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Inherent control delays and changeable grid operational conditions pose significant challenges to the stability of the Modular multilevel converter-based high voltage direct current (MMC-HVDC) system, inducing the risk of high-frequency resonances (HFR). This paper proposes a passivity enhancement based on the second-order digital differentiator (DD) and lead-lag compensator, ensuring reliable and robust HFR suppression performance even under the resonance frequency drift and fault earthing scenes. First, the passivity-based stability analysis is provided based on the system output impedance model, elucidating the HFR mechanisms and frequency drift problems. Second, the proposed passivity enhancement scheme's control structure and impedance reshaping principle are analyzed to verify resonance suppression ability. Third, the control parameters tuning process and direct realization of differentiator are detailed, reinforcing the stable margin and harmonic rejection ability. Finally, several case studies and simulation results are provided to validate the effectiveness of the proposed passivity-based HFR suppression scheme. • The proposed scheme integrates a second-order digital differentiator plus a lead-lag compensator. • Superior passivity and harmonic rejection ability are ensured, with frequency drift risk-solving ability. • Parameters tuning and differentiator discretization realization are elaborated. • Large phase lag and noise amplification problems are solved by impedance reshaping. [ABSTRACT FROM AUTHOR]

• If the frequency is contemplated in models, the estimates in signals are better. • The importance to increase and decrease the sampling rate in dynamic signals. • Update parameters in models achieve better performance in dynamic signals. This paper presents a method to obtain good synchronous and instantaneous estimates in position, velocity and acceleration; using a position measurement only. The proposed method shows better estimates in position, velocity and acceleration than other methods such as nonlinear tracking differentiator (TD), extended state estimation (ESO) and digital differentiator based on Taylor series (DDBTS). The proposed method allows for an increased accuracy of estimates by generating a feedback frequency obtained to the position measurement signals. The model and method proposed in this paper reduce the error when the measurement signal presents a change in frequency. The model update and adjusts simultaneously to changes in sample rates using a feedback frequency estimate. The proposed method was validated with the QNET DC Motor Control Trained (DCMCT). Since the method requires the measurement position only from an encoder, it eliminates the need for more sensors for velocity and acceleration, thus begin less costly. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic algorithm called Interior Search Algorithm (ISA), which is applied for digital differentiator design problem. ISA is based on the principles of aesthetic techniques commonly used in interior design and decoration. ISA has a very quick convergence rate and only one control parameter. The approach presented here has alleviated from the problems of premature convergence, stagnation and revisiting of the same solution over and over again, which is common in other optimization techniques. Statistical and simulation results have been compared with already existing differentiator design methods such as segment rule, genetic algorithm (GA), simulated annealing (SA), pole zero method (PZ) and particle swarm optimization (PSO). The results affirm that the proposed method outperforms its counterparts in terms of absolute magnitude error and phase error. [ABSTRACT FROM AUTHOR]

Abstract: Studies on analysis, design and applications of analog and digital differentiators and integrators of fractional order is the main objective of this paper. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active and passive realization of fractance device of order using continued fraction expansion is carried out. Later, time and frequency domain analysis of fractance based circuits is considered. The variations of rise time, peak time, settling time, time constant, percent overshoot with respect to fractional order is presented. Digital differentiators and integrators of fractional order can be obtained by using direct and indirect discretization techniques. The s to z transforms used for this purpose are revisited. In this paper by using indirect discretization technique fractional order differentiators and integrators of order and are designed. These digital differentiators and integrators are implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS). The designed fractional order differentiators have been used for the detection of QRS sequences as well as the occurrence of Sino Atrial Rhythms in an ECG signal and also for the detection of edges in an image. The obtained results are in comparison with the conventional techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the variable fractional-order (VFO) differintegrator is designed based on IIR-typed Farrow structure. The stability of the designed VFO IIR differintegrator is achieved by incorporating a constrained function into the objective error function. But the minimization of the original objective error function is a highly nonlinear problem, so an iterative quadratic method is proposed to overcome it. Comparing with the design based on FIR-typed Farrow structure, several designed examples, including a VFO differintegrator, a pure VFO differentiator and a pure VFO integrator, are presented to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In the paper, a new method is proposed for the design of variable fractional-order (VFO) FIR differintegrators. Comparing with the existing methods, the elements of relevant matrices can be determined just by the given specification, which makes the method easier. An iterative technique is also incorporated to adjust the weighting function, such that the peak absolute error of variable frequency response can be reduced drastically. Several design examples, including a VFO differintegrator, two VFO differentiators and a VFO integrator, are presented to demonstrate the effectiveness and flexibility of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the design of fractional order Simpson digital integrator is investigated. First, the conventional transfer function of second-order IIR Simpson integrator is factorized into product of first-order factors. Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion. Next, truncating the length of series expansion, the transfer functions of FIR and IIR fractional order Simpson integrators are obtained. It is shown that the IIR fractional integrator is always stable. Finally, design examples are demonstrated to illustrate the performance of the proposed method and some further improvement using fractional delay is also discussed. [Copyright &y& Elsevier]

This paper proposes an approach based on a weighted L 1 -norm optimization criterion and employs it in conjunction with salp swarm algorithm (SSA) to design 2nd- to 4th-order wideband infinite impulse response (IIR) digital differentiators (DDs). Integration of the proposed fitness function and SSA allows both the magnitude and phase responses to be improved. An extensive simulation is carried out to explore the performance of the proposed approach. First, a comparative study with widely used methods, namely, real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO), is performed to examine accuracy, robustness, consistency and efficiency. Afterwards, the magnitude and phase responses of the proposed digital differentiators are compared with those of the existing designs in the literature. New wideband IIR digital integrators (DIs) are derived by inverting transfer functions of their respective digital differentiators and then compared with the existing designs in the literature in terms of the magnitude and phase responses. Simulation and statistical results reveal that the superiority of the proposed approach is statistically significant and demonstrate that the proposed digital differentiators and integrators significantly outperform all state-of-the-art designs in terms of the magnitude response as measured by the absolute relative error (A R E) with almost linear phase responses in wideband frequency regions. [ABSTRACT FROM AUTHOR]