The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained accor...The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.展开更多
Mathematical modelling of glucose-insulin system is very important in medicine as a necessary tool to understand the homeostatic control of human body. It can also be used to design clinical trials and in the evaluati...Mathematical modelling of glucose-insulin system is very important in medicine as a necessary tool to understand the homeostatic control of human body. It can also be used to design clinical trials and in the evaluation of the diabetes prevention. In the last three decades so much work has been done in this direction. One of the most notable models is the global six compartment-mathematical model with 22 ordinary differential equations due to John Thomas Sorensen. This paper proposes a more simplified three compartment-mathematical model with only 6 ordinary differential equations by introducing a tissue compartment comprising kidney, gut, brain and periphery. For model parameter identification, we use inverse problems technique to solve a specific optimal control problem where data are obtained by solving the global model of John Thomas Sorensen. Numerical results show that the proposed model is adaptable to data and can be used to adjust diabetes mellitus type I or type II for diabetic patients.展开更多
In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpend...In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpendicular directions used as the initial information. The inverse problem is considered, taking into account the error of the mathematical description of rotor-bearings system. To obtain estimates of real unbalance characteristics, the hypothesis as to the exact solutions is applied. The method of Tikhonov regularization is used to obtain stable results. Test calculations are given to illustrate the proposed approach.展开更多
This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measur...This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.展开更多
This paper presents a method for determining specific models of overhead power lines with presence of corona phenomenon. The obtained models provide stable numerical solutions for computer simulation of transients cau...This paper presents a method for determining specific models of overhead power lines with presence of corona phenomenon. The obtained models provide stable numerical solutions for computer simulation of transients caused by direct lightning strikes. The corona non- linear charge-voltage characteristics obtained from experimental tests are used for identification of the corona parameters based on System Identification Toolbox implemented in Matlab package. Different transfer functions, which give the same waveshapes of overvoltages are de- termined using two parametric models. A circuit representation of the obtained transfer functions is proposed and the corona model is implemented in the EMTP-RV as a hierarchical structure composed of a overhead power line divided into sections with corona branches. Some computer simulations of lightning overvoltages propagated in a typical 220 kV power line due to direct lightning strikes to a line tower are presented. The proposed method and the model implemented in EMTP-RV are still valid for multi-conductor lines and for higher voltages of power lines but new corona nonlinear charge-voltage characteristics are required as an input parameter for the identification procedure.展开更多
Hydrodynamic coefficients strongly affect the dynamic performance of underactuated unmanned surface vehicle (USV) . Towing tank test is the traditional approach to identify these coefficients,however, the obtained val...Hydrodynamic coefficients strongly affect the dynamic performance of underactuated unmanned surface vehicle (USV) . Towing tank test is the traditional approach to identify these coefficients,however, the obtained values are not completely reliable since experimental difficulties and errors are involved. In this paper,an extended Kalman filter (EKF) method and a least squares (LS) method are proposed,only using onboard sensor data for identification of a small underactuated USV. The vehicle prototype as well as the system integration is delineated. Performance of the identification is evaluated by comparing the estimated coefficients,and the feasibility and accuracy of the proposed approach is demonstrated by simulation.展开更多
Based on the ε - support vector regression, three modelling methods for the ship manoeuvring motion, i.e., the white-box modelling, the grey-box modelling and the black-box modelling, are investigated. The 10°/1...Based on the ε - support vector regression, three modelling methods for the ship manoeuvring motion, i.e., the white-box modelling, the grey-box modelling and the black-box modelling, are investigated. The 10°/10°, 20°/20° zigzag tests and the 35° turning circle manoeuvre are simulated. Part of the simulation data for the 20°/20° zigzag test are used to train the support vectors, and the trained support vector machine is used to predict the whole 20° / 20° zigzag test. Comparison between the simula- ted and predicted 20° / 20° zigzag test shows a good predictive ability of the three modelling methods. Then all mathematical models obtained by the modelling methods are used to predict the 10°/10° zigzag test and 35° turning circle manoeuvre, and the predicted results are compared with those of simulation tests to demonstrate the good generalization performance of the mathematical models. Finally, the modelling methods are analyzed and compared with each other in terms of the application conditions, the prediction accuracy and the computation speed. An appropriate modelling method can be chosen according to the intended use of the mathematical models and the available data for the system identification.展开更多
文摘The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.
文摘Mathematical modelling of glucose-insulin system is very important in medicine as a necessary tool to understand the homeostatic control of human body. It can also be used to design clinical trials and in the evaluation of the diabetes prevention. In the last three decades so much work has been done in this direction. One of the most notable models is the global six compartment-mathematical model with 22 ordinary differential equations due to John Thomas Sorensen. This paper proposes a more simplified three compartment-mathematical model with only 6 ordinary differential equations by introducing a tissue compartment comprising kidney, gut, brain and periphery. For model parameter identification, we use inverse problems technique to solve a specific optimal control problem where data are obtained by solving the global model of John Thomas Sorensen. Numerical results show that the proposed model is adaptable to data and can be used to adjust diabetes mellitus type I or type II for diabetic patients.
基金Partially Supported by the Special Item for the Fujian Provincial Department of Ocean and Fisheries(No.MHGX-16)the Special Item for Universities in Fujian Province by the Education Department(No.JK15003)
文摘In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpendicular directions used as the initial information. The inverse problem is considered, taking into account the error of the mathematical description of rotor-bearings system. To obtain estimates of real unbalance characteristics, the hypothesis as to the exact solutions is applied. The method of Tikhonov regularization is used to obtain stable results. Test calculations are given to illustrate the proposed approach.
文摘This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.
基金Project supported by the National Science Center, Poland
文摘This paper presents a method for determining specific models of overhead power lines with presence of corona phenomenon. The obtained models provide stable numerical solutions for computer simulation of transients caused by direct lightning strikes. The corona non- linear charge-voltage characteristics obtained from experimental tests are used for identification of the corona parameters based on System Identification Toolbox implemented in Matlab package. Different transfer functions, which give the same waveshapes of overvoltages are de- termined using two parametric models. A circuit representation of the obtained transfer functions is proposed and the corona model is implemented in the EMTP-RV as a hierarchical structure composed of a overhead power line divided into sections with corona branches. Some computer simulations of lightning overvoltages propagated in a typical 220 kV power line due to direct lightning strikes to a line tower are presented. The proposed method and the model implemented in EMTP-RV are still valid for multi-conductor lines and for higher voltages of power lines but new corona nonlinear charge-voltage characteristics are required as an input parameter for the identification procedure.
文摘Hydrodynamic coefficients strongly affect the dynamic performance of underactuated unmanned surface vehicle (USV) . Towing tank test is the traditional approach to identify these coefficients,however, the obtained values are not completely reliable since experimental difficulties and errors are involved. In this paper,an extended Kalman filter (EKF) method and a least squares (LS) method are proposed,only using onboard sensor data for identification of a small underactuated USV. The vehicle prototype as well as the system integration is delineated. Performance of the identification is evaluated by comparing the estimated coefficients,and the feasibility and accuracy of the proposed approach is demonstrated by simulation.
基金Project supported by the National Natural Science Foundation of China(Grant No.51279106)the Special Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110073110009)
文摘Based on the ε - support vector regression, three modelling methods for the ship manoeuvring motion, i.e., the white-box modelling, the grey-box modelling and the black-box modelling, are investigated. The 10°/10°, 20°/20° zigzag tests and the 35° turning circle manoeuvre are simulated. Part of the simulation data for the 20°/20° zigzag test are used to train the support vectors, and the trained support vector machine is used to predict the whole 20° / 20° zigzag test. Comparison between the simula- ted and predicted 20° / 20° zigzag test shows a good predictive ability of the three modelling methods. Then all mathematical models obtained by the modelling methods are used to predict the 10°/10° zigzag test and 35° turning circle manoeuvre, and the predicted results are compared with those of simulation tests to demonstrate the good generalization performance of the mathematical models. Finally, the modelling methods are analyzed and compared with each other in terms of the application conditions, the prediction accuracy and the computation speed. An appropriate modelling method can be chosen according to the intended use of the mathematical models and the available data for the system identification.
