77 results about "Fractional order calculus" patented technology

The invention discloses a fractional order sliding mode optimization control method for a flexible joint mechanical arm. In order to solve the problem that in flexible integer order sliding mode dynamics control over joints of a mechanical arm, chattering and trail tracking control exist, in combination with the advantages of sliding mode variable structure control, a fractional order calculus theory is introduced, based on the features of the rapid convergence, information memorability and heritability of a fractional differential operator and on the basis of a common fractional order indirection discretization Qustaloup algorithm, the approximate precision of the fractional differential operator is optimized and promoted, and therefore a novel fractional order sliding mode variable structure controller which is better in strong robustness, interference resistance and effect of weakening clattering is provided. A joint flexible dynamics control system of the mechanical arm has bettercontinuity, rapidness and robustness and good interference resistance, and finally design of the fractional order sliding mode variable structure control method is realized.

The invention discloses a lithium battery fractional order discretization impedance model, which is used for describing strong-nonlinearity electrochemical reaction of a lithium battery as a simple mathematical model. The fractional order discretization impedance model is built by the following steps of: 1) building a lithium battery equivalent circuit model, wherein the model comprises impedance, a parallel combination of a first resistor and a first constant phase element (CPE) and a parallel combination of a second resistor and a second CPE, and all the three are orderly connected in series; 2) introducing G-L fractional order calculus definition according to the built lithium battery equivalent circuit model, and building a lithium battery fractional order impedance model; 3) discretizing the built lithium battery fractional order impedance model based on the G-L fractional order calculus definition, and thereby obtaining the lithium battery fractional order discretization impedance model.

The invention discloses a model-free control method for an aerodynamic heat superhelix nonlinear fractional order sliding mode, and the method comprises the steps: building a mathematical model between the input electric energy and the output temperature of an aerodynamic heat ground simulation system of a hypersonic aircraft based on the law of conservation of energy, and converting the mathematical model into a model-free control superlocal model; constructing a nonlinear fractional order sliding mode surface according to the defined output tracking error, the nonlinear function and the fractional order calculus; and in combination with the nonlinear fractional order sliding mode surface, the super-spiral approaching rate, the super-local model and a time delay observer, a model-free controller of the super-spiral nonlinear fractional order sliding mode is built, and buffeting in the control process is suppressed. According to the design of the nonlinear fractional order sliding mode surface, the stability of control is ensured, the convergence speed is high, the steady-state error and the saturation error are reduced, and the shaking problem of the sliding mode surface is improved through the combination of the super-spiral approaching rate.

The invention provides a fractional calculus filter of digital images of high-precision computation, which is a circuit device for fractionally enhancing or smoothing complex texture detail characteristics of digital images at high precision. The filter is formed by connecting a RGB-to-HSI converter, a line memory group, a phase locking / shift circuit group, a fractional calculus mask convolution circuit, a maximum comparator and an HSI-to-RGB converter in cascade. Special fractional calculus mask convolution algorithms are used by a first algorithm unit circuit to an eighth algorithm unit circuit in the fractional calculus mask convolution circuit to realize high-precision computation of fractional calculus. The fractional calculus filter of digital images of high-precision computation, which is provided by the invention, is especially suitable for application occasions for fractionally enhancing or smoothing complex texture detail characteristics of high-definition digital televisions, biomedical images, bank bills, satellite remote sensing images, biological characteristic patterns and the like at high precision.

The invention discloses a fractional order PID control method for an electrostatic dust collection power source. The phase angle and gain of an open-loop system are obtained in combination with a transfer function of the high-frequency electrostatic dust collection power source and a transfer function of the fractional order PID control method; a margin relation is used for obtaining a KP, a KI and a KD of a fractional order PID control system; furthermore, multiple sets of KPs, KI s and KDs are obtained according to different differential integral orders; according to a time domain expression, the output quantity of a fractional order PID controller is obtained through calculation; according to an ITAE measurement criterion, system output error values of different sets of data are obtained; one set of data is adopted as setting parameters when an ITAE value is minimum; in combination with the linear relation between the output quantity of the PID controller and IGBT driving frequency, driving frequency for reasonably controlling an IGBT is obtained. Fractional order PPID parameters can be accurately set, so that ideal control over the high-frequency electrostatic dust collection system is achieved; a floating-point type DSP is adopted for efficiently processing fractional order calculus calculation; the fractional order PID control method has the advantages of being short in rise time, small in steady-state error, high in robustness, wide in application range and the like.

A vegetable oil paper insulation state evaluation method based on a fractional Zener model comprises the following steps of firstly, deriving the fractional Zener model by utilizing a fractional calculus theory, and establishing a relational expression suitable for vegetable oil paper insulation system fractional Zener model parameters and frequency domain dielectric spectrum characteristic quantity complex dielectric constants; identifying parameter values of the score Zener model respectively; calculating a complex dielectric constant real part theta 'and a complex dielectric constant imaginary part theta ', introducing a concept of coincidence degree, comparing a complex dielectric constant calculated value with a measured value to find that the coincidence degree of the complex dielectric constant calculated value and the measured value is high, and enabling a low frequency band to have higher accuracy, which indicates that the fractional Zener model is suitable for describing therelaxation process of vegetable oil paper; selecting appropriate model parameters a, shape parameters and relaxation time as characteristic quantities for evaluating the aging of the vegetable oil paper insulation system, and establishing a functional relation between the model parameters and the acid value in the oil. According to the method, the fractional order theory is applied to the relaxation process of the dielectric medium, it is found that the fractional Zener model carries more effective information in the test sample, and therefore the aging state of the vegetable oil paper insulation system is evaluated more accurately.

The invention discloses a closed-loop iterative learning control method and system based on fractional calculus, and the method comprises the following steps: building a discrete fractional order closed-loop iterative learning controller, building a permanent magnet synchronous motor position servo system based on vector control, and carrying out equivalent transformation of the closed-loop iterative learning controller based on fractional calculus; respectively carrying out the comparison of iq and id with the values (shown in the description) to obtain difference values, and substituting thedifference values into a current regulator, and obtaining voltage controlled variables ud and uq through a current regulator; converting ud and uq into voltage control quantities u<alpha> and u<beta>in an alpha-beta coordinate system through PARK inverse transformation; generating a pulse modulation PWM signal according to u<alpha> and u<beta>, and controlling a three-phase inverter to generatea three-phase voltage signal through an SVPWM principle. The method has higher control precision, and meanwhile, the practicability and the accuracy are considered.