CN118295238B - Online robust tracking method, device and equipment for aircraft track - Google Patents
Online robust tracking method, device and equipment for aircraft track Download PDFInfo
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Abstract
The application relates to an aircraft track online robust tracking method, device and equipment. The method comprises the following steps: constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft; constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, obtaining a final flight control law by removing an expansion observed quantity in the nonlinear state observer, and obtaining an optimal control quantity of an aircraft according to the final flight control law to calculate and acquire the on-line robust tracking of the flight track of the aircraft; when the flight trajectory is tracked online, the control parameters are optimized and adjusted by adopting a particle swarm algorithm which considers an oscillation mechanism, a chaotic disturbance mechanism and a boundary contraction and escape strategy. By adopting the method, the high-precision tracking control of the flight track of the aircraft can be realized.
Description
Technical Field
The present application relates to the field of track tracking technologies, and in particular, to an online robust tracking method, device and equipment for an aircraft track.
Background
The aircraft has the advantages of high flying speed, high efficiency-cost ratio, high detection difficulty, strong burst prevention capability and the like, receives wide attention of various countries, and is a strategic high point of aerospace technology. However, in the actual flight process, factors such as a large flight envelope, a complex flight mission and the like bring great challenges to the trajectory tracking control of the aircraft. As an effective control method, active disturbance rejection control (Active Disturbance Rejection Control, ADRC) introduces an extended state observer, a tracking differentiator and a state error feedback control law based on a traditional PID (proportional-integral-derivative) algorithm, has stronger robust performance, and is also applied to the control aspect of an aircraft, but mainly has two problems: 1) Parameter tuning is difficult. For example, for a three-freedom aircraft model, ADRC typically requires 6-9 parameters, which is a great challenge for practical engineering applications; 2) Selection of tracking targets and control amounts lacks criteria. The aircraft has a complex structure, and when the controller is designed, how to select proper tracking targets and control amounts has great significance on the design and control effect of the actual controller.
For parameter tuning, in the engineering field, an empirical adjustment method is mostly adopted to obtain a better parameter combination, and other researches adopt intelligent group decision algorithms such as a Particle Swarm Optimization (PSO) algorithm, a genetic algorithm and the like. In the aspects of tracking target and control quantity selection of an aircraft, some researches are mainly based on a simplified linear model, the aircraft model is directly expressed in a standard state equation form, and a tracking control method is designed.
However, the empirical adjustment method has a certain chance, requires a lot of experience, and is extremely unfriendly to the operator. The traditional PSO and other parameter setting methods are easy to fall into local optimum, and cannot obtain the optimum control parameter combination. For the selection of tracking targets and control amounts, the nonlinear characteristics of the system cannot be reflected well based on a tracking control strategy of a simplified linear model, so that the tracking accuracy cannot meet the actual striking requirements.
Disclosure of Invention
Based on the above, it is necessary to provide an on-line robust tracking method, device and equipment for an aircraft track, which can improve the tracking accuracy of the aircraft track.
An aircraft trajectory online robust tracking method, the method comprising:
constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft; wherein the state variables include altitude, mach number and ballistic inclination of the aircraft, and the control quantity includes attack angle and equivalence ratio of the aircraft;
Constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, removing an expansion observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
Acquiring optimal control quantity corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity;
In the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity, the control parameters in the final flight control law are optimized and adjusted by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary contraction and escape strategies.
In one embodiment, constructing a nonlinear state equation based on state variables and control amounts of an aircraft includes:
Selecting altitude of an aircraft Mach numberInclination angle of trajectoryAs a state variable, the angle of attack of the aircraft is selectedEquivalent ratio ofAs a control quantity, a state equation is constructed, expressed as
；
Wherein,Respectively the heights ofMach numberInclination angle of trajectoryIs used as a first derivative of (a),AndRepresenting two unknown nonlinear functions related to state variables and control amounts;
by introducing axial overload And normal overloadTwo intermediate variables optimize the state equation to obtain a nonlinear state equation expressed as
；
Wherein,For the radius of the earth,Representing the aircraft mass.
In one embodiment, constructing a nonlinear state observer observes three state variables in a nonlinear state equation, including:
The nonlinear state observer is represented as
；
Wherein,Respectively the heights ofMach numberInclination angle of trajectoryAn observer of the three state quantities,In order to expand the observed quantity,AndRespectively representAndIs used as a first derivative of (a),、、AndRespectively isAndIs used for the gain factor of (a),The scale factor is represented as such,AndTwo non-linear functions are represented and,As a known nonlinear function, expressed as
；
Wherein,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value and。
In one embodiment, establishing a nonlinear state error feedback control law by observing the resulting state feedback error includes:
the nonlinear state error feedback control law is established through the state feedback error observed by the nonlinear state observer and is expressed as
；
；
Wherein,AndTwo control intermediate variables in the nonlinear state error feedback control law,Respectively the heights ofMach numberInclination angle of trajectoryThe state feedback errors of these three state quantities,Three gains representing a state error feedback control law,、、The scaling factors representing the three state quantities.
In one embodiment, the method includes removing the dilation observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating to obtain an optimal axial overload and an optimal normal overload of the aircraft according to the final flight control law, including:
By extending observations in a nonlinear state observer Removing from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law, wherein the optimal axial overload and the optimal normal overload are respectively expressed as
；
；
Wherein,For an optimal axial overload the device is provided with,For an optimal normal overload the device is provided with,Is thatIs used to determine the scaling factor of (a),As a known non-linear function,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value.
In one embodiment, in the process of performing online robust tracking of an aircraft flight trajectory through an optimal control amount, a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary shrinkage and escape strategy is adopted to perform optimization adjustment on control parameters in a final flight control law, including:
in the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal attack angle and the optimal equivalence ratio, carrying out particle sampling on the flight track of the aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, obtaining the position vector and the speed vector of each particle, introducing the control parameters in the final flight control law into the position vector of each particle, and realizing the optimization adjustment on the control parameters by updating the position vector of the particle;
Calculating average tracking errors of the altitude and Mach number of the aircraft according to the tracking result of the flight track, and calculating the adaptability of each particle according to the average tracking errors of the altitude and Mach number The specific form of the fitness is as follows:
；
Wherein, Representing a summation function; A function representing averaging; is highly feedback error Absolute value of (2); feedback error for Mach number Absolute value of (2);
The fitness of the single particle is respectively compared with the fitness extreme value of the single particle and the fitness extreme value of the particle population, and the fitness extreme value of the single particle and the fitness extreme value of the particle population are updated according to the comparison result;
Updating the position vector and the speed vector of the single particle according to the updated fitness extremum of the single particle and the fitness extremum of the particle population;
Sequencing the fitness of single particles according to ascending order, updating the optimal position of each particle and the optimal position of a particle population for the first 30% of particles by adopting a chaotic disturbance mechanism, shrinking the position boundary of each particle based on a boundary shrinkage strategy, and updating the position vector and the speed vector for the rest 70% of particles by adopting an escape strategy;
Repeating the steps until the optimization error of the control parameter reaches the preset precision or the iteration reaches the maximum circulation times, and completing the optimization adjustment of the control parameter.
In one embodiment, the method for performing particle sampling on the flight trajectory of the aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, obtaining a position vector and a speed vector of each particle, introducing control parameters in a final flight control law into the position vector of each particle, and performing optimization adjustment on the control parameters by updating the position vector of the particle comprises the following steps:
The method comprises the steps of sampling particles of a flight track of an aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, and obtaining a position vector and a speed vector of each particle; wherein, the particle swarm algorithm taking the oscillation mechanism into consideration is expressed as
；
；
Wherein,AndRespectively represent the firstParticle NoThe velocity vector and the position vector of the next iteration,AndRespectively represent the firstParticle NoA velocity vector and a position vector for the second iteration; And Is an intermediate parameter; And Representing the individual and global random learning factors respectively,For the number of iterations,As the coefficient of the weight of the inertia,For an optimal position of the individual particles,Is the optimal position of the particle population;
Importing control parameters in the final flight control law into the first Particle NoIn the position vector of the next iteration,Represented as
；
Wherein,AndThe gain coefficients of three observers and one dilation observers of the nonlinear state observer respectively,Three gains representing a state error feedback control law; and optimizing and adjusting the control parameters by updating the position vectors of the particles.
In one embodiment, comparing the fitness of the single particle with the fitness extremum of the single particle and the fitness extremum of the particle population, respectively, and updating the fitness extremum of the single particle and the fitness extremum of the particle population according to the comparison result comprises:
Comparing the fitness of the single particle with the fitness extremum of the single particle and the fitness extremum of the particle population respectively, and if the fitness of the single particle is larger than the fitness extremum of the single particle, replacing the fitness extremum of the single particle with the fitness of the single particle; if the fitness of the single particle is greater than the fitness extremum of the particle population, replacing the fitness extremum of the particle population with the fitness of the single particle.
In one embodiment, the fitness of the single particles is ordered in ascending order, and the optimal position of each particle and the optimal position of the particle population are updated for the first 30% of particles by adopting a chaotic disturbance mechanism, which comprises the following steps:
sequencing the fitness of single particles according to ascending order, and applying chaotic disturbance to the first 30% of particles;
Initializing chaotic variables The chaotic state of the chaotic variable meeting the chaotic logic mapping function is expressed as; Wherein,Is the firstParticle NoThe position vector of the number of iterations,AndIs the firstUpper and lower boundaries of individual particles;
Chaotic variable is obtained on the basis of chaotic logic mapping function The state value of the iteration is expressed as; Wherein,Representing a chaotic control parameter;
According to chaos variable in the first place The state value of the iteration generates a new particle position vector, expressed as; Wherein,Is the firstParticle NoA position vector of the second iteration;
Updating the optimal position of the single particle and the optimal position of the particle population according to the adaptability of the particles; wherein the optimal position of the single particle is expressed as
；
Wherein,Is the firstParticle NoThe degree of adaptation of the number of iterations,Is the firstParticle NoFitness of the multiple iterations.
In one embodiment, shrinking the positional boundaries of each particle based on a boundary shrink strategy includes:
Boundary shrinkage strategy based on boundary shrinkage strategy for ith particle upper boundary And lower boundaryThe method comprises the following steps of:
；
；
Wherein, Indicating the optimal position of the particle population,Representation ofRandom numbers in between;
After boundary shrinkage, the first The upper and lower boundaries of the individual particles are limited to a rangeAnd (3) inner part.
In one embodiment, updating the position vector and the velocity vector for the remaining 70% of the particles using the escape strategy comprises:
Updating position vector and velocity vector again for the remaining 70% of particles using escape strategy, expressed as
；
；
Wherein,AndRespectively represent the firstParticle NoThe velocity vector and the position vector of the next iteration,Represent the firstUpper boundary of individual particlesAnd lower boundaryIs a vector dimension of (c).
An on-line robust tracking apparatus for aircraft trajectories, the apparatus comprising:
The state equation construction module is used for constructing a nonlinear state equation based on the state variable and the control quantity of the aircraft; wherein the state variables include altitude, mach number and ballistic inclination of the aircraft, and the control quantity includes attack angle and equivalence ratio of the aircraft;
The error feedback control module is used for constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, obtaining a final flight control law after the expansion observed quantity in the nonlinear state observer is removed from the nonlinear state error feedback control law, and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
The flight track tracking module is used for acquiring optimal control amounts corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft by the optimal control amounts;
The control parameter optimization module is used for optimizing and adjusting the control parameters in the final flight control law by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary shrinkage and escape strategy in the process of carrying out online robust tracking on the flight track of the aircraft through the optimal control quantity.
A computer device comprising a memory storing a computer program and a processor which when executing the computer program performs the steps of:
constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft; wherein the state variables include altitude, mach number and ballistic inclination of the aircraft, and the control quantity includes attack angle and equivalence ratio of the aircraft;
Constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, removing an expansion observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
Acquiring optimal control quantity corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity;
In the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity, the control parameters in the final flight control law are optimized and adjusted by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary contraction and escape strategies.
The method, the device and the equipment for on-line robust tracking of the aircraft track have the following technical effects:
1. according to the application, a nonlinear state equation is constructed based on the state variables and the control amounts of the aircraft, a nonlinear state observer is constructed to observe three state variables in the nonlinear state equation, and a nonlinear state error feedback control law is established through the state feedback errors obtained by observation, so that the final flight control law is obtained to control the flight track of the aircraft, the problem that the traditional control algorithm is too dependent on the linearization of the aircraft is solved, the nonlinear characteristics of the aircraft are reflected, and the high-precision tracking control of the flight track is realized.
2. The application further considers the problems of multiple control parameters and difficult parameter setting in the tracking control of the aircraft flight trajectory, and in the process of carrying out online robust tracking on the aircraft flight trajectory through the optimal control quantity, the particle swarm algorithm which considers the oscillation mechanism, the chaotic disturbance mechanism, the boundary contraction and escape strategy is adopted to carry out optimization adjustment on the control parameters in the final flight control law, thereby overcoming the defects of the traditional particle swarm algorithm in the aspect of global stable convergence and the defect of easy incidence on local optimal, and improving the global stable convergence characteristic of the algorithm.
Drawings
FIG. 1 is a flow diagram of an aircraft trajectory online robust tracking method in one embodiment;
FIG. 2 is an internal block diagram of a computer device in one embodiment.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In one embodiment, as shown in fig. 1, an on-line robust tracking method for an aircraft trajectory is provided, comprising the steps of:
step S1, constructing a nonlinear state equation based on state variables and control amounts of an aircraft; wherein the state variables include altitude, mach number, and ballistic tilt angle of the aircraft, and the control quantity includes angle of attack and equivalence ratio of the aircraft.
S2, constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, removing an expansion observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; the nonlinear state observer comprises three state variable observers and an expansion observance.
And S3, acquiring optimal control amounts corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft through the optimal control amounts.
And S4, in the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity, optimizing and adjusting the control parameters in the final flight control law by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary contraction and escape strategy.
In one embodiment, constructing a nonlinear state equation based on state variables and control amounts of an aircraft includes:
Selecting altitude of an aircraft Mach numberInclination angle of trajectoryAs a state variable, the angle of attack of the aircraft is selectedEquivalent ratio ofAs a control quantity, a state equation is constructed, expressed as
；
Wherein,Respectively the heights ofMach numberInclination angle of trajectoryIs used as a first derivative of (a),AndRepresenting two unknown nonlinear functions related to state variables and control amounts; wherein it is difficult to obtain directly due to the complex dynamics of the aircraftAndAn explicit expression of (2);
Thus, by introducing axial overload And normal overloadTwo intermediate variables optimize the state equation to obtain a nonlinear state equation expressed as
；
Wherein,For the radius of the earth,Representing the aircraft mass.
In one embodiment, constructing a nonlinear state observer observes three state variables in a nonlinear state equation, including:
The nonlinear state observer is represented as
；
Wherein,Respectively the heights ofMach numberInclination angle of trajectoryAn observer of the three state quantities,To expand the observables, representing an estimate of the internal and external disturbances of the aircraft; And Respectively representAndIs used as a first derivative of (a),AndRespectively isAndIs used for the gain factor of (a),The scale factor is represented as such,AndTwo non-linear functions are represented and,As a known nonlinear function, expressed as
；
Wherein,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value and。
In one embodiment, establishing a nonlinear state error feedback control law by observing the resulting state feedback error includes:
the nonlinear state error feedback control law is established through the state feedback error observed by the nonlinear state observer and is expressed as
；
；
Wherein,AndTwo control intermediate variables in the nonlinear state error feedback control law,Respectively the heights ofMach numberInclination angle of trajectoryThe state feedback errors of these three state quantities,Three gains representing a state error feedback control law,、、The scaling factors representing the three state quantities.
In one embodiment, the method includes removing the dilation observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating to obtain an optimal axial overload and an optimal normal overload of the aircraft according to the final flight control law, including:
By extending observations in a nonlinear state observer Removing from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law, wherein the optimal axial overload and the optimal normal overload are respectively expressed as
；
；
Wherein,For an optimal axial overload the device is provided with,For an optimal normal overload the device is provided with,Is thatIs used to determine the scaling factor of (a),As a known non-linear function,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value.
Further, after the optimal axial overload and the optimal normal overload are obtained, an optimal attack angle and an optimal equivalence ratio corresponding to the optimal axial overload and the optimal normal overload are obtained by adopting an optimizing algorithm, and on-line robust tracking of the flight track of the aircraft is carried out through the optimal attack angle and the optimal equivalence ratio, so that effective tracking control of the flight track is realized.
Further consider that the final flight control law designed by the present application contains many unknown parameters, and 7 of them, namelyThe convergence speed and the robustness are decisive, so that an effective control parameter optimization algorithm is needed to be designed, and the value of the control parameter is subjected to online optimization calculation.
In one embodiment, in the process of performing online robust tracking of an aircraft flight trajectory through an optimal control amount, a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary shrinkage and escape strategy is adopted to perform optimization adjustment on control parameters in a final flight control law, including:
in the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal attack angle and the optimal equivalence ratio, carrying out particle sampling on the flight track of the aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, obtaining the position vector and the speed vector of each particle, introducing the control parameters in the final flight control law into the position vector of each particle, and realizing the optimization adjustment on the control parameters by updating the position vector of the particle;
Calculating average tracking errors of the altitude and Mach number of the aircraft according to the tracking result of the flight track, and calculating the adaptability of each particle according to the average tracking errors of the altitude and Mach number The specific form of the fitness is as follows:
；
Wherein, Representing a summation function; A function representing averaging; is highly feedback error Absolute value of (2); feedback error for Mach number Absolute value of (2);
The fitness of the single particle is respectively compared with the fitness extreme value of the single particle and the fitness extreme value of the particle population, and the fitness extreme value of the single particle and the fitness extreme value of the particle population are updated according to the comparison result;
Updating the position vector and the speed vector of the single particle according to the updated fitness extremum of the single particle and the fitness extremum of the particle population;
Sequencing the fitness of single particles according to ascending order, updating the optimal position of each particle and the optimal position of a particle population for the first 30% of particles by adopting a chaotic disturbance mechanism, shrinking the position boundary of each particle based on a boundary shrinkage strategy, and updating the position vector and the speed vector for the rest 70% of particles by adopting an escape strategy;
Repeating the steps until the optimization error of the control parameter reaches the preset precision or the iteration reaches the maximum circulation times, and completing the optimization adjustment of the control parameter.
In one embodiment, the method for performing particle sampling on the flight trajectory of the aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, obtaining a position vector and a speed vector of each particle, introducing control parameters in a final flight control law into the position vector of each particle, and performing optimization adjustment on the control parameters by updating the position vector of the particle comprises the following steps:
the method comprises the steps of sampling particles of a flight track of an aircraft by adopting a particle swarm algorithm taking a second-order vibration mechanism into consideration, and obtaining a position vector and a speed vector of each particle;
wherein, the particle swarm algorithm taking the oscillation mechanism into consideration is expressed as
；
；
Wherein,AndRespectively represent the firstParticle NoThe velocity vector and the position vector of the next iteration,AndRespectively represent the firstParticle NoA velocity vector and a position vector for the second iteration; And Is an intermediate parameter; And Representing the individual and global random learning factors respectively,For the number of iterations,As the coefficient of the weight of the inertia,For an optimal position of the individual particles,Is the optimal position of the particle population;
the acceleration of the particles obtainable from the above is expressed as
；
Wherein,Represent the firstParticle NoAcceleration for a number of iterations.
Solving the equation, the characteristic root of the equation is shown below:
；
When (when) The oscillation convergence condition is satisfied:
；
Wherein, ；
When (when)The oscillation convergence condition is satisfied:
；
Wherein, ；
Importing the control parameters in the final flight control law into a firstParticle NoPosition vector for multiple iterationsIn (a) is expressed as
；
Wherein,AndThe gain coefficients of three observers and one dilation observers of the nonlinear state observer respectively,Three gains representing a state error feedback control law; and optimizing and adjusting the control parameters by updating the position vectors of the particles.
It can be understood that the second-order oscillation mechanism can increase the diversity of particles and can overcome the problems of non-convergence and local optimization of the conventional particle swarm algorithm. Moreover, the algorithm has stronger global searching capability in the early stage of iteration, and then adopts an asymptotic convergence mechanism to enhance the fine searching capability.
In one embodiment, comparing the fitness of the single particle with the fitness extremum of the single particle and the fitness extremum of the particle population, respectively, and updating the fitness extremum of the single particle and the fitness extremum of the particle population according to the comparison result comprises:
Comparing the fitness of the single particle with the fitness extremum of the single particle and the fitness extremum of the particle population respectively, and if the fitness of the single particle is larger than the fitness extremum of the single particle, replacing the fitness extremum of the single particle with the fitness of the single particle; if the fitness of the single particle is greater than the fitness extremum of the particle population, replacing the fitness extremum of the particle population with the fitness of the single particle.
In one embodiment, the fitness of the single particles is ordered in ascending order, and the optimal position of each particle and the optimal position of the particle population are updated for the first 30% of particles by adopting a chaotic disturbance mechanism, which comprises the following steps:
as a common phenomenon in nonlinear systems, chaos has the characteristics of ergodic and internal randomness. It can traverse all states according to its own law within a certain range without repetition. The chaotic logic mapping function is used here as:
wherein, the method comprises the steps of, wherein, ;
The application provides a method for updating the optimal position of each particle and the optimal position of a particle population by adopting a chaotic disturbance mechanism, and the specific process can be expressed as follows:
Sequencing the fitness of single particles according to ascending order, and applying chaotic disturbance to the first 30% of particles; the position of the particle is further optimized by utilizing good ergodic property of the chaotic variable, and the optimal solution around the particle is found out;
Initializing chaotic variables The chaotic state of the chaotic variable meeting the chaotic logic mapping function is expressed as; Wherein,Is the firstParticle NoThe position vector of the number of iterations,AndIs the firstUpper and lower boundaries of individual particles;
Chaotic variable is obtained on the basis of chaotic logic mapping function The state value of the iteration is expressed as; Wherein,Representing a chaotic control parameter;
According to chaos variable in the first place The state value of the iteration generates a new particle position vector, expressed as; Wherein,Is the firstParticle NoA position vector of the second iteration;
Wherein, AndAre allDimension vector, in the form of
；
；
Updating the optimal position of the single particle and the optimal position of the particle population according to the adaptability of the particles; wherein the optimal position of the single particle is expressed as
；
Wherein,Is the firstParticle NoThe degree of adaptation of the number of iterations,Is the firstParticle NoFitness of the multiple iterations.
In one embodiment, shrinking the positional boundaries of each particle based on a boundary shrink strategy includes:
boundary shrink policy pair Upper boundary of individual particlesAnd lower boundaryThe method comprises the following steps of:
；
；
Wherein, Indicating the optimal position of the particle population,Representation ofRandom numbers in between;
After boundary shrinkage, the first The upper and lower boundaries of the individual particles are limited to a rangeAnd (3) inner part.
It will be appreciated that a typical problem faced by particle swarm algorithms is boundary control. By shrinking the boundaries of parameters, such as particle position, the search efficiency and stability of the solution will be greatly improved.
Further, once the globally optimal solution for the population is obtained, 30% of the excellent particles with better fitness values are retained in each iteration, and chaotic perturbation is applied to further optimize the local solutions for these particles. For the rest, a mutation operation is performed to spread the particles along the center of the locally optimal solution and into other regions of the solution space for searching. Further, when a multimodal problem arises, the particle swarm algorithm tends to fall into a local optimum, which is a premature phenomenon, due to a decrease in the diversity of the population. To address this problem, in one embodiment, the updating of the position vector and velocity vector for the remaining 70% of the particles with an escape strategy includes:
Updating position vector and velocity vector again for the remaining 70% of particles using escape strategy, expressed as
；
；
Wherein,AndRespectively represent the firstParticle NoThe velocity vector and the position vector of the next iteration,Represent the firstUpper boundary of individual particlesAnd lower boundaryIs a vector dimension of (c).
It should be understood that, although the steps in the flowchart of fig. 1 are shown in sequence as indicated by the arrows, the steps are not necessarily performed in sequence as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in fig. 1 may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of other steps or sub-steps of other steps.
In one embodiment, an aircraft trajectory online robust tracking device is provided, comprising:
The state equation construction module is used for constructing a nonlinear state equation based on the state variable and the control quantity of the aircraft; wherein the state variables include altitude, mach number and ballistic inclination of the aircraft, and the control quantity includes attack angle and equivalence ratio of the aircraft;
The error feedback control module is used for constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, obtaining a final flight control law after the expansion observed quantity in the nonlinear state observer is removed from the nonlinear state error feedback control law, and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
The flight track tracking module is used for acquiring optimal control amounts corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft by the optimal control amounts;
The control parameter optimization module is used for optimizing and adjusting the control parameters in the final flight control law by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary shrinkage and escape strategy in the process of carrying out online robust tracking on the flight track of the aircraft through the optimal control quantity.
For specific limitations on the online robust tracking device for an aircraft trajectory, reference may be made to the above limitation on the online robust tracking method for an aircraft trajectory, and no further description is given here. The various modules in the online robust tracking device for aircraft trajectories described above may be implemented in whole or in part by software, hardware, and combinations thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
In one embodiment, a computer device is provided, which may be a terminal, and the internal structure of which may be as shown in fig. 2. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement an on-line robust tracking method of aircraft trajectories. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by persons skilled in the art that the architecture shown in fig. 2 is merely a block diagram of some of the architecture relevant to the present inventive arrangements and is not limiting as to the computer device to which the present inventive arrangements are applicable, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
In one embodiment, a computer device is provided comprising a memory storing a computer program and a processor that when executing the computer program performs the steps of:
constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft; wherein the state variables include altitude, mach number and ballistic inclination of the aircraft, and the control quantity includes attack angle and equivalence ratio of the aircraft;
Constructing a nonlinear state observer to observe three state variables in a nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, removing an expansion observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
Acquiring optimal control quantity corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity;
In the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity, the control parameters in the final flight control law are optimized and adjusted by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary contraction and escape strategies.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the present application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of the application should be assessed as that of the appended claims.
Claims (12)
1. An on-line robust tracking method for aircraft trajectories, the method comprising:
Constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft; wherein the state variables include altitude, mach number, and ballistic tilt of the aircraft, and the control quantities include angle of attack and equivalence ratio of the aircraft;
Constructing a nonlinear state observer to observe three state variables in the nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, removing an expansion observed quantity in the nonlinear state observer from the nonlinear state error feedback control law to obtain a final flight control law, and calculating and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
Acquiring the optimal control quantity corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft by the optimal control quantity;
In the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal control quantity, optimizing and adjusting the control parameters in the final flight control law by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary contraction and escape strategy;
wherein constructing a nonlinear state observer observes three state variables in the nonlinear state equation, including:
the nonlinear state observer is represented as
；
Wherein,、、Respectively the heights ofMach numberInclination angle of trajectoryAn observer of the three state quantities,In order to expand the observed quantity,、、AndRespectively represent、、AndIs used as a first derivative of (a),、、AndRespectively is、、AndIs used for the gain factor of (a),The scale factor is represented as such,AndTwo non-linear functions are represented and,As a known nonlinear function, expressed as
Wherein,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value and。
2. The method of claim 1, wherein constructing a nonlinear state equation based on the state variables and the control amounts of the aircraft comprises:
selecting altitude h, mach number of aircraft Inclination angle of trajectoryAs a state variable, the angle of attack of the aircraft is selectedThe equivalence ratio ER is used as a control quantity to construct a state equation expressed as
；
Wherein,、、Respectively is the height h and Mach numberInclination angle of trajectoryIs used as a first derivative of (a),AndRepresenting two unknown nonlinear functions related to state variables and control amounts;
Optimizing the state equation by introducing two intermediate variables of axial overload N x and normal overload N y to obtain a nonlinear state equation expressed as
；
Wherein,For the radius of the earth,Representing the aircraft mass.
3. The method of claim 1, wherein establishing a nonlinear state error feedback control law by observing the resulting state feedback error comprises:
establishing a nonlinear state error feedback control law by the state feedback error observed by the nonlinear state observer, which is expressed as
；
；
Wherein,AndTwo control intermediate variables in the nonlinear state error feedback control law,，，Respectively is the height h and Mach numberInclination angle of trajectoryThe state feedback errors of these three state quantities,、、Three gains representing a state error feedback control law,、、The scaling factors representing the three state quantities.
4. A method according to claim 3, wherein obtaining a final flight control law by removing the dilation observables in the nonlinear state observer from the nonlinear state error feedback control law, and obtaining an optimal axial overload and an optimal normal overload of the aircraft according to the final flight control law calculation comprises:
By extending observations in a nonlinear state observer Removing the error feedback control law from the nonlinear state to obtain a final flight control law, and calculating and acquiring the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law, wherein the optimal axial overload and the optimal normal overload are respectively expressed as
；
；
Wherein,For an optimal axial overload the device is provided with,For an optimal normal overload the device is provided with,Is thatIs used to determine the scaling factor of (a),As a known non-linear function,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value.
5. The method of claim 1, wherein optimizing the control parameters in the final flight control law by employing a particle swarm algorithm that considers an oscillation mechanism, a chaotic disturbance mechanism, a boundary contraction and escape strategy in the process of performing online robust tracking of the aircraft flight trajectory by the optimal control quantity comprises:
in the process of carrying out on-line robust tracking on the flight track of the aircraft through the optimal attack angle and the optimal equivalence ratio, carrying out particle sampling on the flight track of the aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, obtaining the position vector and the speed vector of each particle, introducing the control parameters in the final flight control law into the position vector of each particle, and realizing the optimization adjustment on the control parameters by updating the position vector of the particle;
Calculating average tracking errors of the altitude and Mach number of the aircraft according to the tracking result of the flight track, and calculating the adaptability of each particle according to the average tracking errors of the altitude and Mach number The specific form of the fitness is as follows:
Wherein, Representing a summation function; A function representing averaging; is highly feedback error Absolute value of (2); feedback error for Mach number Absolute value of (2);
The fitness of the single particle is respectively compared with the fitness extreme value of the single particle and the fitness extreme value of the particle population, and the fitness extreme value of the single particle and the fitness extreme value of the particle population are updated according to the comparison result;
Updating the position vector and the speed vector of the single particle according to the updated fitness extremum of the single particle and the fitness extremum of the particle population;
Sequencing the fitness of single particles according to ascending order, updating the optimal position of each particle and the optimal position of a particle population for the first 30% of particles by adopting a chaotic disturbance mechanism, shrinking the position boundary of each particle based on a boundary shrinkage strategy, and updating the position vector and the speed vector for the rest 70% of particles by adopting an escape strategy;
Repeating the steps until the optimization error of the control parameter reaches the preset precision or the iteration reaches the maximum circulation times, and completing the optimization adjustment of the control parameter.
6. The method of claim 5, wherein the steps of sampling the flight path of the aircraft by using a particle swarm algorithm taking into account an oscillation mechanism, obtaining a position vector and a velocity vector of each particle, introducing the control parameters in the final flight control law into the position vectors of each particle, and optimizing the control parameters by updating the position vectors of the particles include:
The method comprises the steps of sampling particles of a flight track of an aircraft by adopting a particle swarm algorithm considering an oscillation mechanism, and obtaining a position vector and a speed vector of each particle; wherein, the particle swarm algorithm taking the oscillation mechanism into consideration is expressed as
Wherein,AndRespectively represent the ith particleThe velocity vector and the position vector of the next iteration,AndRespectively represent the ith particleA velocity vector and a position vector for the second iteration; And Is an intermediate parameter; And Representing the individual and global random learning factors respectively,For the number of iterations, w is the inertial weight coefficient,For an optimal position of the individual particles,Is the optimal position of the particle population;
Introducing control parameters in the final flight control law into the ith particle Position vector for multiple iterationsIn (a) is expressed as
Wherein,、、AndThe gain coefficients of three observers and one dilation observers of the nonlinear state observer respectively,、、Three gains representing a state error feedback control law; and optimizing and adjusting the control parameters by updating the position vectors of the particles.
7. The method of claim 6, wherein comparing the fitness of the individual particles to fitness extremum of the individual particles and fitness extremum of the population of particles, respectively, and updating the fitness extremum of the individual particles and the fitness extremum of the population of particles based on the comparison comprises:
Comparing the fitness of the single particle with the fitness extremum of the single particle and the fitness extremum of the particle population respectively, and if the fitness of the single particle is larger than the fitness extremum of the single particle, replacing the fitness extremum of the single particle with the fitness of the single particle; if the fitness of the single particle is greater than the fitness extremum of the particle population, replacing the fitness extremum of the particle population with the fitness of the single particle.
8. The method of claim 7, wherein the step of sorting the fitness of individual particles in ascending order, and updating the optimal position of each particle and the optimal position of the particle population for the first 30% of particles using a chaotic perturbation mechanism, comprises:
sequencing the fitness of single particles according to ascending order, and applying chaotic disturbance to the first 30% of particles;
Initializing chaotic variables The chaotic state of the chaotic variable meeting the chaotic logic mapping function is expressed as; Wherein,Is the ith particleThe position vector of the number of iterations,AndUpper and lower boundaries for the ith particle;
Chaotic variable is obtained on the basis of chaotic logic mapping function The state value of the iteration is expressed as; Wherein,Representing a chaotic control parameter;
According to chaos variable in the first place The state value of the iteration generates a new particle position vector, expressed as; Wherein,Is the ith particleA position vector of the second iteration;
Updating the optimal position of the single particle and the optimal position of the particle population according to the adaptability of the particles; wherein the optimal position of the single particle is expressed as
；
Wherein,For the fitness of the ith particle in the kth iteration,Fitness for the (k+1) th iteration of the (i) th particle.
9. The method of claim 8, wherein shrinking the location boundaries of each particle based on a boundary shrink strategy comprises:
Boundary shrinkage strategy based on boundary shrinkage strategy for ith particle upper boundary And lower boundaryThe method comprises the following steps of:
Wherein, Representing the optimal position of the particle population, rand represents a random number between [0,1 ];
After boundary shrinkage, the upper and lower boundaries of the ith particle are limited to a range And (3) inner part.
10. The method of claim 9, wherein updating the position vector and the velocity vector for the remaining 70% of the particles using the escape strategy comprises:
Updating position vector and velocity vector again for the remaining 70% of particles using escape strategy, expressed as
Wherein,AndRespectively represent the ith particleThe velocity vector and the position vector of the next iteration, d representing the upper boundary of the ith particleAnd lower boundaryIs a vector dimension of (c).
11. An on-line robust tracking apparatus for aircraft trajectories, the apparatus comprising:
the state equation construction module is used for constructing a nonlinear state equation based on the state variable and the control quantity of the aircraft; wherein the state variables include altitude, mach number, and ballistic tilt of the aircraft, and the control quantities include angle of attack and equivalence ratio of the aircraft;
The error feedback control module is used for constructing a nonlinear state observer to observe three state variables in the nonlinear state equation, establishing a nonlinear state error feedback control law through state feedback errors obtained by observation, obtaining a final flight control law after the expansion observed quantity in the nonlinear state observer is removed from the nonlinear state error feedback control law, and obtaining the optimal axial overload and the optimal normal overload of the aircraft according to the final flight control law; wherein the nonlinear state observer comprises three state variable observers and an expansion observance;
the flight track tracking module is used for acquiring the optimal control quantity corresponding to the optimal axial overload and the optimal normal overload by adopting an optimizing algorithm, and carrying out on-line robust tracking on the flight track of the aircraft by the optimal control quantity;
The control parameter optimization module is used for optimizing and adjusting the control parameters in the final flight control law by adopting a particle swarm algorithm considering an oscillation mechanism, a chaotic disturbance mechanism, boundary shrinkage and escape strategy in the process of carrying out online robust tracking on the flight track of the aircraft through the optimal control quantity;
wherein constructing a nonlinear state observer observes three state variables in the nonlinear state equation, including:
the nonlinear state observer is represented as
；
Wherein,、、Respectively the heights ofMach numberInclination angle of trajectoryAn observer of the three state quantities,In order to expand the observed quantity,、、AndRespectively represent、、AndIs used as a first derivative of (a),、、AndRespectively is、、AndIs used for the gain factor of (a),The scale factor is represented as such,AndTwo non-linear functions are represented and,As a known nonlinear function, expressed as
Wherein,The amount of deviation is indicated and,Is a coefficient of proportionality and is used for the control of the power supply,Is a threshold value and。
12. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any one of claims 1 to 10 when the computer program is executed.
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