CN109581878B - Control method based on mode conversion stage of tilt rotor aircraft - Google Patents

Control method based on mode conversion stage of tilt rotor aircraft Download PDF

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CN109581878B
CN109581878B CN201910062363.0A CN201910062363A CN109581878B CN 109581878 B CN109581878 B CN 109581878B CN 201910062363 A CN201910062363 A CN 201910062363A CN 109581878 B CN109581878 B CN 109581878B
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aircraft
tilt rotor
rotor aircraft
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CN109581878A (en
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朱平芳
曾建平
柯津
鲁麟宏
黄锦涛
杨航
李颖
凌彦聪
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Xiamen University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a control method based on a mode conversion stage of a tilt rotor aircraft, which comprises the steps of firstly establishing a longitudinal nonlinear model of the tilt rotor aircraft, establishing a longitudinal nonlinear error model of the tilt rotor aircraft according to track tracking information of the tilt rotor aircraft, and converting the longitudinal nonlinear error model of the tilt rotor aircraft into a nonlinear time-varying state space form by selecting appropriate state variables and parameter variables; secondly, constructing a nonlinear time-varying state controller; and finally, converting the design problem of the controller into a square and convex optimization problem to solve. The invention effectively solves the control problem of the tilt rotor aircraft in the mode conversion stage.

Description

Control method based on mode conversion stage of tilt rotor aircraft
Technical Field
The invention relates to the technical field of aerospace, in particular to a control method based on a mode conversion stage of a tilt rotor aircraft.
Background
The tilt rotor aircraft combines the characteristics of fixed wing aircraft and helicopters, and has important civil and military values. However, the control mechanism of the tilt rotor aircraft has both aerodynamic layout and aerodynamic control surface, which causes the modeling and flight control of the tilt rotor aircraft to have certain difficulties. The tilt rotor aircraft system has dynamics characteristics of time variation, nonlinearity, nonradiation, strong coupling, control redundancy and the like. Therefore, the study of the control problem of tiltrotor aircraft, in which the control of the mode-change phase of a tiltrotor aircraft is the most difficult and complicated, is a challenging task.
At present, the literature on tiltrotor aircraft basically uses the tilt angle as a control input. However, in the modeling, the tilt angle and other control input variables such as an accelerator and a control surface have coupling terms, and the modeling method causes great difficulty in the design of the controller. Later, some scholars considered the nacelle tilter mechanism in the modeling, which eliminated the multiplicative term for the control inputs. However, this processing method is mainly used for processing mode control of a helicopter of a tilt rotor aircraft, and particularly, the system is required to be linear and time-varying, and the processing methods have certain limitations.
Disclosure of Invention
The invention aims to solve the control problem of a tilt rotor aircraft in a mode conversion stage, and provides a control method based on the mode conversion stage of the tilt rotor aircraft.
In order to solve the problems, the invention is realized by the following technical scheme:
a control method based on a mode conversion phase of a tilt rotor aircraft specifically comprises the following steps:
step 1, establishing a longitudinal nonlinear model of a tilt rotor aircraft;
step 2, giving a reference track of the tilt rotor aircraft, namely giving the speed, the attack angle, the pitch angle rate and the height of the reference tilt rotor aircraft, and giving the reference force along the x axis of the aircraft body, the force along the y axis and the pitch moment, and converting the established longitudinal nonlinear model of the tilt rotor aircraft into an error model;
step 3, selecting a state variable x and a control input variable u, and converting a longitudinal nonlinear error model of the tilt rotor aircraft into a form of an easily-processed state space; wherein
Figure BDA0001954557810000012
Figure BDA0001954557810000011
Step 4, a nonlinear time-varying control controller is constructed by assuming that the speed, the attack angle, the pitch angle rate and the height of the tilt rotor aircraft can be measured;
and 5, converting the design problem of the nonlinear time-varying control controller of the tilt rotor aircraft into a quadratic sum convex optimization problem to solve, namely
Figure BDA0001954557810000021
In the above formulae, V and V*Representing the actual and reference speeds of the tiltrotor aircraft, respectively; alpha and alpha*Respectively representing the actual and reference angles of attack of the tiltrotor aircraft;
Figure BDA00019545578100000216
and
Figure BDA00019545578100000217
respectively representing the actual and reference pitch angles of the tiltrotor aircraft; q and q*Representing actual and reference pitch rates of a tiltrotor aircraft, respectively; h and H*Representing the actual and reference altitudes of the tiltrotor aircraft, respectively; fxtAnd
Figure BDA0001954557810000022
representing the actual and reference force components along the x-axis of the body, respectively; fytAnd
Figure BDA0001954557810000023
representing the actual and reference force components along the y-axis of the body, respectively; mzAnd
Figure BDA0001954557810000024
representing the actual and reference pitching moments along the body, respectively;
Figure BDA0001954557810000025
A12＝-Fyt*/m，
Figure BDA0001954557810000026
Figure BDA0001954557810000027
Figure BDA00019545578100000218
A52＝-V*，A53＝V*；Aj(x, τ) denotes a j-th row of a (x, τ), j being 1,2, …, 5;
Figure BDA0001954557810000028
B11＝1/m，B12＝-(α*+Δα)/m，B43＝1/Iz，
Figure BDA0001954557810000029
a＝8.791×10-4，b＝-0.03274，c＝0.3491；
Figure BDA00019545578100000210
the method comprises the following steps of (1) obtaining a Lyapunov matrix to be solved;
Figure BDA00019545578100000211
a gain matrix of the nonlinear time-varying control controller to be solved; x represents a state variable which is represented by,
Figure BDA00019545578100000212
represents a state variable such that the row vectors of B (x, τ) are all 0, τ represents the tilt angle of the tiltrotor aircraft,
Figure BDA00019545578100000213
representing the derivative of the tilt angle of a tiltrotor aircraft over time;
Figure BDA00019545578100000214
and ivrespectively represent
Figure BDA00019545578100000215
Upper and lower bounds of (a); i represents an adaptive identity matrix; z is a radical of1Representing an adaptive non-zero column vector;1，2and3respectively represent given normal numbers;
and 6, utilizing the solved nonlinear time-varying control controller to realize a control target of the tilt rotor aircraft in a mode conversion stage.
And in the step 4, constructing the nonlinear time-varying state controller.
In the step 5, the square and convex optimization problem is solved by using a tool box sosolols in Matlab.
Compared with the prior art, the invention has the following characteristics:
1. the tilting angle tau of the tilting rotor aircraft is taken as a parameter rather than control input, so that a coupling term generated by modeling is solved, and the calculated amount is reduced;
2. solving the nonlinear time-varying controller through a square sum convex optimization algorithm, and effectively reducing conservatism due to an S-process for the derivative of the parameter;
3. the designed nonlinear time-varying controller is a polynomial function of a state and a parameter, and is easy for engineering realization;
4. each reference signal of tilting rotor wing is effectively and quickly tracked, and a good control effect is achieved.
Drawings
Fig. 1 is a flow chart of a control method based on a mode transition phase of a tiltrotor aircraft.
Fig. 2 is a diagram of a simulation locus of a tilt angle.
Fig. 3 is a diagram of a simulation locus of the tilt angular velocity.
Fig. 4 is a diagram of a simulation locus of the tilt angular acceleration.
Fig. 5 is a graph of the velocity V tracking trajectory of a tiltrotor aircraft. In the figure, (a) represents a reference speed track, (b) represents a speed track obtained by a linear time-varying model, and (c) represents a speed track obtained by the invention.
Fig. 6 is a graph of the tracking trajectory of the angle of attack α of a tiltrotor aircraft, in which (a) represents a reference velocity trajectory, (b) represents a velocity trajectory obtained by a linear time-varying model, and (c) represents a velocity trajectory obtained by the present invention.
FIG. 7 is a pitch angle for a tiltrotor aircraft
Figure BDA0001954557810000031
Tracing track graph, wherein (a) represents reference speed track, (b) represents speed track obtained by linear time-varying model, and (c) represents speed track obtained by the invention.
Fig. 8 is a graph of pitch rate q-tracking trajectory for a tiltrotor aircraft, where (a) represents a reference velocity trajectory, (b) represents a velocity trajectory obtained by a linear time-varying model, and (c) represents a velocity trajectory obtained by the present invention.
Fig. 9 is a graph of altitude H tracking trajectory for a tiltrotor aircraft, where (a) represents a reference velocity trajectory, (b) represents a velocity trajectory obtained by a linear time-varying model, and (c) represents a velocity trajectory obtained by the present invention.
FIG. 10 is force F along the x-axis for a tiltrotor aircraftxtThe locus graph is shown in the figure, wherein (a) represents a reference speed locus, (b) represents a speed locus obtained by a linear time-varying model, and (c) represents a speed locus obtained by the invention.
FIG. 11 is force F along the y-axis for a tiltrotor aircraftytThe locus graph is shown in the figure, wherein (a) represents a reference speed locus, (b) represents a speed locus obtained by a linear time-varying model, and (c) represents a speed locus obtained by the invention.
FIG. 12 is a pitch moment M for a tiltrotor aircraftzTracing track graph, wherein (a) represents reference speed track, (b) represents speed track obtained by linear time-varying model, and (c) represents speed track obtained by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings in conjunction with specific examples.
The invention avoids the coupling term with other control vectors in a modeling stage by taking the tilting angle of the tilt rotor aircraft as a parameter, and designs the nonlinear time-varying state controller by utilizing the information of the tilting angle. However, the tiltrotor aircraft is a system with nonlinear and strong time-varying characteristics, and the calculation of corresponding solvability conditions is a difficult problem. The method utilizes a technology, namely a square sum technology, which is developed and matured in recent years to convert the stability problem based on the mode conversion stage of the tilt rotor aircraft into a square sum convex optimization problem, and utilizes a tool box (SOStools) in Matlab to solve, so that the calculation difficulty can be effectively overcome.
To this end, the present invention provides a control method based on a mode transition phase of a tiltrotor aircraft, as shown in fig. 1, including the following steps:
step 1: and establishing a longitudinal nonlinear model of the tilt rotor aircraft. The model is as follows:
Figure BDA0001954557810000041
wherein V represents the actual speed of the tiltrotor aircraft,
Figure BDA0001954557810000042
representing the first derivative of the actual speed of the tiltrotor aircraft, alpha representing the actual angle of attack of the tiltrotor aircraft,
Figure BDA0001954557810000043
representing the first derivative of the actual angle of attack of a tiltrotor aircraft,
Figure BDA0001954557810000048
representing the actual pitch angle of the tiltrotor aircraft,
Figure BDA0001954557810000044
representing the first derivative of the actual pitch angle of the tiltrotor aircraft, q representing the actual pitch rate of the tiltrotor aircraft,
Figure BDA0001954557810000045
representing the first derivative of the actual pitch rate of the tiltrotor aircraft, H representing the actual altitude of the tiltrotor aircraft,
Figure BDA0001954557810000046
representing the first derivative of the actual height of the tiltrotor aircraft, m representing the mass of the tiltrotor aircraft, IzRepresenting the moment of inertia of the tiltrotor aircraft about the pitch axis, FxtRepresenting the actual force component along the x-axis of the body, FytRepresenting the actual force component, M, along the y-axis of the bodyzRepresenting the actual pitching moment along the body,
Figure BDA00019545578100000410
the state of the tilt rotor aircraft is shown, and tau (t) shows the tilt angle of the tilt rotor aircraft and shows the longitudinal control surface of the tilt rotor aircraft.
Step 2: and (4) converting the established longitudinal nonlinear model of the tilt rotor aircraft into an error model by considering the problem of trajectory tracking of the tilt rotor aircraft.
Given reference trajectory of tiltrotor aircraft, i.e. given reference speed V of tiltrotor aircraft*Angle of attack alpha*And a pitch angle
Figure BDA0001954557810000049
Pitch angle rate q*And height H*And force along the x-axis of the body
Figure BDA0001954557810000047
Force of y-axis
Figure BDA0001954557810000051
And pitching forceMoment
Figure BDA0001954557810000052
Converting the established longitudinal nonlinear model of the tilt rotor aircraft into an error model:
Figure BDA0001954557810000053
wherein Δ V ═ V-V*，Δα＝α-α*，
Figure BDA00019545578100000513
Δq＝q-q*，ΔH＝H-H*，
Figure BDA0001954557810000054
And step 3: and selecting a proper state variable, and controlling the input variable to convert a longitudinal nonlinear error model of the tilt rotor aircraft into a form of a state space easy to process.
In order to facilitate the design of the nonlinear time-varying state controller, the invention firstly carries out the following processing on a longitudinal nonlinear model of the tilt rotor aircraft.
Selecting a state variable x1＝ΔV，x2＝Δα，
Figure BDA00019545578100000514
x4＝Δq，x5Δ H, and a control input variable u1＝ΔFxt，u2＝ΔFyt，u3＝ΔMz. For ease of calculation, and assuming sin α ≈ α, cos α ≈ 1,
Figure BDA00019545578100000515
and non-polynomial
Figure BDA0001954557810000055
To form a polynomial, i.e.
Figure BDA0001954557810000056
And then converting the longitudinal nonlinear model of the tilt rotor aircraft into a state space form as follows:
Figure BDA0001954557810000057
wherein the content of the first and second substances,
Figure BDA0001954557810000058
Figure BDA0001954557810000059
Figure BDA00019545578100000516
A52＝-V*，A53＝V*，
Figure BDA00019545578100000510
B11＝1/m，B12＝-(α*+Δα)/m，B43＝1/Iz，
Figure BDA00019545578100000511
Figure BDA00019545578100000512
a＝8.791×10-4，b＝-0.03274，c＝0.3491。
Figure BDA0001954557810000061
in the form of a state vector, the state vector,
Figure BDA0001954557810000062
the input vector is controlled.
And 4, step 4: a nonlinear time varying state controller is constructed by assuming that the speed, angle of attack, pitch angle rate and altitude of a tiltrotor aircraft are measurable.
According to the state space equation (3) of the tilt rotor aircraft, a nonlinear time-varying controller in the following form is constructed:
Figure BDA0001954557810000063
wherein the content of the first and second substances,
Figure BDA0001954557810000064
for the gain matrix of the nonlinear time varying control controller to be designed,
Figure BDA0001954557810000065
for the Lyapunov matrix to be solved, x represents the selected state variable,
Figure BDA0001954557810000066
to make the combination of state variables for which the row vector of the corresponding B (x, τ) is 0, J ═ J is defined in the present invention1,j2,j3Is the set of matrices B (x, θ) with corresponding row matrices of 0. τ represents the tilt angle of a tiltrotor aircraft, having N components, written as τ ═ τ1,τ2,…,τN]，
Figure BDA0001954557810000067
For the derivative of the tilting angle of a tiltrotor aircraft with respect to time, corresponding notes
Figure BDA0001954557810000068
And each component has a corresponding upper bound
Figure BDA0001954557810000069
And lower bound iv；
And 5: the design problem of the nonlinear time-varying control controller of the tilt rotor is converted into a square and convex optimization problem to be solved.
Step 5.1: the connection system (3) and the nonlinear time-varying controller (4) form a closed loop system as follows:
Figure BDA00019545578100000610
in the present invention, we need the closed loop system (4) to be locally consistent exponentially stable at x ═ 0. Thus, the design problem of the nonlinear time-varying controller can be translated into solving the unknown gain control
Figure BDA00019545578100000611
And Lyapunov matrix
Figure BDA00019545578100000612
So that the closed loop system (5) is locally consistent and exponentially stable.
Step 5.2: for the closed-loop system (5), selecting a candidate Lyapunov function as follows:
Figure BDA00019545578100000613
the Lyapunov (Lyapunov) function is derived over time to yield:
Figure BDA00019545578100000614
Figure BDA00019545578100000615
where He denotes the sum of its number inside the brackets and its transpose.
Step 5.3: known from the nonlinear time-varying controller (4) and the Lyapunov function (6) by utilizing the Lyapunov stability theorem and the quadratic sum convex optimization theory, in order to reduce the conservatism, the design problem of the nonlinear time-varying controller of the tilt rotor aircraft can be converted into the solution of the following convex optimization inequality by utilizing the S-process:
Figure BDA00019545578100000616
wherein the content of the first and second substances,
Figure BDA0001954557810000071
Figure BDA0001954557810000072
the method comprises the following steps of (1) obtaining a Lyapunov matrix to be solved;
Figure BDA0001954557810000073
a gain matrix of the nonlinear time-varying control controller to be solved; x represents a state variable which is represented by,
Figure BDA0001954557810000074
represents a state variable such that the row vectors of B (x, τ) are all 0, τ represents the tilt angle of the tiltrotor aircraft,
Figure BDA0001954557810000075
representing the derivative of the tilt angle of a tiltrotor aircraft over time;
Figure BDA0001954557810000076
and ivrespectively represent
Figure BDA0001954557810000077
Upper and lower bounds of (a); i represents an adaptive identity matrix; z is a radical of1Representing an adaptive non-zero column vector;1，2and3respectively, represent a given normal number.
Step 6: by solving the convex optimization problem using the tool box (sosools) in Matlab, a controller (4) with stable local consistency indexes can be obtained.
The nonlinear time-varying controller ensures the stability of local consistent index of a closed-loop system, and further realizes the control target of the tilt rotor aircraft in the mode conversion stage.
In order to verify the feasibility and effectiveness of the method, the nonlinear time-varying controller designed by the invention is applied to the control problem of the mode conversion stage of a certain tilt rotor aircraft.
Simulation parameters:1＝10-3，2＝104，3＝10-3initial conditions are as follows: x is the number of0＝[1 0.01 0.01 0.01 0.1]TAs can be understood from fig. 2 to 4, as shown in fig. 2 to 12, the tilt angle tau,
Figure BDA0001954557810000078
and
Figure BDA0001954557810000079
are continuous, it makes sense to use the tilt angle τ as a parameter, and at time t 39s, the tiltrotor aircraft completes the mode of conversion from helicopter to airplane. As is clear from fig. 5-9, for the state variables, although both methods finally converge to the equilibrium point, the method proposed by the present invention can quickly track the reference signal, and has a faster convergence speed. As can be seen from fig. 10-12, the proposed method has smaller input for the input variables. Therefore, the nonlinear time-varying controller provided by the invention can effectively solve the problem of mode conversion of the tilt rotor aircraft and effectively complete the whole flight phase.
The method comprises the steps of firstly establishing a longitudinal nonlinear model of the tilt rotor aircraft, establishing a longitudinal nonlinear error model of the tilt rotor aircraft according to the trajectory tracking information of the tilt rotor aircraft, and converting the longitudinal nonlinear error model of the tilt rotor aircraft into a nonlinear time-varying state space form by selecting appropriate state variables and parameter variables; secondly, constructing a nonlinear time-varying state controller; and finally, the design problem of the controller is converted into a square and convex optimization problem to be solved, so that the control problem of the tilt rotor aircraft in a mode conversion stage is effectively solved.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims (3)

1. A control method based on a mode conversion stage of a tilt rotor aircraft is characterized by specifically comprising the following steps:
step 1, establishing a longitudinal nonlinear model of a tilt rotor aircraft;
step 2, giving a reference track of the tilt rotor aircraft, namely giving the speed, the attack angle, the pitch angle rate and the height of the reference tilt rotor aircraft, and giving the reference force along the x axis of the aircraft body, the force along the y axis and the pitch moment, and converting the established longitudinal nonlinear model of the tilt rotor aircraft into an error model;
step 3, selecting a state variable x and a control input variable u, and converting a longitudinal nonlinear error model of the tilt rotor aircraft into a form of an easily-processed state space; wherein
x＝[(V-V*)T (α-α*)T (θ-θ*)T (q-q*)T (H-H*)T]T
Figure FDA0002758057070000011
Step 4, a nonlinear time-varying control controller is constructed by assuming that the speed, the attack angle, the pitch angle rate and the height of the tilt rotor aircraft can be measured;
and 5, converting the design problem of the nonlinear time-varying control controller of the tilt rotor aircraft into a square and convex optimization problem for solving by utilizing an S-process based on the Lyapunov stability theorem and the square and convex optimization theory, namely:
Figure FDA0002758057070000012
step 6, a control target of a mode conversion stage of the tilt rotor aircraft can be realized by utilizing the solved nonlinear time-varying control controller;
in the above formulae, V and V*Representing the actual and reference speeds of the tiltrotor aircraft, respectively; alpha and alpha*Respectively representing the actual and reference angles of attack of the tiltrotor aircraft; theta and theta*Respectively representing the actual and reference pitch angles of the tiltrotor aircraft; q and q*Representing actual and reference pitch rates of a tiltrotor aircraft, respectively; h and H*Representing the actual and reference altitudes of the tiltrotor aircraft, respectively; fxtAnd
Figure FDA0002758057070000013
representing the actual and reference force components along the x-axis of the body, respectively; fytAnd
Figure FDA0002758057070000014
representing the actual and reference force components along the y-axis of the body, respectively; mzAnd
Figure FDA0002758057070000015
representing the actual and reference pitching moments along the body, respectively; m represents the mass of the tiltrotor aircraft, IzRepresenting the moment of inertia of the tiltrotor aircraft about the pitch axis;
Figure FDA0002758057070000021
Figure FDA0002758057070000022
Figure FDA0002758057070000023
A51＝Δθ-Δα，A52＝-V*，A53＝V*；Aj(x, τ) denotes a j-th row of a (x, τ), j being 1,2, …, 5;
Figure FDA0002758057070000024
B11＝1/m，B12＝-(α*+Δα)/m，B43＝1/Iz，
Figure FDA0002758057070000025
a＝8.791×10-4，b＝-0.03274，c＝0.3491；ΔV＝V-V*，Δα＝α-α*，Δθ＝θ-θ*；
Figure FDA0002758057070000026
the method comprises the following steps of (1) obtaining a Lyapunov matrix to be solved;
Figure FDA0002758057070000027
a gain matrix of the nonlinear time-varying control controller to be solved; x represents a state variable which is represented by,
Figure FDA0002758057070000028
represents a state variable such that all the row vectors of B (x, τ) are 0, τ represents the tilt angle of the tiltrotor aircraft, and τ ═ τ1,τ2,…,τN]；
Figure FDA0002758057070000029
Represents the derivative of the tilt angle of a tiltrotor aircraft over time,
Figure FDA00027580570700000210
Figure FDA00027580570700000211
and viRespectively represent
Figure FDA00027580570700000212
Upper and lower bounds of (a); i represents an adaptive identity matrix; z is a radical of1Representing an adaptive non-zero column vector;1，2and3respectively represent given normal numbers;
2. the method of claim 1 wherein in step 4, a nonlinear time varying state controller is configured.
3. The method for controlling the mode transition phase of a tiltrotor aircraft according to claim 1, wherein in step 5, the square and convex optimization problem is solved by using a tool box sosolols in Matlab.
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