CN117092961A - Switching control method and system for transition section of gyroplane based on equivalent input interference - Google Patents
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Abstract
The invention discloses a switching control method of a rotorcraft transition section based on equivalent input interference, which constructs a linear switching system comprising external interference based on a flight dynamics model of a tilting rotorcraft transition section; obtaining disturbance information output by a linear switching system by external disturbance, constructing an equivalent input disturbance estimator to estimate the disturbance information, and returning the estimated equivalent input disturbance to a controller for constructing the linear switching system; solving to obtain the average residence time of each subsystem which enables the switching process to be stable, obtaining the limited time stability condition of the linear switching system based on the switching rule of the average residence time, and solving the gain matrix of the controller by utilizing the linear matrix inequality in the condition to obtain the actual controller; the switching of the transition section of the tiltrotor aircraft is controlled by an actual controller. The influence of external interference on the system stability can be effectively restrained through equivalent input interference, and the disturbance restraining performance of the whole control system is improved.
Description
Technical Field
The invention relates to switching control of a transition section of a tiltrotor aircraft, in particular to a switching control method and a switching control system of a transition section of a tiltrotor aircraft based on equivalent input interference.
Background
Tiltrotor aircraft is a new configuration of composite aircraft that can be divided into helicopter mode, transitional mode, and fixed wing mode depending on the flight mode. The rotor wing of the tiltrotor aircraft tilts along with the nacelle in the transitional flight process, and in the process, the aerodynamic characteristics of the aircraft change greatly, so that the aerodynamic interference caused by the aerodynamic characteristics directly threatens the stability of the aircraft. For such a complex system of strong nonlinearity, strong coupling, and time-varying dynamics, the design of the flight control system faces significant difficulties. Therefore, how to design an efficient transition mode flight controller is a challenging task.
In recent years, in research on transitional modes of tiltrotors, common control methods include a neural network PID, a gain scheduling method, a multi-model self-adaptive method and the like. From the aspect of control method analysis, the existing nonlinear control method has a certain difficulty in processing control under the whole transition mode, and is difficult to ensure the stability and reliability of the system, and the nacelle of the tilting rotor aircraft is generally tilted synchronously between 0 and 95 degrees, so that the multi-mode-based smooth switching control method has more advantages in solving the flight control problem of the transition mode. In addition, during the control of the transition mode, the system response time must be completed within a certain time range, so the problem of the limited time stability of the switching system needs to be considered during the design of the controller.
In the transitional flight process of the tiltrotor aircraft, the tiltrotor aircraft can be subjected to various interferences, besides the interferences caused by the aerodynamic characteristics of the tiltrotor aircraft, the interferences existing in the external environment exist, and the existence of the composite interferences can influence the system performance and even directly threaten the flight safety.
In addition, in the actual process of the controller, the actual output of the controller has certain perturbation due to the influence of the perturbation of parameters such as an actuator, a sensor and the like, the actual output of the controller is expressed as uncertainty of the controller, and the performance of the switching control system is greatly influenced.
Disclosure of Invention
The invention aims to: aiming at the defects, the invention provides a switching control method and a switching control system for a transition section of a tiltrotor aircraft based on equivalent input interference, which are smooth and stable in a transition flight mode.
The technical scheme is as follows: in order to solve the problems, the invention adopts a switching control method of a transition section of a rotorcraft based on equivalent input interference, which comprises the following steps:
(1) Constructing a linear switching system comprising external disturbances based on a flight dynamics model of the tiltrotor aircraft transition section;
(2) Obtaining disturbance information output by the external disturbance on the linear switching system, constructing an equivalent input disturbance estimator to estimate the disturbance information, and obtaining equivalent input disturbance;
(3) Returning the estimated equivalent input interference to a controller for constructing a linear switching system;
(4) According to the switching times of the linear switching system, solving to obtain the average residence time of each subsystem which enables the switching process to be stable, and obtaining a switching rule based on the average residence time;
(5) Obtaining a limited time stable condition of a linear switching system based on a switching rule, and solving a gain matrix of the controller by using a linear matrix inequality in the condition to obtain an actual controller;
(6) The switching of the transition section of the tiltrotor aircraft is controlled by an actual controller.
Further, the linear switching system including external interference in the step (1) is:
，
wherein,for a state vector of a linear switching system, +.>Is a state vector +>About time->First derivative of>Control input for a linear switching systemGo into (I)>For switching signals +.>For external disturbance->For the system matrix->For input matrix +.>Is an interference matrix.
Further, the linear switching system including the equivalent input interference is:
，
wherein,representing equivalent input disturbances.
Further, in the step (2), disturbance information is obtained through a state observer, and a state observer model is as follows:
，
wherein,is a state vector +>Is>For observations +.>About time->Is used as a first derivative of (a),is an input vector of the state observer model, +.>Is an observer gain matrix;
estimate of equivalent input interferenceThe method comprises the following steps:
，
wherein,for matrix->Is the generalized inverse of>For tunable gain matrix for improved design flexibility, < >>For observing errors +.>。
Further, the high-frequency noise in the estimated value of the equivalent input interference is filtered by a filter, and the estimated valueFor the filter input, the following state space equation is obtained:
，
，
wherein,for the process vector +.>For vector->About time->First derivative of>For the filtered estimate of the equivalent input disturbance, < >>、/>、/>Are constant coefficient matrices.
Further, the controller constructed in the step (3) is as follows:
，
an elastic controller for reducing the sensitivity of control gain perturbation is designed, and the following formula is adopted:
，
，
，
wherein,、/>for the controller gain, +>、/>Is elastic item->、/>、、/>Is a constant matrix>、/>Is a bounded real matrix function.
Further, the elastic controller comprises an internal model:
，
wherein,is a state vector of the internal model, +.>For vector->About time->Is used as a first derivative of (a),is an input vector of the internal model, +.>And->Is a known constant matrix.
The invention also adopts a switching control system of the transition section of the rotorcraft based on equivalent input interference, which comprises a model building module, a switching control module and a switching control module, wherein the model building module is used for building a linear switching system comprising external interference based on a flight dynamics model of the transition section of the rotorcraft;
the interference equivalent estimation module is used for acquiring disturbance information output by the external interference on the linear switching system, constructing an equivalent input interference estimator to estimate the disturbance information and obtaining equivalent input interference;
the controller construction module is used for returning the estimated equivalent input interference to a controller for constructing the linear switching system; obtaining a limited time stable condition of the linear switching system based on a switching rule, and solving a gain matrix of the controller by using a linear matrix inequality in the condition to obtain an actual controller;
the switching rule determining module is used for solving and obtaining the average residence time of each subsystem which enables the switching process to be stable according to the switching times of the linear switching system, and obtaining the switching rule based on the average residence time;
and the control module is used for controlling the switching of the transition section of the tiltrotor aircraft through the actual controller.
The beneficial effects are that: compared with the prior art, the invention has the remarkable advantages that the influence of external interference on the system stability can be effectively restrained through equivalent input interference, the disturbance restraining performance of the whole control system is improved, the control gain perturbation problem existing in control is solved through the elastic controller, the tilting rotor aircraft is stably switched in a transition mode through the controller designed in the technology, and the robustness and the non-fragility of the system are enhanced.
Drawings
Fig. 1 is a schematic diagram of a switching control method according to the present invention.
Fig. 2 is a schematic flow chart of a switching control method according to the present invention.
Detailed Description
As shown in fig. 1 and 2, a switching control method for a transitional section of a gyroplane based on equivalent input interference in the present embodiment includes the following steps:
step 1: based on a flight dynamics model of the transition section of the tiltrotor aircraft, a linear switching system comprising external interference is constructed, and an equivalent input interference estimator based on a state observer is constructed to estimate the equivalent interference.
The tiltrotor aircraft XV-15 in this embodiment may be considered as flying longitudinally at altitude during the transition, and the nonlinear flying kinematics model at this time may be represented by the following formula:
（1.1），
wherein,for forward speed, < >>For vertical speed, ++>And->Respectively representing pitch angle speed and pitch angle; />Representing tiltrotor aircraft mass; />And->The aerodynamic forces of the parts of the body such as the left and right rotor wings, the elevator, the rudder and the fuselage of the aircraft are represented in the body coordinate system +.>Shaft and->Resultant force generated on the shaft; similarly, a->In the machine body coordinate system for each part of the machine bodyThe sum torque generated on the shaft; in addition, a->Indicating the acceleration of gravity>Representing the moment of inertia of the body.
The nonlinear flight kinematics model (1.1) is selected from the range of 0-90 degrees of the nacelle inclination angleThe individual balance points are linearized with small disturbances and take into account external disturbances, so the tiltrotor aircraft transition can be modeled as a linear switching system with occasional external disturbances as follows:
（1.2），
，
wherein,a state vector for a linear switching system; />For the control input of a linear switching system, +.>For rotor transversal period variation->For rotor longitudinal period variation->The deflection angle of the elevator; switch signal->Is a piecewise constant function, when +.>At the time, represent the firstiThe subsystem is running; />、/>、/>Is a matrix known to have appropriate dimensions; />Is an external disturbance. />、 />、/>Respectively represent real number sets, & lt & gt>Uygur type spaceIs a real matrix of (a).
To estimate external disturbanceAn equivalent input interference estimator is constructed, wherein the equivalent input interference is defined as an input end interference equivalent to external disturbance according to the influence effect of disturbance on system output. The principle is that disturbance information is obtained by constructing a full-dimensional state observer and mapped to the input end of the system, and disturbance of the input end is estimated and reversely compensated, so that disturbance inhibition performance of the whole control system is improved. Thus for a linear switching system (1.2), it can be rewritten as: />（1.3），
Wherein,representing equivalent input disturbances.
The following full-dimensional state observer is constructed:
（1.4），
wherein,representing state vector +.>Is>For the observer gain matrix to be designed, +.>Is the input vector of the state observer.
Define the observed error asDeriving and substituting (1.3) the obtained product can obtain:
（1.5），
assuming a control input variable existsThe following equation is established:
（1.6），
let the estimated value of equivalent input interferenceThe method comprises the following steps:
（1.7），
substitution of (1.6) into (1.4) can result in:
（1.8），
then combining (1.4) and (1.7) can result in:
（1.9），
wherein,for matrix->Is the generalized inverse of>For a tunable gain matrix +.>To observe errorsDifference (S)>。
To filter out the obtained interference estimation valueThe high frequency noise in (1) is filtered by a filter shown in the following formula>Representation of->Is the cut-off angular frequency. Let->As an input to the filter, the form of the following state space equation can be obtained:
（1.10），
wherein,、/>and->Are constant coefficient matrix>Is the filtered equivalent interference estimate.
Step 2: and returning the estimated equivalent input interference to an elastic state feedback switching controller for constructing a linear switching system, wherein the elastic state feedback switching controller comprises the following specific steps of:
the reference signal tracked by a given system is the output of a reference model derived from the state characteristics of the transitional phase of the tiltrotor aircraft, expressed by the following formula:
（1.11），
wherein,for reference signal, +.>Is->First derivative of>For reference input, all information about the reference model is known.
In order to improve the tracking precision of the controller, the following internal model is introduced firstly:
（1.12），
wherein,is a state vector of the internal model, +.>Is an input vector for the internal model,and->Is a known constant matrix and matrix +.>。
Based on the internal model (1.12) and the full-dimensional state observer (2.4), the observer inputs are designed as:
（1.13），
wherein,and->Are both control gains.
In an actual flight control system, when the controller outputs a control signal, it is susceptible to many factors such as ambient temperature, digital conversion accuracy, and the like. This effect is more pronounced in switching systems, and the resultant control gain perturbation can degrade control performance. Thus, constructing the spring controller reduces the sensitivity to the control gain perturbation described above, namely, rewrites equation (1.13) to the form:
（1.14），
wherein,and->Gain for the controller; />、/>Is an elastic term with the expression +.>，/>，/>、/>、/>、Is a constant matrix suitable for dimension>、/>Is a bounded real matrix function, and its elements are all Lebesgue measurable and meet +.>、/>，/>Is an identity matrix.
Therefore, the actual controller of the linear switching system (1.3) is:
（1.15），
step 3: according to the switching times of the linear switching system, solving to obtain the average residence time of each subsystem which enables the switching process to be stable, and obtaining the switching rule based on the average residence time.
Defining vectorsFor the state of an augmentation system, then the state space expression of the augmentation system is:
（1.16），
wherein the symbols are usedReplace->I.e. +.>、/>、/>、/>、，/>，/>，。
To facilitate the design of switching rules and subsequent computational solutions for the elastic controller, definitions of average residence time and continuous system finite time stability and two arguments are given here:
definition 1: for switching signalsAnd optionally->Let->Representing time intervalsIf there is a scalar +.>So that the following inequality holds:
（1.17），
then the constant isReferred to as the average residence time.
Definition 2: given three constants、/>And->A positive definite matrix->And a switching signalIf->Then the following continuous switching system (1.18) is about +.>The limited time is stable:
（1.18），
lemma 1: given a symmetric matrix：
，
Wherein,there are the following threeThe following conditions are equivalent:
1. ；
2. ；
3. 。
and (4) lemma 2: given matrix、/>、/>，/>Is a bounded real matrix function and its element Lebesgue is measurable, satisfying +.>Then ∈0 for any scalar>There is。
Based on definition 1 and definition 2, average residence timeThe method comprises the following steps:
（1.19），
wherein,，/>，/>，/>taking tiltrotor aircraft XV-15 as an example for the time required for the tiltrotor aircraft to engineering complete the transition state>。
Order theIs->The switching-in time of the subsystem,/->First->The switching-out time of the subsystem is dependent on the average residence time +.>The following switching rule is obtained, namely +.>The residence time of the subsystem satisfies:
（1.20），
step 4: the limited time stable condition of the switching system can be obtained by combining a multi-Lyapunov function method and a switching rule, and a gain matrix of the controller is solved by utilizing a linear matrix inequality in the condition to obtain an actual controller;
theorem 1: the switching system (1.16) is arbitraryRecord->Assuming a presence matrixAnd a constant->Such that: /> （1.21），
（1.22），
Wherein,，/>，/>and switching signal based on average dwell time +.>The following inequality is satisfied:
（1.23），
the switching system is concerned withIs stable for a limited time.
And (3) proving: the following form of Lyapunov function was selected:
（1.24），
when (when)When (I)>Taking the first derivative with respect to time along the switching system is:
（1.25），
from formula (1.21):
（1.26），
in the time domainThe upper integral can be obtained:
（1.27），
at the moment of switchingAccording to->The definition is as follows:
（1.28），
combining formulas (1.21) and (1.22) can result in:
（1.29），
for any timeRecord->For switching signals +.>At->The number of times of switching is thatBecause of->According to->The method can obtain the following inequality:
（1.30），
according to a limited time stability definition, there areTherefore:
（1.31），
in addition, byAnd->Is defined as follows:
（1.32），
（1.33），
the general formulae (1.31), (1.32) and (1.33) can be obtained:
（1.34），
then apparent from formula (1.22)The recombination of formula (1.17) can be obtained:
（1.35），
then, according to formulas (1.33), (1.34) and (1.35), it is possible to obtain:
（1.36）
switching the system for a limited time according to the definition of the stability of the limited timeInternal stabilization.
Based on theorem 1, to solve for controller and equivalent input interference estimator gains, the inequality (1.21) is analyzed: taking positive definite matrix，/>Due to the matrix->Also positive definite matrix, can make matrix，/>The following steps are:
（1.37），
wherein,，/>， ，/>，，/>，
due to，/>And->，Based on lemma 1 and lemma 2, the following inequality can be obtained for the matrix:
（1.38），
wherein,，，/>， />。
so for the switching system, for anyThere is a positive definite matrix +.>Sum constant ofThe following inequality is established:
（1.39），
（1.40），
and average dwell time based switching signalsThe following inequality is satisfied:
（1.41）
the system switch system is concernedIs stable for a limited time.
Finally, let the，/>Solving the matrix inequality (1.39), (1.40) by using the LMI toolbox in MATLAB to obtain the matrix +.>、/>、/>、/>And->Further, it can be calculated to obtain，/>And obtaining an actual controller.
Step 5: the switching of the transition section of the tiltrotor aircraft is controlled by an actual controller.
Claims (10)
1. The switching control method of the transition section of the gyroplane based on equivalent input interference is characterized by comprising the following steps of:
(1) Constructing a linear switching system comprising external disturbances based on a flight dynamics model of the tiltrotor aircraft transition section;
(2) Obtaining disturbance information output by the external disturbance on the linear switching system, constructing an equivalent input disturbance estimator to estimate the disturbance information, and obtaining equivalent input disturbance;
(3) Returning the estimated equivalent input interference to a controller for constructing a linear switching system;
(4) According to the switching times of the linear switching system, solving to obtain the average residence time of each subsystem which enables the switching process to be stable, and obtaining a switching rule based on the average residence time;
(5) Obtaining a limited time stable condition of a linear switching system based on a switching rule, and solving a gain matrix of the controller by using a linear matrix inequality in the condition to obtain an actual controller;
(6) The switching of the transition section of the tiltrotor aircraft is controlled by an actual controller.
2. The handover control method according to claim 1, wherein the linear handover system including external interference in the step (1) is:
，
wherein,for a state vector of a linear switching system, +.>Is a state vector +>About time->Is used as a first derivative of (a),for the control input of a linear switching system, +.>For switching signals +.>For external disturbance->In the form of a system matrix,for input matrix +.>Is an interference matrix.
3. The handover control method according to claim 2, wherein the linear handover system including equivalent input interference is:
，
wherein,representing equivalent input disturbances.
4. The handover control method according to claim 3, wherein the disturbance information is acquired in the step (2) by a state observer, and the state observer model is:
，
wherein,is a state vector +>Is>For observations +.>About time->First derivative of>Is an input vector of the state observer model, +.>Is an observer gain matrix;
estimate of equivalent input interferenceThe method comprises the following steps:
，
wherein,for matrix->Is the generalized inverse of>For a tunable gain matrix +.>In order to observe the error in the image,。
5. the handover control method according to claim 4, wherein high frequency noise in the estimated value of equivalent input interference is filtered out by a filter, the estimated valueFor the filter input, the following state space equation is obtained:
，
，
wherein,is a process vector，/>For vector->About time->First derivative of>For the filtered estimate of the equivalent input disturbance, < >>、/>、/>Are constant coefficient matrices.
6. The handover control method according to claim 5, wherein the controller constructed in step (3) is:
。
7. the switching control method according to claim 6, wherein the step (3) is to design an elastic controller for reducing sensitivity of control gain perturbation by using the following formula:
，
，
，
wherein,、/>for the controller gain, +>、/>Is elastic item->、/>、/>、Is a constant matrix>、/>Is a bounded real matrix function.
8. The switching control method according to claim 1, wherein the elastic controller includes an internal model:
，
wherein,is a state vector of the internal model, +.>For vector->About time->First derivative of>Is an input vector of the internal model, +.>And->Is a known constant matrix.
9. The handover control method according to claim 1, wherein the average residence time in step (4)The method comprises the following steps:
，
wherein,is the minimum value of the average residence time, +.>Time required for tiltrotor aircraft to complete transition state, +.>、/>Is a constant; />For the mean residence time parameter, +.>Is a constant;
the switching rule is as follows:
，
wherein,is->The switching-in time of the subsystem,/->Is->The subsystem's cut-out time.
10. The switching control system of the rotorcraft transition section based on equivalent input interference is characterized by comprising a model building module, a switching control module and a switching control module, wherein the model building module is used for building a linear switching system comprising external interference based on a flight dynamics model of the tilting rotorcraft transition section;
the interference equivalent estimation module is used for acquiring disturbance information output by the external interference on the linear switching system, constructing an equivalent input interference estimator to estimate the disturbance information and obtaining equivalent input interference;
the controller construction module is used for returning the estimated equivalent input interference to a controller for constructing the linear switching system; obtaining a limited time stable condition of the linear switching system based on a switching rule, and solving a gain matrix of the controller by using a linear matrix inequality in the condition to obtain an actual controller;
the switching rule determining module is used for solving and obtaining the average residence time of each subsystem which enables the switching process to be stable according to the switching times of the linear switching system, and obtaining the switching rule based on the average residence time;
and the control module is used for controlling the switching of the transition section of the tiltrotor aircraft through the actual controller.
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