This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncerta...This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.展开更多
In this study,a theoretical nonlinear dynamic model was established for a saddle ring based on a dynamic force analysis of the launching process and the structure according to contact-impact theory.The ADAMS software ...In this study,a theoretical nonlinear dynamic model was established for a saddle ring based on a dynamic force analysis of the launching process and the structure according to contact-impact theory.The ADAMS software was used to build a parameterized dynamic model of the saddle ring.A parameter identification method for the ring was proposed based on the particle swarm optimization algorithm.A loading test was designed and performed several times at different elevation angles.The response histories of the saddle ring with different loads were then obtained.The parameters of the saddle ring dynamic model were identified from statistics generated at a 500 elevation angle to verify the feasibility and accuracy of the proposed method.The actual loading history of the ring at a 70°elevation angle was taken as the model input.The response histories of the ring under these working conditions were obtained through a simulation.The simulation results agreed with the actual response.Thus,the effectiveness and applicability of the proposed dynamic model were verified,and it provides an effective method for modeling saddle rings.展开更多
A new modified LuGre friction model is presented for electromagnetic valve actuator system.The modification to the traditional LuGre friction model is made by adding an acceleration-dependent part and a nonlinear cont...A new modified LuGre friction model is presented for electromagnetic valve actuator system.The modification to the traditional LuGre friction model is made by adding an acceleration-dependent part and a nonlinear continuous switch function.The proposed new friction model solves the implementation problems with the traditional LuGre model at high speeds.An improved artificial fish swarm algorithm(IAFSA)method which combines the chaotic search and Gauss mutation operator into traditional artificial fish swarm algorithm is used to identify the parameters in the proposed modified LuGre friction model.The steady state response experiments and dynamic friction experiments are implemented to validate the effectiveness of IAFSA algorithm.The comparisons between the measured dynamic friction forces and the ones simulated with the established mathematic friction model at different frequencies and magnitudes demonstrate that the proposed modified LuGre friction model can give accurate simulation about the dynamic friction characteristics existing in the electromagnetic valve actuator system.The presented modelling and parameter identification methods are applicable for many other high-speed mechanical systems with friction.展开更多
Several parameter identification methods of thermal response test were evaluated through numerical and experimental study.A three-dimensional finite-volume numerical model was established under the assumption that the...Several parameter identification methods of thermal response test were evaluated through numerical and experimental study.A three-dimensional finite-volume numerical model was established under the assumption that the soil thermal conductivity had been known in the simulation of thermal response test.The thermal response curve was firstly obtained through numerical calculation.Then,the accuracy of the numerical model was verified with measured data obtained through a thermal response test.Based on the numerical and experimental thermal response curves,the thermal conductivity of the soil was calculated by different parameter identification methods.The calculated results were compared with the assumed value and then the accuracy of these methods was evaluated.Furthermore,the effects of test time,variable data quality,borehole radius,initial ground temperature,and heat injection rate were analyzed.The results show that the method based on cylinder-source model has a low precision and the identified thermal conductivity decreases with an increase in borehole radius.For parameter estimation,the measuring accuracy of the initial temperature of the deep ground soil has greater effect on identified thermal conductivity.展开更多
A new experimental apparatus was set up to investigate the actual fi-iction characteristics on the basis of speed control of the serve system.A modified friction model was proposed due to real time varying deformation...A new experimental apparatus was set up to investigate the actual fi-iction characteristics on the basis of speed control of the serve system.A modified friction model was proposed due to real time varying deformation resistance.The approach to identify the parameters of comprehensive friction behaviors based on the modified model was proposed and applied to the forging press.The impacts on parameters which the external load had were also investigated.The results show that friction force decreases with velocity in the low velocity regime whereas the friction force increases with the velocity in the high velocity regime under no external load.It is also shown that the Coulomb friction force,the maximum static friction force and the vicious friction coefficient change linearly with the external load taking the velocity at which the magnitude of the steady state friction force becomes minimum as the critical velocity.展开更多
In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood ...In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.展开更多
Accurate parameter identification is essential when designing controllers for inertially stabilized platforms （lSPs）. But traditional identification methods suffer from observation measurement noise and operating re...Accurate parameter identification is essential when designing controllers for inertially stabilized platforms （lSPs）. But traditional identification methods suffer from observation measurement noise and operating restrictions of ISPs. To address this issue, a novel identification method based on current command design and multilevel coordinate search （MCS） algorithm without any higher order measurement differentiations was proposed. The designed current commands were adopted to obtain parameter decoupled models with the platform operating under allowable conditions. MCS algorithm was employed to estimate the parameters based on parameter decoupled models. A comparison experiment between the proposed method and non-linear least square method was carried out and most of the relative errors of identified parameters obtained by the proposed method were below 10%. Simulation and experiment based on identified parameters were conducted. A velocity control structure was also developed with disturbance observer （DOB） for application in disturbance compensation control system of an ISR Experimental results show that the control scheme based on the identified parameters with DOB has the best disturbance rejection performance. It reduces the peak to peak value （PPV） of velocity error integral to 0.8 mrad which is much smaller than the value （10 mrad） obtained by the single velocity controller without DOB. Compared with the control scheme based on sweep model with DOB compensation, the proposed control scheme improves the PPV of velocity error integral by 1.625 times.展开更多
The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewis...The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.展开更多
A model to describe the hysteresis damping characteristic of rubber material was presented.It consists of a parallel spring and damper,whose coefficients change with the vibration amplitude and frequency.In order to a...A model to describe the hysteresis damping characteristic of rubber material was presented.It consists of a parallel spring and damper,whose coefficients change with the vibration amplitude and frequency.In order to acquire these relations,force decomposition was carried out according to some sine vibration measurement data of nonlinear forces changing with the deformation of the rubber material.The nonlinear force is decomposed into a spring force and a damper force,which are represented by the amplitude-and frequency-dependent spring and damper coefficients,respectively.Repeating this step for different measurements gives different coefficients corresponding to different amplitudes and frequencies.Then,the application of a parameter identification method provides the requested approximation functions over amplitude and frequency.Using those formulae,as an example,the dynamic characteristic of a hollow shaft system supported by rubber rings was analyzed and the acceleration response curve in the centroid position was calculated.Comparisons with the sine vibration experiments of the real system show a maximal inaccuracy of 8.5%.Application of this model and procedure can simplify the modeling and analysis of mechanical systems including rubber materials.展开更多
In mechanical, hydraulic and electronic systems, the determination of system parameters is often challenging because liquid parameters often change significantly, due to variations in working and environmental conditi...In mechanical, hydraulic and electronic systems, the determination of system parameters is often challenging because liquid parameters often change significantly, due to variations in working and environmental conditions. Therefore, it is of significant practical importance to identify those parameters through experimental procedures. A systematic approach to identifying parameters in the valve controlling cylinder system of hydraulic manipulators is provided. It first derives the transfer function of the system, and then uses P control of PID control to predict system parameters. The predicted parameters are further validated using PID control. The prediction through simulation using MatLab language is utilized, which agrees well with experimental results.展开更多
针对过程复杂且结构未知的对象,在保证模型有效性的前提下,根据数据信息构建简单模型来简化控制器的求解是亟待解决的问题。以受控自回归模型为例,提出一种基于修正最小角回归算法的稀疏辨识方法。首先将系统模型转化为过参数化的高维...针对过程复杂且结构未知的对象,在保证模型有效性的前提下,根据数据信息构建简单模型来简化控制器的求解是亟待解决的问题。以受控自回归模型为例,提出一种基于修正最小角回归算法的稀疏辨识方法。首先将系统模型转化为过参数化的高维稀疏模型,然后将最小角回归算法用于稀疏系统辨识,并提出绝对角度停止准则,使算法经过少量的迭代即可获得模型的稀疏参数估计,并同时获得有效的时滞和阶次估计。结合辨识得到的受控自回归模型,引入一种基于指定相位点频率和增益的比例-积分-微分(proportional integral derivative,PID)控制器。数值仿真和平衡机器人的姿态控制仿真表明,该稀疏辨识算法在低数据量下具有较高的辨识精度,建立的模型具有较好的泛化性能,控制器具有良好的控制效果。展开更多
An improved particle swarm algorithm based on the D-Tent chaotic model is put forward aiming at the standard particle swarm algorithm. The convergence rate of the late of proposed algorithm is improved by revising the...An improved particle swarm algorithm based on the D-Tent chaotic model is put forward aiming at the standard particle swarm algorithm. The convergence rate of the late of proposed algorithm is improved by revising the inertia weight of global optimal particles and the introduction of D-Tent chaotic sequence. Through the test of typical function and the autotuning test of proportionalintegral-derivative （PID） parameter, finally a simulation is made to the servo control system of a permanent magnet synchronous motor （PMSM） under double-loop control of rotating speed and current by utilizing the chaotic particle swarm algorithm. Studies show that the proposed algorithm can reduce the iterative times and improve the convergence rate under the condition that the global optimal solution can be got.展开更多
The observation error model of the underwater acous-tic positioning system is an important factor to influence the positioning accuracy of the underwater target.For the position inconsistency error caused by consideri...The observation error model of the underwater acous-tic positioning system is an important factor to influence the positioning accuracy of the underwater target.For the position inconsistency error caused by considering the underwater tar-get as a mass point,as well as the observation system error,the traditional error model best estimation trajectory(EMBET)with little observed data and too many parameters can lead to the ill-condition of the parameter model.In this paper,a multi-station fusion system error model based on the optimal polynomial con-straint is constructed,and the corresponding observation sys-tem error identification based on improved spectral clustering is designed.Firstly,the reduced parameter unified modeling for the underwater target position parameters and the system error is achieved through the polynomial optimization.Then a multi-sta-tion non-oriented graph network is established,which can address the problem of the inaccurate identification for the sys-tem errors.Moreover,the similarity matrix of the spectral cluster-ing is improved,and the iterative identification for the system errors based on the improved spectral clustering is proposed.Finally,the comprehensive measured data of long baseline lake test and sea test show that the proposed method can accu-rately identify the system errors,and moreover can improve the positioning accuracy for the underwater target positioning.展开更多
Enlightened by distribution of creatures in natural ecology environment, the distributionpopulation-based genetic algorithm (DPGA) is presented in this paper. The searching capability ofthe algorithm is improved by co...Enlightened by distribution of creatures in natural ecology environment, the distributionpopulation-based genetic algorithm (DPGA) is presented in this paper. The searching capability ofthe algorithm is improved by competition between distribution populations to reduce the search zone.This method is applied to design of optimal parameters of PID controllers with examples, and thesimulation results show that satisfactory performances are obtained.展开更多
基金partially supported by the Natural Science Foundation of China (Grant Nos.62103052,52272358)partially supported by the Beijing Institute of Technology Research Fund Program for Young Scholars。
文摘This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.
基金supported by National Natural Science Foundation of China(11472137)the Natural Science Foundation of Jiangsu Province,China(BK20140773)。
文摘In this study,a theoretical nonlinear dynamic model was established for a saddle ring based on a dynamic force analysis of the launching process and the structure according to contact-impact theory.The ADAMS software was used to build a parameterized dynamic model of the saddle ring.A parameter identification method for the ring was proposed based on the particle swarm optimization algorithm.A loading test was designed and performed several times at different elevation angles.The response histories of the saddle ring with different loads were then obtained.The parameters of the saddle ring dynamic model were identified from statistics generated at a 500 elevation angle to verify the feasibility and accuracy of the proposed method.The actual loading history of the ring at a 70°elevation angle was taken as the model input.The response histories of the ring under these working conditions were obtained through a simulation.The simulation results agreed with the actual response.Thus,the effectiveness and applicability of the proposed dynamic model were verified,and it provides an effective method for modeling saddle rings.
基金Project(2015BAG06B00)supported by the National Key Technology Research from Development Program of the Ministry of Science and Technology of China
文摘A new modified LuGre friction model is presented for electromagnetic valve actuator system.The modification to the traditional LuGre friction model is made by adding an acceleration-dependent part and a nonlinear continuous switch function.The proposed new friction model solves the implementation problems with the traditional LuGre model at high speeds.An improved artificial fish swarm algorithm(IAFSA)method which combines the chaotic search and Gauss mutation operator into traditional artificial fish swarm algorithm is used to identify the parameters in the proposed modified LuGre friction model.The steady state response experiments and dynamic friction experiments are implemented to validate the effectiveness of IAFSA algorithm.The comparisons between the measured dynamic friction forces and the ones simulated with the established mathematic friction model at different frequencies and magnitudes demonstrate that the proposed modified LuGre friction model can give accurate simulation about the dynamic friction characteristics existing in the electromagnetic valve actuator system.The presented modelling and parameter identification methods are applicable for many other high-speed mechanical systems with friction.
基金Project(xjj20100078) supported by the Fundamental Research Funds for the Central Universities in China
文摘Several parameter identification methods of thermal response test were evaluated through numerical and experimental study.A three-dimensional finite-volume numerical model was established under the assumption that the soil thermal conductivity had been known in the simulation of thermal response test.The thermal response curve was firstly obtained through numerical calculation.Then,the accuracy of the numerical model was verified with measured data obtained through a thermal response test.Based on the numerical and experimental thermal response curves,the thermal conductivity of the soil was calculated by different parameter identification methods.The calculated results were compared with the assumed value and then the accuracy of these methods was evaluated.Furthermore,the effects of test time,variable data quality,borehole radius,initial ground temperature,and heat injection rate were analyzed.The results show that the method based on cylinder-source model has a low precision and the identified thermal conductivity decreases with an increase in borehole radius.For parameter estimation,the measuring accuracy of the initial temperature of the deep ground soil has greater effect on identified thermal conductivity.
基金Project(51005251)supported by the National Natural Science Foundation of ChinaProject(2011CB706802)supported by the National Basic Research Development Program of China(973 Program)
文摘A new experimental apparatus was set up to investigate the actual fi-iction characteristics on the basis of speed control of the serve system.A modified friction model was proposed due to real time varying deformation resistance.The approach to identify the parameters of comprehensive friction behaviors based on the modified model was proposed and applied to the forging press.The impacts on parameters which the external load had were also investigated.The results show that friction force decreases with velocity in the low velocity regime whereas the friction force increases with the velocity in the high velocity regime under no external load.It is also shown that the Coulomb friction force,the maximum static friction force and the vicious friction coefficient change linearly with the external load taking the velocity at which the magnitude of the steady state friction force becomes minimum as the critical velocity.
文摘In this paper a method of aerodynamic parameter identification of vehicle, the maximum likelihood method, is introduced. The aerodynamic model of vehicle is identified and the basic equations using maximum likelihood method are established. After that, the simulation data is identified to verify the correctness of the mathematic model and identification method. Last, the practical flight data is identified and analyzed.
基金Project(50805144) supported by the National Natural Science Foundation of China
文摘Accurate parameter identification is essential when designing controllers for inertially stabilized platforms （lSPs）. But traditional identification methods suffer from observation measurement noise and operating restrictions of ISPs. To address this issue, a novel identification method based on current command design and multilevel coordinate search （MCS） algorithm without any higher order measurement differentiations was proposed. The designed current commands were adopted to obtain parameter decoupled models with the platform operating under allowable conditions. MCS algorithm was employed to estimate the parameters based on parameter decoupled models. A comparison experiment between the proposed method and non-linear least square method was carried out and most of the relative errors of identified parameters obtained by the proposed method were below 10%. Simulation and experiment based on identified parameters were conducted. A velocity control structure was also developed with disturbance observer （DOB） for application in disturbance compensation control system of an ISR Experimental results show that the control scheme based on the identified parameters with DOB has the best disturbance rejection performance. It reduces the peak to peak value （PPV） of velocity error integral to 0.8 mrad which is much smaller than the value （10 mrad） obtained by the single velocity controller without DOB. Compared with the control scheme based on sweep model with DOB compensation, the proposed control scheme improves the PPV of velocity error integral by 1.625 times.
文摘The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.
基金Project(50675042) supported by the National Natural Science Foundation of China
文摘A model to describe the hysteresis damping characteristic of rubber material was presented.It consists of a parallel spring and damper,whose coefficients change with the vibration amplitude and frequency.In order to acquire these relations,force decomposition was carried out according to some sine vibration measurement data of nonlinear forces changing with the deformation of the rubber material.The nonlinear force is decomposed into a spring force and a damper force,which are represented by the amplitude-and frequency-dependent spring and damper coefficients,respectively.Repeating this step for different measurements gives different coefficients corresponding to different amplitudes and frequencies.Then,the application of a parameter identification method provides the requested approximation functions over amplitude and frequency.Using those formulae,as an example,the dynamic characteristic of a hollow shaft system supported by rubber rings was analyzed and the acceleration response curve in the centroid position was calculated.Comparisons with the sine vibration experiments of the real system show a maximal inaccuracy of 8.5%.Application of this model and procedure can simplify the modeling and analysis of mechanical systems including rubber materials.
文摘In mechanical, hydraulic and electronic systems, the determination of system parameters is often challenging because liquid parameters often change significantly, due to variations in working and environmental conditions. Therefore, it is of significant practical importance to identify those parameters through experimental procedures. A systematic approach to identifying parameters in the valve controlling cylinder system of hydraulic manipulators is provided. It first derives the transfer function of the system, and then uses P control of PID control to predict system parameters. The predicted parameters are further validated using PID control. The prediction through simulation using MatLab language is utilized, which agrees well with experimental results.
文摘针对过程复杂且结构未知的对象,在保证模型有效性的前提下,根据数据信息构建简单模型来简化控制器的求解是亟待解决的问题。以受控自回归模型为例,提出一种基于修正最小角回归算法的稀疏辨识方法。首先将系统模型转化为过参数化的高维稀疏模型,然后将最小角回归算法用于稀疏系统辨识,并提出绝对角度停止准则,使算法经过少量的迭代即可获得模型的稀疏参数估计,并同时获得有效的时滞和阶次估计。结合辨识得到的受控自回归模型,引入一种基于指定相位点频率和增益的比例-积分-微分(proportional integral derivative,PID)控制器。数值仿真和平衡机器人的姿态控制仿真表明,该稀疏辨识算法在低数据量下具有较高的辨识精度,建立的模型具有较好的泛化性能,控制器具有良好的控制效果。
基金supported by the National Natural Science Foundation of China(61301011)the Fundamental Research Funds for the Central Universities(HIT.NSRIF.2012010)+1 种基金the China Postdoctoral Science Foundation(2013M540279)the Heilongjiang Postdoctoral Financial Assistance(LBH-Z11157)
文摘An improved particle swarm algorithm based on the D-Tent chaotic model is put forward aiming at the standard particle swarm algorithm. The convergence rate of the late of proposed algorithm is improved by revising the inertia weight of global optimal particles and the introduction of D-Tent chaotic sequence. Through the test of typical function and the autotuning test of proportionalintegral-derivative （PID） parameter, finally a simulation is made to the servo control system of a permanent magnet synchronous motor （PMSM） under double-loop control of rotating speed and current by utilizing the chaotic particle swarm algorithm. Studies show that the proposed algorithm can reduce the iterative times and improve the convergence rate under the condition that the global optimal solution can be got.
基金This work was supported by the National Natural Science Foundation of China(61903086,61903366,62001115)the Natural Science Foundation of Hunan Province(2019JJ50745,2020JJ4280,2021JJ40133)the Fundamentals and Basic of Applications Research Foundation of Guangdong Province(2019A1515110136).
文摘The observation error model of the underwater acous-tic positioning system is an important factor to influence the positioning accuracy of the underwater target.For the position inconsistency error caused by considering the underwater tar-get as a mass point,as well as the observation system error,the traditional error model best estimation trajectory(EMBET)with little observed data and too many parameters can lead to the ill-condition of the parameter model.In this paper,a multi-station fusion system error model based on the optimal polynomial con-straint is constructed,and the corresponding observation sys-tem error identification based on improved spectral clustering is designed.Firstly,the reduced parameter unified modeling for the underwater target position parameters and the system error is achieved through the polynomial optimization.Then a multi-sta-tion non-oriented graph network is established,which can address the problem of the inaccurate identification for the sys-tem errors.Moreover,the similarity matrix of the spectral cluster-ing is improved,and the iterative identification for the system errors based on the improved spectral clustering is proposed.Finally,the comprehensive measured data of long baseline lake test and sea test show that the proposed method can accu-rately identify the system errors,and moreover can improve the positioning accuracy for the underwater target positioning.
文摘Enlightened by distribution of creatures in natural ecology environment, the distributionpopulation-based genetic algorithm (DPGA) is presented in this paper. The searching capability ofthe algorithm is improved by competition between distribution populations to reduce the search zone.This method is applied to design of optimal parameters of PID controllers with examples, and thesimulation results show that satisfactory performances are obtained.
