CN106777739B - Solving method for tilt transition process of tilt rotor aircraft - Google Patents
Solving method for tilt transition process of tilt rotor aircraft Download PDFInfo
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Abstract
The invention discloses a solving method for a tilting transition process of a tilting rotor aircraft, which comprises the following steps: 1) establishing a flight dynamic model suitable for calculating a tilting transition process of a tilting rotorcraft; 2) establishing proper boundary conditions, path constraints and performance indexes according to different flight tasks, and converting the tilting transition process of the tilting rotorcraft into a nonlinear dynamic optimal control problem; 3) and (3) solving the nonlinear dynamic optimal control problem in the step 2) by designing a numerical optimization algorithm to obtain the tilting transition process of the tilting rotorcraft. The solving method provided by the invention has the advantages of high calculation efficiency, fast convergence and high reliability of the calculation result, and can be used for researching the optimal tilting transition process of the tilting rotorcraft.
Description
Technical Field
The invention belongs to the technical field of flight mechanics and flight simulation, and particularly relates to a solving method for a tilting transition process of a tilting rotorcraft.
Background
The tilt rotor aircraft is a novel aircraft integrating the characteristics of a helicopter and a fixed-wing aircraft, and has wide application prospect. Tiltrotor aircraft have three flight modes: helicopter mode, fixed wing aircraft mode, and tilt transition mode; in order to meet the requirements of a helicopter mode and a fixed-wing airplane mode, the tilt rotor aircraft has two sets of operation modes of the helicopter and the fixed wing at the same time, and the operation modes are gradually changed along with the change of the tilt angle of the nacelle. Therefore, the tilt rotor aircraft has the problem of operation redundancy in the tilt transition process, and the operation of a driver becomes very complicated; in addition, the entire tilt transition process must be guaranteed to be completed in the tilt corridor because too low forward flight speeds can cause the tilt rotor wing to stall, and too high forward flight speeds can be limited by the rotor forward blade compressibility, the rotor aft blade stall, and the available power of the rotor. It can be seen that the tilting transition process of the tilting rotorcraft is an extremely important and complex flight process, how to solve the problem of operation redundancy and successfully complete the mutual conversion between the helicopter mode and the fixed-wing aircraft mode is an important subject of domestic and foreign research.
At present, a control method for tilt transition of a tilt rotor aircraft mainly focuses on presetting a control scheme to solve the problem of control redundancy, and a control system is designed to track a preset command (a tilt rule, a flight path and the like), so that an optimal control strategy and a flight path under different flight tasks cannot be obtained. In fact, the optimal tilting transition process of the tilting rotorcraft is researched, a corresponding optimal operation strategy, a flight track and the like are obtained, the problem of operation redundancy can be solved, the working load of a driver can be effectively reduced, the tilting transition efficiency is improved, the posture of the aircraft body is stabilized, the design of a tilting transition system is facilitated, and therefore the optimal tilting transition process of the tilting rotorcraft is necessary to be researched.
Disclosure of Invention
In view of the above disadvantages of the prior art, an object of the present invention is to provide a method for solving a tilt transition process of a tilt-rotor aircraft, so as to solve the problem that the prior art cannot obtain an optimal operation strategy and flight trajectory of the tilt-rotor aircraft under different flight tasks.
In order to achieve the purpose, the invention discloses a solving method of a tilting transition process of a tilting rotor aircraft, which comprises the following steps:
1) establishing a flight dynamic model suitable for calculating a tilting transition process of a tilting rotorcraft;
2) establishing proper boundary conditions, path constraints and performance indexes according to different flight tasks, and converting the tilting transition process of the tilting rotorcraft into a nonlinear dynamic optimal control problem;
3) and (3) solving the nonlinear dynamic optimal control problem in the step 2) by designing a numerical optimization algorithm to obtain the tilting transition process of the tilting rotorcraft.
Preferably, the model in step 1) can take the limit of the characteristic of the steering system on the change speed of the steering quantity into consideration during the solving process of the tilting transition, and can avoid jump discontinuity during the numerical solving process.
Preferably, the mold in the step 1) above comprises: basic nonlinear flight dynamics model, mixed manipulation equation and control quantity differential equation.
Preferably, the hybrid steering equation is:
preferably, the differential equation of the control amount is:
taking into account the limit of the characteristics of the steering system on the speed of change of the steering variables, and at the same time avoiding the occurrence of jump discontinuities or the form of bang-bang type control of the steering variables during the optimization, use is made ofcol、lon、lat、pedAndinas a control quantity, andcol、lon、lat、pedandinas new state variables:
preferably, the performance index in step 2) is specifically:
wherein the content of the first and second substances,
in the formula wt,w1,w2,w3,w4,w5The weighting factor is constant, and the greater the weighting factor is, the more important the corresponding item is; in the tilting transition process, a driver tilts the engine nacelle at a fixed angular speed through a thumb roller and focuses on controlling the collective pitch rod and the longitudinal rod; in addition, the change of pitch angle rate and pitch angle is also paid attention to in the tilting transition process, so each proportion is different, and the weight coefficient is given as: w is at＝1.0,w1＝2.0,w2＝2.0,w3＝1.0,w4＝1.5,w5＝1.5。
Preferably, the path constraint in step 2) is specifically: in order to keep the altitude within an acceptable range, certain limits are imposed on the altitude change according to different flight mission requirements in the path constraint; furthermore, pitch attitude angles and angular rates are also limited in path constraints:
determining path constraint by using a tilting angle-speed envelope analysis method of the nacelle of the tilt rotor aircraft, so that a tilting transition process is kept in the tilting angle-speed envelope of the nacelle;
in the whole transition process that verts, driver's manipulation speed is according to the booster speed limit of the rotorcraft that verts that corresponds the model and confirms:
preferably, the boundary conditions in step 2) are specifically: optimizing an initial boundary condition to be the current flight state of the aircraft by the operating strategy; the end boundary conditions are set to the target tilt angle and the forward flight speed, namely:
wherein intFor the target nacelle tilt angle,
the specific value is determined according to the flight mission requirement for the target forward flight speed.
Preferably, the numerical optimization algorithm in step 3) is specifically: solving by adopting a direct conversion method and a sequence quadratic programming algorithm;
when numerical calculation is carried out, firstly, dimensionless scaling is carried out on parameters in a flight dynamics model;
defining a constant k1，k2，k3，k4Dimensionless scaling of state quantities, control quantities and time:
dimensionless scaling of length, mass, aerodynamic force and aerodynamic moment is as follows:
in order to make the dimensionless scaled state variable and control variable size approach 1, k is taken1＝k2＝100,k3＝1,k4＝0.01；
The dimensionless scaled flight dynamics equation of state is expressed as:
equally dividing dimensionless τ of time into N-1 time segments:
dispersing the state variable and the control variable in the continuous space by using a direct conversion method to obtain a design variable of a nonlinear programming problem;
the discretized design variables are:
wherein:
τmk＝(τk+τk+1)/2
dispersing a differential equation in the nonlinear dynamic optimal control problem to obtain the following defect equation constraint equation:
wherein:
dispersing the performance indexes to obtain:
the boundary conditions act on the last node:
path constraints are applied to each time segment node and intermediate node:
after the nonlinear dynamic optimal control problem is converted into a nonlinear programming problem, solving the nonlinear programming problem by applying a sequential quadratic programming algorithm to obtain an optimal solution; and performing Hermite interpolation on the state variables and the control variables at all nodes in the optimal solution for 3 times in a segmented mode to obtain the rod quantity change, the tilting rule and the flight track.
The invention has the beneficial effects that:
(1) the invention can obtain the optimal tilting transition process of the tilting rotorcraft according to different flight task requirements, and can obtain the optimal operation strategy and flight path while solving the problem of operation redundancy, thereby effectively reducing the work load of a driver, improving the tilting transition efficiency, stabilizing the posture of the aircraft body, and providing certain reference for the driver and a designer. The prior control method for the tilting transition of the tilt rotor aircraft cannot obtain the optimal control strategy and flight path under different flight tasks.
(2) The solving method provided by the invention has the advantages of high calculation efficiency, fast convergence and high reliability of the calculation result, and can be used for researching the optimal tilting transition process of the tilting rotorcraft.
Drawings
FIG. 1 is a flow chart of the steps of the present invention;
FIG. 2a is a schematic diagram of comparison between a calculated trim state for establishing a flight dynamics model and power data required by a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 90 degrees, and flaperon is configured to be 40 degrees/25 degrees;
FIG. 2b is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model and pitch attitude angle data of a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 90 degrees, and flaperon is configured to be 40 degrees/25 degrees;
FIG. 2c is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model and total pitch data of a propeller root in a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 90 degrees, and flaperon is configured to be 40 degrees/25 degrees;
FIG. 2d is a schematic diagram showing comparison between a calculated trim state for establishing a flight dynamics model and flight test total pitch rod data, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 90 degrees, and flaperon is configured to be 40 degrees/25 degrees;
FIG. 2e is a schematic diagram showing comparison between a calculated trim state of the flight dynamics model and flight test longitudinal period variable pitch rod data, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 90 degrees, and flaperon is configured to be 40 degrees/25 degrees;
FIG. 3a is a schematic diagram of comparison between a calculated trim state for establishing a flight dynamics model and power demand data of a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 60 degrees, and flaperon configuration is 20 degrees/12.5 degrees;
FIG. 3b is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model and pitch attitude angle data of a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 60 degrees, and flaperon is configured to be 20 degrees/12.5 degrees;
FIG. 3c is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model established by the invention and total pitch data of a propeller root of a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 60 degrees, and flaperon is configured to be 20 degrees/12.5 degrees;
FIG. 3d is a schematic diagram showing comparison between a calculated trim state and flight test collective pitch rod data of a flight dynamics model established by the invention, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 60 degrees, and flaperon is configured to be 20 degrees/12.5 degrees;
FIG. 3e is a schematic diagram showing comparison between a calculated trim state of the flight dynamics model and flight test longitudinal period variable pitch rod data, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 60 degrees, and flaperon configuration is 20 degrees/12.5 degrees;
FIG. 4a is a schematic diagram of comparison between a calculated trim state for establishing a flight dynamics model and power data required by a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 0 degree, and flaperon configuration is 0 degree/0 degree;
FIG. 4b is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model and pitch attitude angle data of a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 0 degree, and flaperon configuration is 0 degree/0 degree;
FIG. 4c is a schematic diagram showing comparison between a calculated trim state of a flight dynamics model and total pitch data of a propeller root in a flight test, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 0 degree, and flaperon configuration is 0 degree/0 degree;
FIG. 4d is a schematic diagram showing comparison between a calculated trim state for establishing a flight dynamics model and flight test total pitch rod data, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 0 degree, and flaperon configuration is 0 degree/0 degree;
FIG. 4e is a schematic diagram showing comparison between a calculated trim state of the flight dynamics model and flight test longitudinal period variable pitch rod data, wherein the model is XV-15, the weight is 5897kg, the rotating speed is 589rpm, the tilting angle of an engine nacelle is 0 degree, and flaperon configuration is 0 degree/0 degree;
FIG. 5 is a schematic diagram of the principle of the direct conversion method;
FIG. 6a is a schematic diagram of the comparison of the calculated forward tilt transition process with the altitude in the pilot flight simulation data according to the present invention;
FIG. 6b is a schematic diagram of the calculated forward tilt transition process of the present invention compared with the forward flight speed in the pilot flight simulation data;
FIG. 6c is a graphical illustration of a calculated data comparison of the rate of descent for a forward tilt transition in accordance with the present invention with pilot flight simulation data;
FIG. 6d is a schematic diagram of the data comparison of the pitch attitude angle in the forward tilt transition process and the pilot flight simulation data calculated in accordance with the present invention;
FIG. 6e is a schematic diagram of the calculated forward tilt transition process of the present invention compared to the data of the nacelle tilt angle in the pilot flight simulation data;
FIG. 6f is a schematic diagram of the calculated forward tilt transition process of the present invention compared to longitudinal cyclic pitch stick data in pilot flight simulation data;
FIG. 6g is a schematic diagram of the calculated data comparison of the collective pitch mast during the forward tilting transition process and the pilot flight simulation data according to the present invention;
FIG. 7a is a graphical illustration of a comparison of calculated reverse tilt transition process of the present invention with altitude data from pilot flight simulation data;
FIG. 7b is a graphical illustration of a comparison of calculated reverse tilt transition process of the present invention with forward flight velocity data from pilot flight simulation data;
FIG. 7c is a graphical illustration of a calculated reverse tilt transition process of the present invention versus a data comparison of descent rate in pilot flight simulation data;
FIG. 7d is a graphical illustration of a comparison of pitch attitude angle data in the calculated reverse tilt transition process of the present invention and the pilot flight simulation data;
FIG. 7e is a graphical illustration of a comparison of calculated inverse tilt transition process of the present invention and the engine nacelle tilt angle data in the pilot flight simulation data;
FIG. 7f is a graphical illustration of a comparison of longitudinal cyclic pitch bars in the calculated reverse tilt transition process of the present invention with pilot flight simulation data;
fig. 7g is a schematic diagram comparing the calculated reverse tilt transition process with the collective pitch stick data in the pilot flight simulation data according to the present invention.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the method for solving the tilt transition process of the tilt rotor aircraft according to the present invention includes the following steps:
1) establishing a flight dynamics model suitable for calculating the tilting transition process of the tilting rotorcraft, wherein the model can consider the limitation of the characteristics of a control system on the change speed of the control quantity in the tilting transition solving process and can avoid discontinuous jump in the numerical solving process;
2) establishing proper boundary conditions, path constraints and performance indexes according to different flight tasks, and converting the tilting transition process of the tilting rotorcraft into a nonlinear dynamic optimal control problem;
3) and (3) solving the nonlinear dynamic optimal control problem in the step 2) by designing a numerical optimization algorithm to obtain the tilting transition process of the tilting rotorcraft.
The method is suitable for calculating the flight dynamics model of the tilt transition process of the tilt rotor aircraft, and comprises the following three parts: basic nonlinear flight dynamics models, hybrid steering equations and controlled variable differential equations.
The basic nonlinear flight dynamics model is expressed in the form of the following first order differential equation:
state quantity x in modelbControl amount ubRespectively as follows:
xb＝[u,v,w,p,q,r,φ,θ,ψ,x,y,h]T
ub＝[θ0,r,θ0,l,θc,r,θc,l,θs,r,θs,l,in,θa,θe,θr]T
wherein the state quantities u, v, w are the speeds corresponding to the three directions of the body axis respectively, p, q, r are the angular speeds corresponding to the three directions of the body axis respectively,
the angle is a rolling angle, theta is a pitch angle, psi is a yaw angle, x is horizontal displacement of the aircraft, y is lateral displacement of the aircraft, and h is sea level height of the aircraft; manipulated variable theta0,r,θ0,lTotal distance theta between right and left rotorsc,r,θc,lRespectively, the transverse cyclic variation of the right and left rotors, thetas,r,θs,lLongitudinal cyclic variation, i, of right and left rotors, respectivelynCabin tilting angle given to the driver, thetaaFor flap angle, θeFor elevator deflection angle, thetarIs the rudder deflection angle.
In the embodiment, the XV-15 tilt rotorcraft is taken as a prototype, mathematical modeling is carried out on each part, and a programming language Fortran is utilized to build a nonlinear mathematical model of the basic tilt rotorcraft.
On the basis, the information of the control lever amount of the driver is introduced, and a hybrid control equation suitable for all flight modes of the XV-15 tilt rotor aircraft is established:
whereincolIs a driver tension bar (from bottom to top 0-1),lonis a longitudinal rod (from back to front-1 to 1) for a driver,latis a transverse rod (from left to right-1 to 1) for a driver,pedfor the driver to pedal (from left to right-1 ~ 1),inis a thumb roller (0-95 degrees) of a driver; coefficient of manipulated variable
And the compensation amount thetagAndB1the method comprises the steps that the method is obtained by looking up an XV-15 tilt rotor aircraft parameter design table; the hybrid maneuver equations reduce the 10 maneuvers in the original basic flight dynamics model to 5, which results in both reduced maneuver variables and driver maneuver information.
Differential equation of control amount:
taking into account the limit of the characteristics of the steering system on the speed of change of the steering variables, and at the same time avoiding the occurrence of jump discontinuities or the form of bang-bang type control of the steering variables during the optimization, use is made ofcol、lon、lat、pedAndinas a control quantity, andcol、lon、lat、pedandinas new state variables:
integrating a basic nonlinear flight dynamics model, a mixed operation equation and a control quantity differential equation in Fortran to obtain a flight dynamics model suitable for calculating the tilting transition process of the tilting rotor aircraft; the tiltrotor aircraft has a longitudinally symmetrical configuration, the tilting transition process is on a longitudinal plane, in order to improve the calculation efficiency of the solving method, the state quantity and the control quantity in the model are further simplified under the condition of no crosswind, and the state space form is as follows:
wherein the state quantity x and the controlled quantity u are respectively:
x＝[u,w,q,θ,x,h,col,lon,in]T
u＝[uc,us,un]T。
in order to verify the accurate determination of the established mathematical model of the XV-15 tilt rotor aircraft and carry out balancing verification on the mathematical model, as can be seen from the attached drawings of 2a-2e, 3a-3e and 4a-4e, the calculation result is well matched with the flight test data of the XV-15 tilt rotor aircraft under the same configuration, which shows that the established flight dynamics model is more accurate and can be used for researching the optimal tilt transition process of the tilt rotor aircraft.
When tiltrotor aircraft began to tilt the transition in this embodiment, the aircraft was in stable flight state, and the equilibrium state of consequently calculating can provide initial value for tiltrotor aircraft's the transition of tilting optimization.
The tilting problem of the tilt rotor aircraft in the tilting transition process is described as follows: an optimal operation strategy is found out from a class of allowable tilting transition operation strategies, so that the performance index of evaluating the quality of the motion process is optimal while the tilting rotorcraft tilts from an initial state mode to a specified target state mode under the action of the operation strategy. In the whole tilting process, the motion, the operation strategy and the performance index of the aircraft are all functions of time and space, so that the tilting transition problem of the tilting rotorcraft can be summarized into a nonlinear dynamic optimal control problem containing state and control constraint. The nonlinear dynamic optimal control problem comprises three parts of performance indexes, boundary conditions and path constraints.
The performance indexes are specifically as follows: in the tilting transition process of the tilting rotorcraft, the tension direction of a rotor and the gravity center of the whole aircraft can change, so that the pitching attitude changes greatly, and the attitude needs to be stabilized by a driver through proper operation, so that the performance index needs to consider the control of the pitching attitude; in addition, the time required for the tilting transition process and the workload of the driver should also be taken into account, so the performance index is defined as:
wherein the content of the first and second substances,
in the formula wt,w1,w2,w3,w4,w5The weighting factor is constant, and the greater the weighting factor is, the more important the corresponding item is; in the tilting transition process, a driver tilts the engine nacelle at a fixed angular speed through a thumb roller and focuses on controlling the collective pitch rod and the longitudinal rod; besides, the change of pitch angle rate and pitch angle is also concerned in the tilting transition process, so the proportion of each item is different, and the weight coefficient is determined as: w is at＝1.0,w1＝2.0,w2＝2.0,w3＝1.0,w4＝1.5,w5＝1.5。
In order to make the driver focus on the steering with a stable posture and thus reduce the steering difficulty, the performance index temporarily does not consider the control of the trajectory (height control in the longitudinal plane). Regarding the height change in the tilting transition process, the height change can be restrained according to different flight mission requirements in the path restraint, and the height change can be kept within an acceptable range.
Boundary conditions: optimizing an initial boundary condition to be the current flight state of the aircraft by the operating strategy; for convenience of study, the tip end boundary conditions were set to the target tilt angle and forward flight velocity, i.e.:
wherein intFor the target nacelle tilt angle,
the specific value is determined according to the flight mission requirement for the target forward flight speed.
And (3) path constraint: in order to keep the altitude within an acceptable range, certain limits can be imposed on the altitude change according to different flight mission requirements in the path constraint; in addition, pitch attitude angles and angular rates are also limited in path constraints;
determining path constraint by using a tilting angle-speed envelope analysis method of the nacelle of the tilt rotor aircraft, so that a tilting transition process is kept in the tilting angle-speed envelope of the nacelle;
when the low-speed tilting is carried out, the lift force provided by the wing is limited by the critical stalling attack angle of the wing, so that when the low-speed section is in the tilting envelope line, the wing attack angle is at the critical attack angle of the wing, and at the moment, the following relations are met:
αw＝αwc＝iw+αf
wherein alpha iswAngle of attack of wing, αwcIs the critical angle of attack, i, of the wingwIs the wing angle of incidence, alphafIs the angle of attack of the fuselage; the inequality path constraint determined by the tilting angle-speed envelope of the nacelle at the low-speed section is as follows:
αwcmin≤αw≤αwcmax
αwcminand alphawcmaxFrom the blowing data of tiltrotor aircraft, in the examples XV-15 was taken as a model, at-20 and 12 respectively.
The maximum forward flying speed during the tilting process is limited by the compression performance of the forward blades and the stall effect of the backward blades of the rotor, the available power and the dynamic stability of the rotor, and the limitation of the available power of the rotor is the most basic and important limiting element. Therefore, when the rotor is in a tilting envelope line at a high-speed section, the total required power of the rotor reaches the rated power output by the engine.
Power factor required by rotor wing CPComprises the following steps:
wherein C isTIs the coefficient of rotor drag, obtained from a flight dynamics model, KindTo induce a velocity correction factor (1.15), fGIs ground effect factor (1.0), viFor dimensionless induced velocity, obtained from a flight dynamics model, σ is rotor solidity (XV-15 is 0.089), cdIs the rotor blade drag coefficient (0.015); the total power demand of the tiltrotor aircraft is then expressed as:
wherein etapIs the transmission power loss (0.95).
The inequality path constraint determined by the tilting angle-speed envelope of the high-speed section engine nacelle is as follows:
0≤Pr≤Pcr
wherein P iscrRated power for tiltrotor aircraft engine output (XV-15 tiltrotor aircraft engine output rated power of 1737.5 kw); in order to further ensure the flight safety in the tilting transition process, the speed corresponding to the tilting angle of 45 degrees of the engine nacelle on the tilting envelope line of the high-speed section is taken as the stopping speed, and the flight speed in the tilting process cannot be greater than the stopping speed VstopThe stopping speed of the XV-15 tiltrotor aircraft is 88 m/s.
Vmax≤Vstop
During the entire tilt transition, the driver's steering rate can be determined from the booster rate limit of the XV-15 tilt rotorcraft:
the designed numerical optimization algorithm specifically comprises the following steps: the state and the control variable of the nonlinear dynamic optimal control problem corresponding to the tilting transition process of the tilting rotorcraft are numerous, and the constraint and the objective function are very complex, so that the analytic solution is not feasible and the solution needs to be carried out through a numerical optimization algorithm; solving by adopting a direct conversion method and a sequence quadratic programming algorithm;
when numerical calculation is carried out, firstly, dimensionless scaling is carried out on parameters in a flight dynamics model;
defining a constant k1，k2，k3，k4Dimensionless scaling of state quantities, control quantities and time:
dimensionless scaling of length, mass, aerodynamic force and aerodynamic moment is as follows:
in order to make the dimensionless scaled state variable and control variable size approach 1, k is taken1＝k2＝100,k3＝1,k4＝0.01；
The dimensionless scaled flight dynamics equation of state is expressed as:
equally dividing dimensionless τ of time into N-1 time segments:
dispersing the state variables and the control variables in the continuous space by using a direct conversion method to obtain the design variables of the nonlinear programming problem, wherein the principle is shown in figure 5;
the discretized design variables are:
wherein:
τmk＝(τk+τk+1)/2
and (3) dispersing a differential equation in the nonlinear dynamic optimal control problem by using a Hermite-Simpson method to obtain the following defect equation constraint equation:
wherein:
dispersing the performance indexes to obtain:
the boundary conditions act on the last node:
path constraints are applied to each time segment node and intermediate node:
after the nonlinear dynamic optimal control problem is converted into a nonlinear programming problem, solving the nonlinear programming problem by applying a sequential quadratic programming algorithm to obtain an optimal solution; the nonlinear programming problem with a large number of design variables and constraint equations can be well solved by the sequential quadratic programming algorithm; and finally, carrying out Hermite interpolation on the state variables and the control variables at all nodes in the optimal solution for 3 times in a segmented mode to obtain smoother rod quantity change, tilting rule and flight trajectory.
The solving method of the tilting transition process of the tilting rotorcraft provided by the invention is utilized to simulate the forward and reverse most tilting transition processes of the tilting rotorcraft, and is compared with flight simulation data of a driver, wherein the flight simulation data of the driver is obtained by performing a tilting transition flight simulation experiment in XV-15 tilting rotorcraft flight simulation equipment by the driver, and the driver can automatically determine the optimal operation strategy and the corresponding flight track in the tilting transition process according to the current flight task without tracking the preset flight track and operation scheme, so that the method is suitable for being compared with the tilting transition process obtained by the invention. The model parameters used for the driver simulation are consistent with the model machine adopted in the embodiment.
Positive tilting transition
By taking the case that the XV-15 tilt rotorcraft continuously tilts forwards from a helicopter mode to a fixed wing airplane mode, the solution method is utilized to optimize the control strategy, and the control strategy is compared with the flight simulation result of a driver. The initial state when the driver makes a forward tilting transition is as follows: speed 32m/s, altitude 88m, track angle 7 deg., at which the aircraft is in a stable flight. The mission requires the pilot to decide on his own the optimal maneuver, allowing altitude changes, and the speed remains 65m/s after the end of the roll.
According to the current flight mission, the target engine nacelle tilts by an angle intIs 0 DEG, target forward flight speed
For 65m/s, the height range in the path constraint is defined as:
80m≤h(t)≤150m
as shown in fig. 6a-6g, it can be seen that the nacelle is tilted directly to fixed wing aircraft mode at an angular velocity of 6.5 °/s, during which the pilot slowly increases collective rod displacement and pushes the rod forward, the forward flight velocity increases, and then the aft drag rod stabilizes the attitude. The whole operation strategy of the forward tilting transition process is easy to realize, and the change of the flight state quantity is stable. The calculation result of the invention is closer to the flight simulation result of the driver, and the change of the pitch angle is more stable.
Reverse tilt transition
By taking the example that the XV-15 tilting rotorcraft continuously tilts reversely from a fixed wing airplane mode to a helicopter mode, the solution method provided by the invention is utilized to optimize the control strategy, and the control strategy is compared with the flight simulation result of a driver. The initial state when the driver makes the reverse tilting transition is as follows: the speed is 62m/s, the altitude is 120m, the flight path angle is-2 degrees, the aircraft is in a stable flight state, and the flight mission requires a driver to determine the optimal control strategy and flight path by himself, and finally the aircraft needs to land.
The reverse tilt transition generally involves the deceleration landing process of the tilt rotor aircraft, and in order to meet the requirements of airworthiness regulations on safe landing, the following modifications need to be made to the terminal boundary conditions and path constraints of the nonlinear dynamic optimal control problem:
as shown in fig. 7a-7g, it can be seen that the nacelle is tilted directly to helicopter-airplane mode at an angular velocity of-6.5 °/s, the rotor tension is gradually increased, the pilot increases the collective pitch and pulls the aft link, the pitch angle is increased, and the forward flying velocity is gradually decreased; after tilting to the helicopter mode, the pilot continues to operate the collective pitch lever and the longitudinal cyclic pitch lever to make the aircraft land safely. Compared with the flight simulation result of a driver, the time history of the flight state quantity calculated by the method is better matched with the literature, the change of the descent rate and the pitch angle is more stable, and the change of the total distance rod is softer.
Through the comparison, the solving method can be used for researching the tilting transition process of the tilting rotorcraft, and obtaining the corresponding optimal operation strategy and flight path, so that certain reference is provided for drivers and designers.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.
Claims (2)
1. A method for solving the tilting transition process of a tilting rotor aircraft is characterized by comprising the following steps:
1) establishing a flight dynamic model suitable for calculating a tilting transition process of a tilting rotorcraft; the model takes the operating quantity of the tension lever of the driver into account in the establishing processcolAnd un；
2) Establishing proper boundary conditions, path constraints and performance indexes according to different flight tasks, flight attitudes, flight times and working loads of drivers, and converting the tilting transition process of the tilt rotor aircraft into a nonlinear dynamic optimal control problem;
3) designing a numerical optimization algorithm to solve the nonlinear dynamic optimal control problem in the step 2) to obtain a tilting transition process of the tilting rotorcraft;
in the step 1), the model can consider the limit of the characteristics of the control system to the change speed of the control quantity in the process of the tilting transition solving, and can avoid discontinuous jump in the process of numerical solving;
the model in the step 1) comprises: a basic nonlinear flight dynamics model, a hybrid manipulation equation and a controlled variable differential equation;
the hybrid operating equation described above is:
the differential equation of the controlled variable is:
taking into account the limit of the characteristics of the steering system on the speed of change of the steering variables, and at the same time avoiding the occurrence of jump discontinuities or the form of bang-bang type control of the steering variables during the optimization, use is made ofcol、lon、lat、pedAndinas a control quantity, andcol、lon、lat、pedandinas new state variables:
the performance indexes in the step 2) are specifically as follows:
wherein the content of the first and second substances,
in the formula，wt,w1,w2,w3,w4,w5The weighting factor is constant, and the greater the weighting factor is, the more important the corresponding item is; in the tilting transition process, a driver tilts the engine nacelle at a fixed angular speed through a thumb roller and focuses on controlling the collective pitch rod and the longitudinal rod; in addition, the change of pitch angle rate and pitch angle is also paid attention to in the tilting transition process, so each proportion is different, and the weight coefficient is given as: w is at＝1.0,w1＝2.0,w2＝2.0,w3＝1.0,w4＝1.5,w5＝1.5；
The path constraint in the step 2) is specifically as follows: in order to keep the altitude within an acceptable range, certain limits are imposed on the altitude change according to different flight mission requirements in the path constraint; pitch attitude angle and angular rate are also limited in the path constraints:
determining path constraint by using a tilting angle-speed envelope analysis method of the nacelle of the tilt rotor aircraft, so that a tilting transition process is kept in the tilting angle-speed envelope of the nacelle;
in the whole transition process that verts, driver's manipulation speed is according to the booster speed limit of the rotorcraft that verts that corresponds the model and confirms:
the boundary conditions in the step 2) are specifically: optimizing an initial boundary condition to be the current flight state of the aircraft by the operating strategy; the end boundary conditions are set to the target tilt angle and the forward flight speed, namely:
wherein intFor the target nacelle tilt angle,
the specific value is determined according to the flight mission requirement for the target forward flight speed.
2. The method for solving the tilt transition process of the tiltrotor aircraft according to claim 1, wherein the numerical optimization algorithm in step 3) is specifically: solving by adopting a direct conversion method and a sequence quadratic programming algorithm;
when numerical calculation is carried out, firstly, dimensionless scaling is carried out on parameters in a flight dynamics model;
defining a constant k1，k2，k3，k4Dimensionless scaling of state quantities, control quantities and time:
dimensionless scaling of length, mass, aerodynamic force and aerodynamic moment is as follows:
in order to make the dimensionless scaled state variable and control variable size approach 1, k is taken1＝k2＝100,k3＝1,k4＝0.01；
The dimensionless scaled flight dynamics equation of state is expressed as:
equally dividing dimensionless τ of time into N-1 time segments:
dispersing the state variable and the control variable in the continuous space by using a direct conversion method to obtain a design variable of a nonlinear programming problem;
the discretized design variables are:
wherein:
τmk＝(τk+τk+1)/2
dispersing a differential equation in the nonlinear dynamic optimal control problem to obtain the following defect equation constraint equation:
wherein:
dispersing the performance indexes to obtain:
the boundary conditions act on the last node:
path constraints are applied to each time segment node and intermediate node:
after the nonlinear dynamic optimal control problem is converted into a nonlinear programming problem, solving the nonlinear programming problem by applying a sequential quadratic programming algorithm to obtain an optimal solution; and performing Hermite interpolation on the state variables and the control variables at all nodes in the optimal solution for 3 times in a segmented mode to obtain the rod quantity change, the tilting rule and the flight track.
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| CN107688705A (en) * | 2017-08-25 | 2018-02-13 | 哈尔滨工业大学 | The axial induced velocity computational methods in the rotor system induction flow field based on finite state |
| CN107992080B (en) * | 2017-12-25 | 2020-12-15 | 成都纵横自动化技术股份有限公司 | Control distribution method and device and multi-rotor aircraft |
| CN108052008B (en) * | 2018-01-10 | 2020-04-07 | 大连理工大学 | Geometric optimal controller design method for transition state switching process of tilt rotor aircraft |
| CN108445895B (en) * | 2018-02-05 | 2021-01-29 | 天津大学 | Robust control method for position control of tilting type three-rotor unmanned aerial vehicle |
| CN109143854A (en) * | 2018-07-27 | 2019-01-04 | 南京航空航天大学 | It is a kind of solve helicopter tail rotor clamping stagnation after safe landing procedures numerical value emulation method |
| CN109946971B (en) * | 2019-04-04 | 2021-09-24 | 南京航空航天大学 | Smooth switching control method for transition section of tilt rotor unmanned aerial vehicle |
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| CN111948940B (en) * | 2020-07-10 | 2021-05-04 | 北京航空航天大学 | Trajectory optimization method of tilt rotor unmanned aerial vehicle based on dynamic optimal control |
| CN111897207B (en) * | 2020-08-13 | 2023-11-14 | 北京中科宇航技术有限公司 | Quick attitude maneuver control method suitable for saturation of actuating mechanism |
| CN114415710A (en) * | 2021-12-02 | 2022-04-29 | 北京电子工程总体研究所 | Tilting path optimization method of tilting rotor aircraft and readable storage medium |
| CN114323551B (en) * | 2022-03-15 | 2022-05-13 | 中国空气动力研究与发展中心低速空气动力研究所 | Tilting transition corridor wind tunnel experiment balancing method and system for tilting rotorcraft |
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