controller is demonstrated via comparative experimental results. [ABSTRACT FROM PUBLISHER]

This work proposes a robust tracking controller for a helicopter laboratory setup known as the twin rotor MIMO system (TRMS) using an integral sliding mode controller. To eliminate the discontinuity in the control signal, the controller is augmented by a sliding mode disturbance observer. The actuator dynamics is handled using a backstepping approach which is applicable due to the continuous chattering-free nature of the command signals generated using the disturbance observer based controller. To avoid the complexity of analytically differentiating the command signals, a first order sliding mode differentiator is used. Stability analysis of the closed loop system and the ultimate boundedness of the tracking error is proved using Lyapunov stability arguments. The proposed controller is validated by several simulation studies and is compared to other schemes in the literature. Experimental results using a hardware-in-the-loop system validate the robustness and effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Non invasive feature detection in wood based application requires exact discrimination between geometrical edges and texture. It has been found that traditional edge detection algorithms are highly sensitive to noise and texture and produces inferior results with wood. The present work encompasses a micro level reconstruction of Palash and Rosewood by using microX-rays CT scanner. It also encompasses a new edge detection algorithm using newly constructed Chebyshev polynomial based fractional order differentiator. Transform based method has been used for reconstruction purpose. Newly designed fractional order filter has been applied on these reconstructed images. Chebyshev polynomial based fractional order differentiator has been used for filtering operation. Quadrature Mirror Filter (QMF) concept has been used for design of high pass filter and low pass filter. Preprocessing has been performed by using this filter. Canny edge detection algorithm has been used on this preprocessed image. The algorithm has been tested on two different test cases of wood images a) Palash and b) Rosewood. The effect of relaxation coefficient has also been presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. [ABSTRACT FROM AUTHOR]

In this paper, a novel design of third and fifth order differentiator based on lattice wave digital filter (LWDF), established on optimizing L1-error approximation function using cuckoo search algorithm (CSA) is proposed. We present a novel realization of minimum multiplier differentiator using LWD structure leading to requirement of optimizing only N coefficients for N th order differentiator. The γ coefficients of lattice wave digital differentiator (LWDD) are computed by minimizing the L1 -norm fitness function leading to a flat response. The superiority of the proposed LWDD is evident by comparing it with other differentiators mentioned in the literature. The magnitude response of the designed LWDD is found to be of high accuracy with flat response in a wide frequency range. The simulation and statistical results validates that the designed minimum multiplier LWDD circumvents the existing one in terms of minimum absolute magnitude error, mean relative error (dB) and efficient structural realization, thereby making the proposed LWDD a promising approach to digital differentiator design. [ABSTRACT FROM AUTHOR]

Location of poles and zeroes greatly affect phase response and magnitude response of a system. Recently, pole-zero optimization emerged as an effective approach to approximately match magnitude response of a system with that of an ideal one. In this brief, a methodology for the design of linear phase integrators and ones with constant phase of -90 degree is proposed. The aim of this method is to simultaneously attain multiple objectives of magnitude and phase optimization. In this method, magnitude response error is minimized under the constraint that the maximum passband phase-response error is below a prescribed level. Examples are included to illustrate the proposed design technique. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of fractional order PID (FO-PID) controller using hardwired modules of constant phase element (CPE). A new approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within the given bandwidth is realized. Analog circuits, which exhibit analog fractional-order integrator and fractional-order differentiator, are used for building the FO-PID controller. The design procedure is developed to obtain the optimal pole-zero pairs and respective 'Fractance' components to realize for any value of fractional differ-integrator. These CPE elements give minimum error tolerance over the set phase value by using commercially available (R-C) components and Op-Amps. The pole-zero location in the root locus plot with constant asymptotic angle under various feed-forward gains is achieved with these analog integrodifferential circuits of the FO-PID. The iso-damping feature of the controller is practically demonstrated. A comparative performance is demonstrated under various settings of feed forward gains, which indicate the constant overshoot with FO-PID against the conventional PID. These circuits are developed and implemented with a DC motor emulator to confirm the designed performance of the controller. [ABSTRACT FROM AUTHOR]

This paper presents a novel filtering method for speed measurements to improve the low-speed performance of the direct-drive permanent magnet traction machines for elevators. Based on the theory of nonlinear tracking differentiator (NTD), this method, which can act as a high performance filter of a raw speed signal, obtains a more accurate speed feedback signal when applying a low-resolution encoder. In addition, it can relieve the interference caused by the position derivative for speed sampling. By analyzing the frequency response of the NTD, the influence of its parameters on the performance of the speed filtering is investigated. Compared with different types of low-pass filters, the proposed method shows a shorter time delay and a stronger ability in terms of noise suppression when the parameters are selected carefully. In addition, when using the measured speed signal through a nonlinear tracking differentiator as the feedback of the system, the motor runs more steadily at low speeds. As a result, the riding comfort of a direct-drive elevator can be improved. The feasibility of the proposed strategy was verified on an 11.7kW elevator traction machine using a commercial inverter. [ABSTRACT FROM AUTHOR]

In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for N th order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the order-frequency characteristics of a promising circuit element: fractor. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator or integrator in an analog circuit. In this paper, we studied some electrical properties of a fractor. In particular, the order-frequency characteristics of a fractor are introduced. First, the order-sensitivity characteristics of a fractor are proposed. Second, the order-frequency characteristics of a fractor are studied. Third, the time constant of a fractor is analyzed. Last, through mathematical analysis and simulation results, we discussed in detail some issues of the electrical properties of a fractor, especially its time constant. [ABSTRACT FROM AUTHOR]

In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald–Letnikov (G–L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G–L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques. [ABSTRACT FROM PUBLISHER]

A novel topology suitable for emulating fractional-order capacitors and inductors using current excitation is achieved using a fractional-order differentiator/integrator block and appropriately configured Operational Transconductance Amplifiers. The scheme is capable of emulating both fractional-order capacitors and fractional-order inductors without any modifications to its structure. This implementation allows for electronic tuning of the order, capacitance/inductance, and bandwidth of operation by modification of only the bias current. Post-layout simulation results of the impedance magnitude and phase confirm the correct emulated behavior of both fractional-order capacitors and inductors. Two examples highlight the applications of this topology in i) realizing a fractional-order bandpass filter and ii) emulating a Cole-impedance model for biological applications. For both examples the characteristics of each circuit are validated in simulation. [ABSTRACT FROM AUTHOR]

We propose a method and apparatus to determine the generalized parameters of multi-component two-port RLC circuits with a balancing signal in the measuring circuit. In this device, reference voltage sources are n differentiators of test voltage pulses which vary with time as a function of degree n. [ABSTRACT FROM AUTHOR]

In this paper, the authors present two topologies of voltage mode third order quadrature oscillator circuit using operational transresistance amplifier (OTRA). The first circuit is based on low-pass filter and integrator combination, whereas the second one is high-pass filter and differentiator combination. Both the circuits utilize two OTRAs and three resistors and capacitors each. The frequency of oscillation and condition of oscillation can be adjusted independent of each other in both the circuits. The non-ideality analysis of the circuits are also included. The PSPICE simulation and experimental results verify the theoretical proposition. [ABSTRACT FROM AUTHOR]

Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractional calculus i.e. fractional integrator and derivative, using Grünwald–Letnikov definition, on field programmable gate array (FPGA) in LabVIEW environment. The simulation and hardware implementation results for fractional order integrator and derivative of sinusoid and square waveform signals for some selected fractional orders have been presented. A close agreement between the simulated and the experimental results demonstrated the suitability of FPGA device in fractional order control and signal processing applications. LabVIEW being one of the finest tools for measurement and control, and signal processing applications the fractional order operator implementation is expected to further enhance the capability of the tool to cater to the needs of advanced experimental research employing fractional order operators. [ABSTRACT FROM AUTHOR]

The traditional processing model of the temperature error for a gyroscope is serial, meaning that de-noising and temperature drift compensation are implemented in a two-step procedure. Hence, the result of the latter depends on the performance of the former; in particular, negative de-noising produces a negative compensation result. To reduce this dependence, we propose a parallel processing algorithm of the temperature error based on variational mode decomposition (VMD) and an augmented nonlinear differentiator (AND). An application to a micro-electro-mechanical system gyroscope is described to demonstrate the effectiveness and applicability of the proposed algorithm. Its major advantages are (i) a combination of VMD, extreme learning machines, and AND is proposed, and an adaptive accelerometer factor determination method for AND is given based on the VMD, both of which improve the effectiveness of the de-noising process; (ii) temperature drift and noise in the temperature error can be extracted and processed synchronously, thereby reducing the dependency of drift compensation on the de-noising result and making the temperature error process more efficient. [ABSTRACT FROM AUTHOR]

This paper presents a decentralized coordinated excitation and steam valve adaptive control combined with a high-order sliding mode differentiator. The aim is to obtain high performance for the terminal voltage and the rotor speed simultaneously under a sudden fault and a wide range of operating conditions. The methodology adopted is based on second order sliding mode technique using the supper twisting algorithm. The proposed scheme requires only local information on the physically available measurements of relative angular speed, active electric power and terminal voltage with the assumption that the power angle and mechanical power input are not available for measurement. It can be implemented locally and dispersedly for individual generators and is convenient for industrial applications. Simulation results in the case of the Kundur 4-machines 2-area power system show the effectiveness, robustness and superiority of the proposed scheme over the classical AVR/PSS controller and steam valve PI regulator. [ABSTRACT FROM AUTHOR]

This paper has proposed a new composite robust guidance law to intercept maneuvering targets without line-of-sight (LOS) angular rate information. The presented guidance law is constructed through a combination of second-order sliding mode, higher-order sliding mode (HOSM) differentiator, and finite-time convergent disturbance observer (FTDOB). More specifically, the HOSM differentiator is used to extract the LOS angular rate information from LOS angle measurement, while the FTDOB is used to estimate and compensate the unknown target maneuvers. The finite-time stability of the closed-loop guidance system is established using finite-time bounded function and Lyapunov function methods. Next, the proposed guidance law is applied to three-dimensional homing engagement, where the FTDOB is used to estimate the target maneuver as well as the cross-coupling terms between the elevation and the azimuth motions. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the improved active disturbance rejection control (ADRC) method is discussed firstly. This method is applied to the high precision positioning table, which is driven by the voice coil motor (VCM). Compared with the conventional ADRC, the proposed ADRC has been improved for its tracking differentiator (TD) is replaced by the reference trajectory optimization (RTO), which is based on 5 order S-shaped curve (FOS). An extended state observer (ESO) of the ADRC can observe disturbances and uncertainties of the system, and cancel them dynamically. Secondly, the hybrid cascaded H-bridge (HCHB) seven-level inverter topology structure is proposed to make sure that the current could possess high power and low ripple at the same time. However, the HCHB inverter has its own drawback that its current flows backwards in it. Therefore, the hybrid frequency carrier-based PWM (HFPWM) modulation method is put forward to solve this problem. Thirdly, the mathematical model of VCM is established accurately, which takes the air damping, eddy current damping and elastic stiffness into consideration. Finally, the experimental and simulation results show that the improved ADRC control method can effectively improve positioning accuracy and robustness; the FOS curve can reduce the impact of shocks and residual vibration; the HCHB inverter resolves the contradiction between high power and low ripple. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural controller is exploited for a constrained flexible air-breathing hypersonic vehicle (FAHV) based on high-order tracking differentiator (HTD). By utilizing functional decomposition methodology, the dynamic model is reasonably decomposed into the respective velocity subsystem and altitude subsystem. For the velocity subsystem, a dynamic inversion based neural controller is constructed. By introducing the HTD to adaptively estimate the newly defined states generated in the process of model transformation, a novel neural based altitude controller that is quite simpler than the ones derived from back-stepping is addressed based on the normal output-feedback form instead of the strict-feedback formulation. Based on minimal-learning parameter scheme, only two neural networks with two adaptive parameters are needed for neural approximation. Especially, a novel auxiliary system is explored to deal with the problem of control inputs constraints. Finally, simulation results are presented to test the effectiveness of the proposed control strategy in the presence of system uncertainties and actuators constraints. [ABSTRACT FROM AUTHOR]

In this paper, an improved stable digital rational approximation of the fractional-order operator $$s^\alpha ,\alpha \in \,R$$ is developed. First, a novel efficient second-order digital differentiator is derived from the transfer function of the digital integrator proposed by Tseng. Then, the fractional power of the new s-to-z transform is expanded using power series expansion (PSE)-signal-modeling technique to obtain stable rational approximation of $$s^\alpha $$ . Simulation results show that the proposed rational approximation has better frequency characteristics in almost the whole frequency range than that of existing first-order s-to-z transforms based approximations for different values of the fractional-order $$\alpha $$ . This paper also shows the benefit of using PSE-signal-modeling approach with first- or second-order mapping functions over PSE-truncation approach that is used in recent works for rational approximation of the operator $$s^\alpha $$ , and highlights the major disadvantage of the latter approach that leads to undesirable rational models with complex conjugate poles and zeros. [ABSTRACT FROM AUTHOR]

Reconfigurable integrator/differentiator circuits based on the current follower are presented. They are essential for realizing configurable analog blocks (CABs) for field programmable analog arrays (FPAAs). The proposed circuits provide functional reconfigurations and components reuse. These functions provide flexibility in the area of filter design within CAB architectures. Circuits based on current follower have the potential to operate at higher frequency ranges and offer improved linearity over their counterparts based on the operational amplifier and transconductance amplifier, respectively. No switches are used in a signal path in order to avoid degrading the frequency response of the proposed circuits. A CMOS current follower realization compatible with implementation of the proposed designs is adopted. Experimental results obtained from a standard 0.35 µm CMOS process are provided. [ABSTRACT FROM AUTHOR]

This paper presents a comparison study of four advanced tracking differentiators, including global robustexact differentiator, hybrid continuous nonlineardifferentiator, robust exact uniformly convergent arbitrary order differentiator and Taylor expansion series based differentiator. The numerical simulations are performed by three typical signals with different type of noise to illustrate the performanceof tracking differentiation, sensibility to noise and robustness ability. The results show that, over all, these differentiators could track derivate signal of low frequencysignal well and Taylor expansion seriesbased differentiatoris more sensitive to noise than other three differentiators. [ABSTRACT FROM AUTHOR]

A multichannel optical temporal differentiator implemented based on twin-core fiber for wavelength-division-multiplexed (WDM) system is proposed. The key feature of the proposed temporal differentiator is that WDM signals at nominal central frequencies can be simultaneously processed. As an example, a 16-channel WDM first-order optical temporal differentiator is designed and numerically proved, the central frequencies are located at the nominal central frequencies which are suggested in IUT-T G.692 recommendation. The designed device is practically feasible and offer the operation bandwidth of 33.5 GHz and the channel spacing of 100 GHz. Furthermore, the channel numbers can be easily expand to 32, 64, even 128. Performance analysis results show a good accuracy calculating the first-order time differentiation of the standard WDM signals centered at the nominal central frequencies with high energetic efficiency. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the design problems of the digital Riesz fractional order differentiator (FOD) are presented. First, the continuous-time Riesz fractional order derivative is reviewed briefly. Then, the fact that the frequency response of Riesz FOD is only the scaling even part of frequency response of the conventional FOD is shown. Based on this fact, the conventional FOD are applied to design fixed Riesz FOD including fractional differencing method, Tustin׳s method and discrete cosine transform method. Next, the fractional sample delay is used to improve the designed Riesz FOD. And, the discussion on the variable Riesz FOD design and implementation issues are made. Finally, numerical and application examples are demonstrated to show the effectiveness of the proposed digital Riesz fractional order differentiators. [Copyright &y& Elsevier]

New IIR digital differintegrators (differentiator and integrator) with very minor absolute relative errors are presented in this paper. The digital integrator is designed by interpolating some of the existing integrators. The optimum value of the interpolation ratio is obtained through linear programming optimization. Subsequently, by modifying the transfer function of the proposed integrator appropriately, new digital differentiator is obtained. Simulation results demonstrate that the proposed differintegrator are a more accurate approximation of ideal ones, than the existing differintegrators. Furthermore, the proposed differentiator has been tested in an image processing application. Edges characterize boundaries and are, therefore, a problem of fundamental importance in image processing. For comparison purpose Prewitt, Sobel, Roberts, Canny, Laplacian of Gaussian (LOG), Zerocross operators were used and their results are displayed. The results of edge detection by some of the existing differentiators are also provided. The simulation results have shown the superiority of the proposed approach over existing ones. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we have proposed and implemented a wideband sinusoidal frequency to voltage converter (FVC) based on R-C network for high frequency to voltage conversion for frequency. In the converter, R-C network is used as a wideband differentiator, whereas absolute value circuit with amplifier as a rectifier and filter circuit to remove the ripples in the output. The circuit was simulated and designed by using PSPICE software. The linearization of the output was verified with consideration of parasitic effect. It is seen in the simulation that the circuit shows linearity (<0.25%) of frequency to voltage conversion up to 100MHz Oscilloscope traces shows ripple voltage of 150mV and 90mV at operating frequency of 1MHz and 4MHz with output converted voltages 1.2V and 4.8V respectively which proves high linearity of conversion in comparison to the existing sinusoidal FVC. [Copyright &y& Elsevier]

This study presents the application of a fractional-order \PI^ \lambda\D^\mu and an active disturbance rejection (ADR) controller to a nonlinear two-mass system. A complete state-space mathematical model for a nonlinear two-mass system is first developed. Then, a fractional-order \PI^\lambda\D^\mu controller and an ADR controller are both designed to regulate the speed of the system. Design procedures for both controllers are given in detail. Finally, corresponding results are compared. The extended state observer in the ADR controller is tested for torsional torque and the load machine speed with open-loop and closed-loop control structures. Performance analysis for both of the proposed controllers is confirmed by experimental results. Obtained results are also compared with the results given in the literature for the same system. [ABSTRACT FROM PUBLISHER]

Abstract: An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated times is that its -th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform differentiator to the classical High-Order Sliding Mode (HOSM) differentiator. The Uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error. Then, the HOSM differentiator is used to bring the differentiation error to zero in finite-time. [Copyright &y& Elsevier]

In this article, tracking differentiator-based nonlinear control method is proposed for wind generation system to follow the power regulation request from the centralized wind farm controller. To avoid the jump of the power set point for wind generation system specified by the centralized wind farm controller, the transient profile is generated through the tracking differentiator. Then, an optimal control method is proposed to regulate the output power of wind generation system. Particularly, the stable nonlinear controller based on dynamic surface control is designed for the rotational speed regulation. Simulation cases are studied to demonstrate the performance of the proposed control method and the efficiency of the tracking differentiator for power control of the wind generation system in the wind farm. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an adaptive sliding mode super-twisting differentiator which allows the gains to adapt based on the ‘quality’ of the sliding motion. A Lyapunov based analysis for the adaptive super-twisting scheme is presented to demonstrate its properties. As an example, the adaptive differentiator proposed in this paper has been used as part of a nonlinear FDI scheme for an Oscillatory Failure Case (OFC) in an actuator. The FDI scheme requires an estimate of the rod speed which is provided by the adaptive super-twisting differentiator. Due to the conditions in which the actuator operates, normally the differentiator gains are initialised at low values to ensure good rod speed estimation in fault free conditions. However for large amplitude/frequency OFCs, the gains must adapt in order to maintain sliding and provide a good estimation. Simulations on a high fidelity nonlinear aircraft benchmark model have been carried out for both liquid and solid OFCs. [Copyright &y& Elsevier]

Twin-core fiber (TCF) can provide the required spectral response for implementing an optical temporal differentiator. It is shown that the output temporal waveform from one core of the TCF providing full energy coupling is proportional to the first derivative of the optical temporal signal launched at the input. Moreover, TCF can also be used as the first order optical temporal differentiator for multiwavelength optical signals, in which the position and the number of central wavelength can be tunable simply by changing the fiber length. Our numerical results confirmed that the TCF has a good accuracy by calculating the first time derivatives of the input optical signals with temporal features in the picosecond and subpicosecond ranges. [ABSTRACT FROM AUTHOR]