43 results about "Fractional-order system" patented technology

The invention discloses a method for realizing the construction of a fractional-order three-system automatic-switchover chaotic system and an analog circuit. The method comprises the following steps: three chaoses and sub-chaoses form an automatic-switchover fractional-order system; the automatic-switchover fractional-order chaotic system is realized by the analog circuit; operational amplifiers U1, U2 and U3 adopt LF346; multiplying units U4 and U5 adopt AD633JN; a voltage comparator U6 adopts LM339; an analog switch U7 adopts CD4052; the operational amplifier U1is connected with the voltage comparator U6, the analog switch U7, the multiplying unit U4 and the operational amplifier U2, the operational amplifier U2 is connected with the voltage comparator U6 and the analog switch U7; the operational amplifier U3 is connected with the operational amplifier U2 and the multiplying unit U4; and the analog switch U7 is connected with the multiplying unit U5; and the multiplying unit U5 is connected with the operational amplifier U3. In the method, the analog circuit is utilized to realize the fractional-order chaotic system in which three subsystems are switched automatically, and the fractional-order three-system automatic-switchover chaotic system is more complicated and has stronger randomness as compared with an automatic-switchover chaotic system composed of two chaotic subsystems and a non-switched fractional-order chaotic system. Therefore, the fractional-order three-system automatic-switchover chaotic system can be a new choice of the signal source of secret communication and has a better application prospect in the secret communication.

The invention provides a nonlinear fractional order auto disturbance rejection damping control method of doubly fed induction generators. The method is characterized by comprising the following steps: establishing a multi-unit system mathematical model comprising the doubly fed induction generators; constructing a mathematical model comprising a fractional order system through diffeomorphism mapping; compensating system parameters and state variables which are included in pre-control variables through design of an extended state observer in an auto disturbance rejection controller; and selecting a fractional order auto disturbance rejection control law and the like. The method provided by the invention effectively improves the damping level of a doubly fed induction generator power grid, effectively estimates model errors and external uncertain disturbance, eliminates errors by use of feedback linearization, effectively enhances the power oscillation inhibition capability of the doubly fed induction generators, reduces investment of additional equipment and improves operation benefits of the power grid, and also has the advantages of scientificalness, rationality, simplicity, effectiveness, quite high robustness, high engineering application value and the like.

The present invention discloses a non-overshot fractional order time-varying sliding mode control method, relating to a time-varying sliding mode control method, belonging to the technical field of control. The method comprises a step of establishing the dynamic model of a fractional order uncertain system, a step of designing a fractional order time-varying sliding mode control law such that the system responds rapidly and has no overshot, a step of taking the control amount u obtained in the step (2) as a command and inputting the command into the dynamic model of the fractional order uncertain system to control the dynamic model, a step of taking a system state as the input of a fractional order time-varying sliding mode controller, and repeating the step (1) and the step (2) such that a tracking error converges to a zero value. According to the method, the characteristic ratio configuration method of an integer order system is promoted to the fractional order system, the system response non overshot is realized through determining the characteristic ratio, a system state is kept on a sliding mode surface from an initial time, and the robustness of the system is enhanced. In addition, the response rate of the system can be changed and the overshot amount of the system is not changed through individually adjusting a time constant.

The invention discloses an improved function projection method of a complicated dynamic network. establishing a four-dimensional segmented Lorenz-Stenflo chaotic system model with an known parameter, and analyzing characteristic of Liapunov exponent; constructing a response system through utilizing the Lorenz-Stenflo chaotic system as a driving system; designing a projection synchronization controller, and automatically adjusting a feedback coefficient according to error magnitude and state change; and designing an adaptive identification estimator and a parameter updating rule. The improved function projection method is based on fractional order system stability theory combined adaptive control; and a lag improvement projection synchronization method is generated so that the method can realize synchronization between the state of a response node and the state of the driving system at a previous certain time according to a preset desired-dimension function matrix.

The invention discloses a fractional order PFC method of an industrial heating furnace system. A traditional PID control method and an integer order PFC method have poor control effects on a kind of fractional order system. The control method of the invention comprises: firstly employing an Oustaloup approximation method to approximate a fractional order system into an integer order system; building a prediction output model based on an Oustaloup approximation model; expanding an integer order PFC method to a fractional order PFC method; introducing a fractional order calculus operator into an object function; and furthermore designing a fractional order prediction function controller based on the prediction model and selected performance indexes. The fractional order PFC method can be well applied to the real process objects described by a fractional order model, omit the order reduction step of the integer order PFC method to control a high order system model, meanwhile increase the flexibility of adjusting controller parameters, and obtain good control performances.

The invention discloses a fractional order dynamic matrix control method for an industrial heating furnace system. The method comprises the steps of approximating a fractional order model as a high integer order model by adopting an Oustaloup approximation method, implementing a step response experiment based on the approximate high order model, acquiring step response data, acquiring a model vector, then expanding an integer order dynamic matrix control method to the fractional order dynamic matrix control method, introducing a fractional order calculus operator into a target function, and designing a fractional order dynamic matrix controller based on the step response model and the selected target function. The method is applied to a practical process object described by the frictional order model, so that the shortcomings of the integer order DMC method for controlling a fractional order system are overcome, meanwhile, the degree of freedom for adjusting the parameter of the controller is increased, so that good control performance is obtained, and the requirements of the practical industrial process can be well met.

The invention discloses an adaptive control method for a fractional order system influenced by saturated nonlinear input, and the method specifically comprises the following steps: building a fractional order system mathematic model for describing a class of physical objects or processes, and carrying out the designing of a fractional order sliding mode surface according to a fractional order calculus theory; determining an adaptive updating law of unknown parameters in the fractional order mathematical model; designing a self-adaptive controller of the controlled system according to a fractional order stability theory and a saturated nonlinear input characteristic; and searching an appropriate Lyapunov function to verify the finite time accessibility of a sliding mode approaching stage. According to the invention, the adaptive control of the fractional order system under the influence of input nonlinearity can be realized; when unmodeled dynamics with unknown upper bound and external interference occur in the system, it can be guaranteed that a state trajectory reaches a sliding mode surface within limited time under the action of a designed controller; through the sliding mode action, the purpose that the state trajectory of the controlled system converges to zero is achieved, the self-adaptive identification of unknown parameters is achieved, and the control purpose is achieved.

The invention discloses a predictive compensation fractional order PI control method aiming at a fractional order time lag system; the method comprises the following steps: building a fractional ordertime lag system with predictive compensation, wherein fractional order time lag system is a controlled object; building a closed loop control system with a predictive compensation fractional order PIcontroller according to the controlled object; providing a steady state error burst, and determining a reasonable proportion coefficient of the predictive compensation fractional order PI controlleraccording to the steady state error burst, wherein the reasonable proportion coefficient enables the fractional order time lag system to reach the provided steady state error burst in a given time interval or at the fastest speed. An existing fractional order system is poor in a control effect, complex in a design process, and cannot be well applied to the fractional order systems; the predictivecompensation fractional order PI control method can solve said problems.

The invention discloses a multi-model fractional order weight prediction function control method of an electric heating furnace. First of all, a work temperature interval of the electric heating furnace is divided into several subintervals, then, fractional order models are established on the corresponding subintervals, then by use of an Oustatloup approximation method, the fractional order models are converted into high-order integer models, by use of a prediction control function method, a controller of each interval is designed, finally, according to errors between the models and actual objects, a proportion factor of each model is established, and accordingly, controller input of a multi-model structure is obtained. According to the invention, a local state space model of a controlled object is established and a previous nonlinear model is converted into a linear local model, such that the control performance of a system is improved, and at the same time, application of a model prediction control method in a fractional order system is facilitated.

The invention discloses a model prediction control parameter analysis and optimization method and system for a multivariate fractional order system. The method comprises the following steps: first, collecting input data and output data of a controlled system, performing discretization to obtain a multivariate first-order plus fractional-order lag model of the controlled system through a system identification method and transforming the model into a state space equation form; secondly, predicting the future output of the multivariate first-order plus fractional-order lag model through the statespace equation, and obtaining an analytical expression of the control signal of a model prediction controller; and finally, deriving to obtain a closed-loop transfer function of the controlled systemand performing decoupling and analysis to transform the optimization problem into a pole placement problem so as to realize analysis and optimization of the model prediction control parameter. The method of the invention can achieve the purpose of improvement of the control system accuracy during control, fast tracking and interference resistance; and meanwhile, the online calculated amount and the storage content of the prediction control parameter optimization can be reduced.

The invention belongs to the technical field of automatic control methods, and particularly relates to a fractional order hidden chaotic system with a linear balance point. A new fractional order chaotic system is provided. A fractional order chaotic system with hidden chaotic attractors is generated, and a finite time synchronization method and a combined synchronization method of the chaotic system are designed. The system enriches the diversity of the fractional order chaotic system with hidden attractors. According to the finite time stability theory, finite time synchronization of the fractional order chaotic system with the hidden attractors is achieved. A reference is provided for finite time stability of other fractional order chaotic systems. A combined synchronization method of the fractional order chaotic system is provided, and due to the natural advantages of combined synchronization in information transmission application and the complexity of the fractional order system,the fractional order chaotic system has higher security than many other types of synchronization and integer order chaotic systems in the aspect of realizing secure communication.

The invention discloses a fractional order prediction function control method for optimizing heating furnace temperature through a genetic algorithm. A fractional order system is approximated as an integer order system by adopting an Oustaloup approximation method. A prediction output model is established based on an Oustaloup approximation model, and then an integer order prediction function control method is extended to the fractional order prediction function control method. A fractional order differential operator is introduced to a target function, and the differential operator is optimized by adopting the genetic algorithm so that the more reasonable control effect can be acquired through optimization. The control performance of the system can be effectively enhanced by the method.

The invention discloses a servo system fractional order model identification method with a time delay link taken into consideration. The method comprises steps as follows: establishing a to-be-identified fractional order model of a servo system with a time delay factor taken into consideration; acquiring frequency domain characteristics of the servo system; constructing a model identification target function; calculating a model parameter matrix of the servo system; determining the optimal fractional order to obtain the fractional order meeting a set threshold value; determining a factor of the time delay link. The fractional order system model with the time delay link is constructed for the servo system, model parameters are acquired by use of frequency domain response data of the system,and the modeling and parameter identification accuracy of the servo system is improved.

The invention discloses a simplest element circuit of which an integral order system and a fractional order system are synchronous. A corresponding simulation circuit consists of a first channel, a second channel, a third channel and a fourth channel; and by four whole circuits, an integral order chaotic system and a fractional order chaotic system can be synchronous. By using the simplest element circuit, the integral order chaotic system and the fractional order chaotic system are synchronous; and the simplest element circuit is a bridge for the integral order chaotic system and the fractional order chaotic system, and can be finally applied to fields such as electronic engineering. The circuit is simple in structure and convenient to understand and integrate, and greatly facilitates technological development on secrete communication and radar application.

The invention discloses a nonlinear ABS control method based on fractional order extremum search. The nonlinear ABS control method mainly comprises the steps that an automobile dynamics model, a tiremodel and a reference slip rate model are established respectively; designing a nonlinear ABS controller and designing a fractional order extremum search controller; setting a filter and integral feedback in extreme value search control to be a fractional calculus algorithm, braking deceleration serves as output of the search control, a fractional coefficient optimization function with the brakingdeceleration as an index is established, the fractional coefficient capable of enabling the fractional coefficient optimization function to be maximum is optimized, and determining the optimal fractional coefficient. The method has the beneficial effects that the advantages of robustness and stability of a fractional order system can be converted into an extreme value search controller to be matched with nonlinear control, the response characteristic of a braking system can be improved, the braking deceleration of a vehicle is increased, and the braking distance is reduced.

The invention discloses a method for using order-different fractional-order system to design a sliding mode interference observer, and the concrete steps of the method comprises: obtaining relevant data by an excitation system; off-line identifying the order-different fractional-order model of the system; and according to the order-different fractional order of the system, designing a sliding mode interference observer for observing the disturbance at present online. The invention also discloses a product corresponding to the application of the method. The invention also discloses a method of applying the corresponding product to control the order-different fractional-order system. Compared with the traditional anti-disturbance method, the method of the invention uses the order-different fractional-order system model to design the sliding mode interference observer, which improves the accuracy of the disturbance observation and can realize the convergence in finite time to ensure the real-time performance of the observed results. In the case of strong interference, the robustness and stability of the order-different fractional-order system are enhanced. In addition, the method proposed by the invention is also applicable to an order-identical fractional-order system.

The invention discloses a fractional order system backstepping sliding mode control method influenced by asymmetric dead zone input. The method includes: establishing strict feedback fractional order system mathematical model; constructing a sliding mode surface in a proper form according to a fractional calculus operator; constructing an auxiliary fractional order system to compensate the influence of asymmetric dead zone input; determining an adaptive updating law of unknown parameters in the fractional order mathematical model; on the basis of a conversion variable system and in combination with a fractional order distribution frequency model, selecting a proper Lyapunov function to determine the form of each virtual controller step by step; and adopting an indirect Lyapunov stability analysis method to verify the stability of the sliding mode in the approaching stage. The use of the indirect Lyapunov stability theory based on the fractional order frequency distribution model can ensure that the whole design process is reasonable and effective, thereby verifying that the backstepping sliding mode control method has a good control effect in the adaptive stabilization control of the fractional order system with a strict feedback structure, and all unknown parameters of the system can be effectively identified; and the system robustness is enhanced.

The invention provides a three-order fractional order chaotic system capable of generating infinite coexisting attractors and a construction method thereof. The method comprises: based on Caputo calculus, constructing a mathematical model of a three-order fractional order chaotic system; obtaining a numerical solution of the three-order fractional order chaotic system by using an Adomain decomposition method; performing numerical simulation on infinite coexistence attractors generated by the third-order fractional order chaotic system; using a digital signal processing technology, tophysically realizing infinite coexisting attractors generated by the three-order fractional order chaotic system based on TMS320F28335. According to the invention, the Adomain decomposition method is utilizedto construct the third-order fractional order chaotic system with infinite coexisting attractors, the technical problems that a conventional fractional order system with the infinite coexisting special physical phenomenon is not beneficial to teaching demonstration due to the complex structure and is not beneficial to being applied to real-time encryption due to the long sequence generation timeare solved.

The invention belongs to the technical field of automatic control methods, and particularly relates to a fractional order hidden chaotic system without a balance point. A new fractional order chaotic system without the balance point is provided, a fractional order chaotic system with a hidden chaotic attractor is generated, and a finite time synchronization method and a combination synchronization method of the chaotic system are designed. The system enriches the diversity of a fractional order chaotic system with the hidden attractors, realizes the finite time synchronization of the fractional order chaotic system with the hidden attractors according to a finite time stability theory, provides the reference for the finite time stability of other fractional order chaotic systems and provides a combined synchronization method of the fractional order chaotic system. Due to the natural advantage of the combined synchronization in information transmission application and the complexity of the fractional order system, the method has higher security at the aspect of realizing the secure communication compared with many other types of synchronization and integer order chaotic systems.

The invention relates to a signal generation circuit of a fractional-order hyperchaotic system required for chaotic traffic flow control and chaotic secret communication, and increases the implementation types of the fractional-order chaotic system. The Lyapunov indexes of the system are positive, positive, negative and zero, and the system is a typical hyperchaotic system, and has the more complex chaotic dynamics behaviors. The fractional-order system accords with the actual natural law better than an integral-order system. The whole signal generator only consists of six TL082 operational amplifiers, three AD633 analogue multipliers and a few of linear resistors and capacitors. Compared with the circuit implemented in other modes, the circuit is simple in structure, is convenient for integration, is high in precision, is high in reliability, is suitable for the experiment teaching of an analog circuit for the undergraduate students, and provides a new selection for the application ofchaos in the secret communication and the traffic flow control.

The invention discloses a method for realizing the construction of a fractional-order three-system automatic-switchover chaotic system and an analog circuit. The method comprises the following steps: three chaoses and sub-chaoses form an automatic-switchover fractional-order system; the automatic-switchover fractional-order chaotic system is realized by the analog circuit; operational amplifiers U1, U2 and U3 adopt LF346; multiplying units U4 and U5 adopt AD633JN; a voltage comparator U6 adopts LM339; an analog switch U7 adopts CD4052; the operational amplifier U1is connected with the voltagecomparator U6, the analog switch U7, the multiplying unit U4 and the operational amplifier U2, the operational amplifier U2 is connected with the voltage comparator U6 and the analog switch U7; the operational amplifier U3 is connected with the operational amplifier U2 and the multiplying unit U4; and the analog switch U7 is connected with the multiplying unit U5; and the multiplying unit U5 is connected with the operational amplifier U3. In the method, the analog circuit is utilized to realize the fractional-order chaotic system in which three subsystems are switched automatically, and the fractional-order three-system automatic-switchover chaotic system is more complicated and has stronger randomness as compared with an automatic-switchover chaotic system composed of two chaotic subsystems and a non-switched fractional-order chaotic system. Therefore, the fractional-order three-system automatic-switchover chaotic system can be a new choice of the signal source of secret communication and has a better application prospect in the secret communication.

The invention discloses a method for constructing a grid multi-wing chaotic attractor generator by a fractional order differential system. The method comprises the following steps of 1, determining afractional order form of a fractional order Rucklige system, and linearizing the fractional order Rucklige system at two symmetrical balance points of the fractional order Rucklige system to obtain two basic fractional order linear systems; and 2, constructing an extraordinary loop, and connecting all balance points of the two basic fractional order linear systems through saturation function switching control to realize the grid multi-wing chaotic attractor generator. A construction system represented by three fractional order differential equations without multipliers can capture basic characteristics of generalized Lorenz attractors and generate a butterfly effect, so that a hardware circuit is simpler to implement, and the invention has potential engineering application.

The invention relates to construction of a two wing and four wing coexistent chaotic system and design of a fractional order system simulation circuit thereof. In order to make dynamic characteristicsof a fractional order chaotic system more complex, a novel two wing and four wing attractor coexistent integer order chaotic system is firstly designed, and since coexistence attractors are complex,application value is higher in the fields of information encryption and secret communication. Secondarily, on the basis of the system, a fractional order system is constructed, the simulation circuitof the fractional order system is designed, and a circuit simulation result and a numerical value simulation result are uniform. The correctness of theoretical analysis of the fractional order systemand realizability of actual physics of the fractional order system are verified. Finally, based on a fractional order system mode, a self-adaptation synchronous controller and a parameter updating lawof the fractional order system are designed, synchronization of a driving system and a responding system is realized in numerical value simulation, and a new selection is provided for further application of the fractional order system to the field of communication engineering.

The invention discloses a state space model calculation method, system and device for a multivariate fractional order system, and the method comprises the steps: obtaining a rational transfer matrix of the multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix; extracting a polynomial transfer vector of the polynomial transfer matrix; constructing a directed graph meeting a preset condition according to the polynomial transfer vector; determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, the polynomial transfer vector, a preset first relational expression and a preset corresponding relation; determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix; and determining a state space model corresponding to the rational transfer matrix according to the second model parameter, a preset operation rule and a preset model relational expression. According to the method, the state space model of which the internal dimension is much lower than that of an existing method can be generated.

The invention discloses a fractional order single-phase inverter modeling method based on a state space averaging method. The fractional order single-phase inverter modeling method comprises the following steps: establishing a mathematical model of a fractional order capacitor and a fractional order inductor by utilizing a fractional order calculus theory; and obtaining a fractional order single-phase inverter model by using a state space averaging method and using the fractional order mathematical model of each element obtained in the previous step. According to the method, a model capable ofaccurately describing the characteristics of an actual fractional order single-phase inverter system can be rapidly obtained. Due to the fact that the single-phase inverter system is relatively widein application and the single-phase inverter system in practice is a fractional order system, modeling and analysis can be rapidly and accurately carried out on the actual system.

The invention discloses a liquid storage tank liquid level control method based on fractional order state spatial prediction function control. The method comprises utilizing a Grunwald-Letnikov fractional calculus definition to convert a fractional order state space model into a discrete form; based on the fractional order state space model, obtaining a prediction output model, and introducing the fractional calculus in a target function; and finally designing a fractional order state spatial prediction function controller based on the fractional order state space model and the selected target function. The liquid storage tank liquid level control method can be preferably applied to a practical process object described by a fractional order model, can modify the deficiencies of a PFC method control fractional order system based on an integer order state space model, can increase the degree of freedom for adjusting the parameters of the controller, can acquire good control performance, and can preferably satisfy the requirement during a practical production process for a distillation column.

Proposed is an analogue circuit for realizing automatic switching of four fractional order systems based on a Chen type system. The analogue circuit for realizing automatic switching of four fractional order systems based on a Chen type system is composed of an operational amplifier U1, an operational amplifier U2, an operational amplifier U3, an operational amplifier U5, an operational amplifier U8, a multiplier U4, a multiplier U9, a multiplier U10, a voltage comparator U7 and an analogue switch U6. In the present utility model, the analogue circuit is used for achieving the fractional order chaotic system with four Chen type subsystems which are automatically switched. The fractional order chaotic system is more complicated and higher in randomness than the automatic switching chaotic system which is composed of two or three sub-chaotic systems and non-switching fractional order chaotic systems, and can be a new choice for the signal source of secret communications and has better application prospects in secret communications.

The invention discloses a liquid storage tank liquid level control method based on fractional order state spatial prediction function control. The method comprises utilizing a Grunwald-Letnikov fractional calculus definition to convert a fractional order state space model into a discrete form; based on the fractional order state space model, obtaining a prediction output model, and introducing the fractional calculus in a target function; and finally designing a fractional order state spatial prediction function controller based on the fractional order state space model and the selected target function. The liquid storage tank liquid level control method can be preferably applied to a practical process object described by a fractional order model, can modify the deficiencies of a PFC method control fractional order system based on an integer order state space model, can increase the degree of freedom for adjusting the parameters of the controller, can acquire good control performance, and can preferably satisfy the requirement during a practical production process for a distillation column.

The invention discloses an adaptive fault-tolerant control method based on a fractional order disturbance observer. The adaptive fault-tolerant control method comprises the following steps: extracting and decomposing information, establishing a new mathematical model of a system, adaptively tracking a disturbance signal by utilizing a disturbance observer, designing a fractional order adaptive fault-tolerant controller of the system and designing active fault-tolerant control of the system. According to the invention, the disturbance observer strategy is integrated into the adaptive fault-tolerant controller method, the disturbance observer is utilized to approach the system disturbance, and the fractional order adaptive fault-tolerant controller of the system is designed by utilizing a dynamic surface method, so that the limitation that a traditional adaptive fault-tolerant control method does not process the system disturbance in time is overcome; and a fractional order disturbance observer is designed to carry out adaptive tracking on system disturbance so as to reduce the influence of the disturbance on system performance, it is guaranteed that the system safely and stably operates under the condition that faults of the system are executed and the system disturbance exists at the same time, and the method is suitable for adaptive fault-tolerant control of a fractional order system and can also be popularized to an integer order system.