Conventional proportional integral derivative(PID)controllers are being used in the industries for control purposes.It is very simple in design and low in cost but it has less capability to minimize the low frequency ...Conventional proportional integral derivative(PID)controllers are being used in the industries for control purposes.It is very simple in design and low in cost but it has less capability to minimize the low frequency noises of the systems.Therefore,in this study,a low pass filter has been introduced with the derivative input of the PID controller to minimize the noises and to improve the transient stability of the system.This paper focuses upon the stability improvement of a wind-diesel hybrid power system model(HPSM)using a static synchronous compensator(STATCOM)along with a secondary PID controller with derivative filter(PIDF).Under any load disturbances,the reactive power mismatch occurs in the HPSM that affects the system transient stability.STATCOM with PIDF controller is used to provide reactive power support and to improve stability of the HPSM.The controller parameters are also optimized by using soft computing technique for performance improvement.This paper proposes the effectiveness of symbiosis organisms search algorithm for optimization purpose.Binary coded genetic algorithm and gravitational search algorithm are used for the sake of comparison.展开更多
为探索用近红外光谱快速检测烤烟填充值的可行性,选取有代表性的94个河南烤烟样品,采用偏最小二乘法(Partial Least Square,PLS)将近红外光谱数据与其填充值的实测值进行拟合,建立填充值预测模型,考察了光谱预处理方法和光谱范围对建模...为探索用近红外光谱快速检测烤烟填充值的可行性,选取有代表性的94个河南烤烟样品,采用偏最小二乘法(Partial Least Square,PLS)将近红外光谱数据与其填充值的实测值进行拟合,建立填充值预测模型,考察了光谱预处理方法和光谱范围对建模效果的影响,并进行了内部交叉验证、外部验证和模型精度检验。结果表明:1标准正态变量变换(Standard normal variate,SNV)结合一阶导数法的光谱预处理方法和全谱范围适合构建填充值的近红外模型;2模型的决定系数达0.960,均方根校正误差(Root mean square error of calibration,RMSEC)为0.094,内部交叉验证和外部验证均表明模型预测值和实测值呈极显著相关;3模型精密度检验的相对标准偏差<3%。填充值近红外预测模型的重复性好,准确性较高,适于批量烤烟填充值的快速检测。展开更多
In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,whic...In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV model.The fractional derivative is taken in the conformable sense.Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package.The results indicate that both methods are easy to implement,effective and reliable.They are therefore ready to apply for various partial fractional differential equations.展开更多
Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different application...Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.展开更多
The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), whe...This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.展开更多
In this paper,we derive the fractional convection(or advection)equations(FCEs)(or FAEs)to model anomalous convection processes.Through using a continuous time random walk(CTRW)with power-law jump length distributions,...In this paper,we derive the fractional convection(or advection)equations(FCEs)(or FAEs)to model anomalous convection processes.Through using a continuous time random walk(CTRW)with power-law jump length distributions,we formulate the FCEs depicted by Riesz derivatives with order in(0,1).The numerical methods for fractional convection operators characterized by Riesz derivatives with order lying in(0,1)are constructed too.Then the numerical approximations to FCEs are studied in detail.By adopting the implicit Crank-Nicolson method and the explicit Lax-WendrofT method in time,and the secondorder numerical method to the Riesz derivative in space,we,respectively,obtain the unconditionally stable numerical scheme and the conditionally stable numerical one for the FCE with second-order convergence both in time and in space.The accuracy and efficiency of the derived methods are verified by numerical tests.The transport performance characterized by the derived fractional convection equation is also displayed through numerical simulations.展开更多
文摘Conventional proportional integral derivative(PID)controllers are being used in the industries for control purposes.It is very simple in design and low in cost but it has less capability to minimize the low frequency noises of the systems.Therefore,in this study,a low pass filter has been introduced with the derivative input of the PID controller to minimize the noises and to improve the transient stability of the system.This paper focuses upon the stability improvement of a wind-diesel hybrid power system model(HPSM)using a static synchronous compensator(STATCOM)along with a secondary PID controller with derivative filter(PIDF).Under any load disturbances,the reactive power mismatch occurs in the HPSM that affects the system transient stability.STATCOM with PIDF controller is used to provide reactive power support and to improve stability of the HPSM.The controller parameters are also optimized by using soft computing technique for performance improvement.This paper proposes the effectiveness of symbiosis organisms search algorithm for optimization purpose.Binary coded genetic algorithm and gravitational search algorithm are used for the sake of comparison.
文摘为探索用近红外光谱快速检测烤烟填充值的可行性,选取有代表性的94个河南烤烟样品,采用偏最小二乘法(Partial Least Square,PLS)将近红外光谱数据与其填充值的实测值进行拟合,建立填充值预测模型,考察了光谱预处理方法和光谱范围对建模效果的影响,并进行了内部交叉验证、外部验证和模型精度检验。结果表明:1标准正态变量变换(Standard normal variate,SNV)结合一阶导数法的光谱预处理方法和全谱范围适合构建填充值的近红外模型;2模型的决定系数达0.960,均方根校正误差(Root mean square error of calibration,RMSEC)为0.094,内部交叉验证和外部验证均表明模型预测值和实测值呈极显著相关;3模型精密度检验的相对标准偏差<3%。填充值近红外预测模型的重复性好,准确性较高,适于批量烤烟填充值的快速检测。
文摘In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV model.The fractional derivative is taken in the conformable sense.Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package.The results indicate that both methods are easy to implement,effective and reliable.They are therefore ready to apply for various partial fractional differential equations.
基金Authors gratefully acknowledge Ajman University for providing facilities for our research under Grant Ref.No.2019-IRG-HBS-11.
文摘Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
文摘This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.
基金The work was partially supported by the National Natural Science Foundation of China under Grant nos.11671251 and 11632008.
文摘In this paper,we derive the fractional convection(or advection)equations(FCEs)(or FAEs)to model anomalous convection processes.Through using a continuous time random walk(CTRW)with power-law jump length distributions,we formulate the FCEs depicted by Riesz derivatives with order in(0,1).The numerical methods for fractional convection operators characterized by Riesz derivatives with order lying in(0,1)are constructed too.Then the numerical approximations to FCEs are studied in detail.By adopting the implicit Crank-Nicolson method and the explicit Lax-WendrofT method in time,and the secondorder numerical method to the Riesz derivative in space,we,respectively,obtain the unconditionally stable numerical scheme and the conditionally stable numerical one for the FCE with second-order convergence both in time and in space.The accuracy and efficiency of the derived methods are verified by numerical tests.The transport performance characterized by the derived fractional convection equation is also displayed through numerical simulations.
