CN106777739A - A kind of tiltrotor is verted the method for solving of transient process - Google Patents

Abstract

A kind of method for solving of transient process of being verted the invention discloses tiltrotor, including：1）Set up the flight dynamics model of transient process of being verted suitable for calculating tiltrotor；2）Suitable boundary condition, path constraint and performance indications are set up according to different aerial missions, the transient process of verting of tiltrotor is converted into Nonlinear Dynamic optimal control problem；3）Design value optimized algorithm is to step 2）In Nonlinear Dynamic optimal control problem solved, obtain the transient process of verting of tiltrotor.Method for solving computational efficiency proposed by the present invention is high, and convergence is fast, and result of calculation is with a high credibility, can be used to study the optimal transient process of verting of tiltrotor.

Description

A kind of tiltrotor is verted the method for solving of transient process

Technical field

The invention belongs to flight mechanics and flight simulation technology field, refer specifically to be verted for a kind of tiltrotor and tide over The method for solving of journey.

Background technology

Tiltrotor is a kind of course of new aircraft that helicopter and fixed wing aircraft feature combine together, with extensive Application prospect.Tiltrotor has three kinds of offline mode：Helicopter mode, fixed wing aircraft pattern and the stage die that verts Formula；In order to meet the requirement of helicopter mode and fixed wing aircraft pattern, tiltrotor has helicopter and fixed-wing simultaneously Two sets of maneuverability patterns, and gradually changed with the change of engine nacelle tilt angle.Therefore tiltrotor is in transition of verting During manipulation redundancy issue occurs, pilot control can become sufficiently complex；In addition, transient process of entirely verting is also Must assure that and completed in corridor of verting, because too low forward flight speed can cause tiltrotor wing stall, it is too high Forward flight speed can then be limited by rotor advancing blade compressibility, retreating blade stall and rotor available horsepower.Can be with Find out, the transient process of verting of tiltrotor is particularly important and complicated flight course how to solve to manipulate redundancy issue, And the mutual conversion between helicopter mode and fixed wing aircraft pattern is smoothly completed, it is the important topic of domestic and international research.

It is concentrated mainly on and presets manipulation schemes to solve on the vert control method of transition of tiltrotor at present Redundancy issue is manipulated, and designs control system and tracked on predetermined instruction (rule of verting, flight path etc.), therefore cannot obtained Optimal Handling Strategy and flight path under different aerial missions.In fact, optimal the verting of research tiltrotor is tided over Journey, obtains corresponding optimal Handling Strategy and flight path etc., can not only solve to manipulate redundancy issue, moreover it is possible to effectively reduce and drive The person's of sailing live load, raising vert crossing efficiency, stabilization body attitude, the design of the transition system that is conducive to verting, therefore have must The optimal transient process of verting of tiltrotor is studied.

The content of the invention

Above-mentioned the deficiencies in the prior art are directed to, were verted it is an object of the invention to provide a kind of tiltrotor and tided over The method for solving of journey, to solve that optimal Handling Strategy of the tiltrotor under different aerial missions cannot be obtained in the prior art And flight path.

To reach above-mentioned purpose, the present invention discloses a kind of tiltrotor and verts the method for solving of transient process, including step It is rapid as follows：

1) flight dynamics model of transient process of being verted suitable for calculating tiltrotor is set up；

2) suitable boundary condition, path constraint and performance indications are set up according to different aerial missions, by tilting rotor The transient process of verting of machine is converted into Nonlinear Dynamic optimal control problem；

3) design value optimized algorithm is to step 2) in Nonlinear Dynamic optimal control problem solve, verted The transient process of verting of gyroplane.

Preferably, above-mentioned steps 1) in model in transition solution procedure of verting it is contemplated that steerable system characteristic to behaviour The limitation of vertical amount pace of change, moreover it is possible to avoid occurring during numerical solution jump discontinuously.

Preferably, above-mentioned steps 1) in model include：Basic nonlinear flight dynamics model, mixing manipulates equation and control The amount differential equation processed.

Preferably, above-mentioned mixing manipulates equation：

Preferably, the above-mentioned controlled quentity controlled variable differential equation is：

Limitation in view of steerable system characteristic to manipulated variable pace of change, while in order to avoid manipulated variable is in optimization process It is middle jump occur discontinuously or the form of bang-bang types control, use δ_col、δ_lon、δ_lat、δ_pedAnd δ_inFirst derivative make It is controlled quentity controlled variable, and δ_col、δ_lon、δ_lat、δ_pedAnd δ_inAs new state variable：

Preferably, above-mentioned steps 2) in performance indications be specially：

Wherein,

W in formula_t,w₁,w₂,w₃,w₄,w₅It is the constant-weight factor, weight coefficient is bigger, and respective items are more important；Verting In transient, driver allows engine nacelle to be verted with fixed angular speed by thumb roller, and be absorbed in always away from The control of bar and longitudinal rod；Additionally, the change of pitch rate and the angle of pitch is also paid close attention in transient process of verting, therefore respectively Item proportion is different, and weight coefficient is set to：w_t=1.0, w₁=2.0, w₂=2.0, w₃=1.0, w₄=1.5, w₅=1.5.

Preferably, above-mentioned steps 2) in path constraint be specially：In order to allow height holding within the acceptable range, Certain limitation has been carried out to height change according to different aerial mission requirements in path constraint；Additionally, in path constraint Limitation is also carried out to pitch attitude angle and angular speed：

Determine path constraint using tiltrotor nacelle tilt angle-speed envelope analysis method, make transient process of verting It is maintained in nacelle tilt angle-speed envelope curve；

In whole transient process of verting, the manipulation speed of driver is fast according to the booster of the tiltrotor of correspondence model Rate limitation determines：

Preferably, above-mentioned steps 2) in boundary condition be specially：Handling Strategy optimization initial boundary conditions are aircraft Current flight state；End boundaries condition is set as target tilt angle and forward flight speed, i.e.,：

Wherein i_ntIt is target engine nacelle tilt angle,It is target forward flight speed, concrete numerical value is according to aerial mission It is required that determining.

Preferably, above-mentioned steps 3) in numerical optimisation algorithms be specially：Using direct transformation approach and SQP Algorithm is solved；

When numerical computations are carried out, dimensionless scaling is carried out to the parameter in flight dynamics model first；

Define constant k₁, k₂, k₃, k₄Dimensionless scaling is carried out to quantity of state, controlled quentity controlled variable and time：

The dimensionless scaling of length, quality, aerodynamic force and aerodynamic moment is as follows：

In order that the state variable and control variables size after dimensionless scaling take k close to 1₁=k₂=100, k₃=1, k₄ =0.01；

Flight dynamics state equation after dimensionless scaling is expressed as：

The dimensionless τ of time is divided into N-1 time period：

The state variable and control variables under continuous space are carried out using direct transformation approach discrete, obtain Non-Linear Programming The design variable of problem；

Design variable after then discrete is：

Wherein：

τ_mk=(τ_k+τ_k+1)/2

The differential equation in Nonlinear Dynamic optimal control problem is carried out discrete, obtain following defect equality constraint side Journey：

Wherein：

Discrete obtaining is carried out to performance indications：

Boundary condition acts on last node：

Path constraint acts on each time period node and intermediate node：

After Nonlinear Dynamic optimal control problem is converted into nonlinear programming problem, application sequence Novel Algorithm is asked Solve the nonlinear programming problem and can obtain optimal solution；And the state variable and control variables at all nodes in optimal solution are entered Row 3 Hermite interpolation of segmentation, obtain rod volume change, rule of verting and flight path.

Beneficial effects of the present invention：

(1) present invention can obtain the optimal transient process of verting of tiltrotor according to different aerial mission requirements, While solving to manipulate redundancy issue, moreover it is possible to obtain optimal Handling Strategy and flight path, so as to effectively reduce drive employee Make load, improve the crossing efficiency that verts, stabilization body attitude, certain reference is provided to driver and designer.And it is conventional Verted optimal Handling Strategy and the flight that the controlling party rule of transition cannot obtain under different aerial missions on tiltrotor Track.

(2) method for solving computational efficiency proposed by the present invention is high, and convergence is fast, and result of calculation is with a high credibility, can be used to grind Study carefully the optimal transient process of verting of tiltrotor.

Brief description of the drawings

Fig. 1 is flow chart of steps of the present invention；

Fig. 2 a are the required horsepower data for calculating trim condition and flight test that the present invention sets up flight dynamics model Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 90 °, flaperon configuration It is 40 °/25 °；

Fig. 2 b are the pitch attitude angle number for calculating trim condition and flight test that the present invention sets up flight dynamics model According to contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 90 °, and flaperon is matched somebody with somebody It is set to 40 °/25 °；

Fig. 2 c are that the present invention sets up the calculating trim condition of flight dynamics model and the blade root of flight test always away from data Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 90 °, flaperon configuration It is 40 °/25 °；

Fig. 2 d are the calculating trim condition and flight test collective-pitch lever Data Comparison that the present invention sets up flight dynamics model Schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 90 °, and flaperon is configured to 40°/25°；

Fig. 2 e are the calculating trim condition and flight test longitudinal direction cyclic that the present invention sets up flight dynamics model Data Comparison schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 90 °, flaperon It is configured to 40 °/25 °；

Fig. 3 a are the required horsepower data for calculating trim condition and flight test that the present invention sets up flight dynamics model Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 60 °, flaperon configuration It is 20 °/12.5 °；

Fig. 3 b are the pitch attitude angle number for calculating trim condition and flight test that the present invention sets up flight dynamics model According to contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 60 °, and flaperon is matched somebody with somebody It is set to 20 °/12.5 °；

Fig. 3 c are that the present invention sets up the calculating trim condition of flight dynamics model and the blade root of flight test always away from data Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 60 °, flaperon configuration It is 20 °/12.5 °；

Fig. 3 d are the calculating trim condition and flight test collective-pitch lever Data Comparison that the present invention sets up flight dynamics model Schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 60 °, and flaperon is configured to 20°/12.5°；

Fig. 3 e are the calculating trim condition and flight test longitudinal direction cyclic that the present invention sets up flight dynamics model Data Comparison schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 60 °, flaperon It is configured to 20 °/12.5 °；

Fig. 4 a are the required horsepower data for calculating trim condition and flight test that the present invention sets up flight dynamics model Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 0 °, flaperon configuration It is 0 °/0 °；

Fig. 4 b are the pitch attitude angle number for calculating trim condition and flight test that the present invention sets up flight dynamics model According to contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 0 °, and flaperon is matched somebody with somebody It is set to 0 °/0 °；

Fig. 4 c are that the present invention sets up the calculating trim condition of flight dynamics model and the blade root of flight test always away from data Contrast schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 0 °, flaperon configuration It is 0 °/0 °；

Fig. 4 d are the calculating trim condition and flight test collective-pitch lever Data Comparison that the present invention sets up flight dynamics model Schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 0 °, flaperon be configured to 0 °/ 0°；

Fig. 4 e are the calculating trim condition and flight test longitudinal direction cyclic that the present invention sets up flight dynamics model Data Comparison schematic diagram, type is XV-15, weight 5897kg, rotating speed 589rpm, and engine nacelle tilt angle is 0 °, flaperon It is configured to 0 °/0 °；

Fig. 5 is the principle schematic of direct transformation approach；

Fig. 6 a are that vert transient process and pilot flying of the forward direction that the present invention is calculated emulates the medium-altitude data pair of data Compare schematic diagram；

Fig. 6 b are that the forward direction that the present invention is calculated is verted the number of forward flight speed in transient process and pilot flying emulation data According to contrast schematic diagram；

Fig. 6 c are that the forward direction that the present invention is calculated is verted the data of rate of descent in transient process and pilot flying emulation data Contrast schematic diagram；

Fig. 6 d are that the forward direction that the present invention is calculated is verted pitch attitude angle in transient process and pilot flying emulation data Data Comparison schematic diagram；

Fig. 6 e be the forward direction that the present invention is calculated vert transient process and pilot flying emulate data in engine nacelle incline The Data Comparison schematic diagram of corner；

Fig. 6 f are that the forward direction that the present invention is calculated is verted longitudinal feathering in transient process and pilot flying emulation data The Data Comparison schematic diagram of bar；

Fig. 6 g are that the forward direction that the present invention is calculated is verted the data of collective-pitch lever in transient process and pilot flying emulation data Contrast schematic diagram；

Fig. 7 a are that the reverse transient process of verting that the present invention is calculated emulates the medium-altitude data pair of data with pilot flying Compare schematic diagram；

Fig. 7 b are reverse transient process and the number of forward flight speed in pilot flying's emulation data of verting that the present invention is calculated According to contrast schematic diagram；

Fig. 7 c are reverse transient process and the data of rate of descent in pilot flying's emulation data of verting that the present invention is calculated Contrast schematic diagram；

Fig. 7 d are reverse transient process and the pitch attitude angle in pilot flying's emulation data of verting that the present invention is calculated Data Comparison schematic diagram；

Fig. 7 e are that the reverse transient process of verting that the present invention is calculated is inclined with engine nacelle in pilot flying's emulation data The Data Comparison schematic diagram of corner；

Fig. 7 f are reverse transient process and the longitudinal feathering in pilot flying's emulation data of verting that the present invention is calculated The Data Comparison schematic diagram of bar；

Fig. 7 g are reverse transient process and the data of collective-pitch lever in pilot flying's emulation data of verting that the present invention is calculated Contrast schematic diagram.

Specific embodiment

For the ease of the understanding of those skilled in the art, the present invention is made further with reference to embodiment and accompanying drawing It is bright, the content that implementation method is referred to not limitation of the invention.

Shown in reference picture 1, a kind of tiltrotor of the invention is verted the method for solving of transient process, including step is such as Under：

1) flight dynamics model of transient process of being verted suitable for calculating tiltrotor is set up, the model was verting Cross in solution procedure it is contemplated that limitation of the steerable system characteristic to manipulated variable pace of change, moreover it is possible to avoid in numerical solution mistake Occurs jump in journey discontinuous；

2) suitable boundary condition, path constraint and performance indications are set up according to different aerial missions, by tilting rotor The transient process of verting of machine is converted into Nonlinear Dynamic optimal control problem；

3) design value optimized algorithm is to step 2) in Nonlinear Dynamic optimal control problem solve, verted The transient process of verting of gyroplane.

The method of the present invention be applied to calculate tiltrotor vert transient process flight dynamics model by three parts Composition, respectively：Basic nonlinear flight dynamics model, mixing manipulate equation and the controlled quentity controlled variable differential equation.

Basic nonlinear flight dynamics model is expressed as the form of following differential equation of first order：

Quantity of state x in model_b, controlled quentity controlled variable u_bRespectively：

x_b=[u, v, w, p, q, r, φ, θ, ψ, x, y, h]^T

u_b=[θ_0,r,θ_0,l,θ_c,r,θ_c,l,θ_s,r,θ_s,l,i_n,θ_a,θ_e,θ_r]^T

Wherein quantity of state u, v, w are respectively the corresponding speed in three directions of body shafting, and p, q, r is respectively three sides of body shafting To corresponding angular speed,It is roll angle, θ is the angle of pitch, and ψ is yaw angle, and x is aircraft horizontal displacement, and y is that aircraft is lateral Displacement, h is aircraft sea level altitude；Manipulated variable θ_0,r,θ_0,lRespectively the dextrorotation wing with the left-handed wing always away from θ_c,r,θ_c,lRespectively It is the dextrorotation wing and the horizontal feathering of the left-handed wing, θ_s,r,θ_s,lRespectively longitudinal feathering of the dextrorotation wing and the left-handed wing, i_nFor The nacelle tilt angle that driver is given, θ_aIt is aileron movement angle, θ_eIt is elevator angle, θ_rIt is control surface steering angle.

In the present embodiment, with XV-15 tiltrotors as model machine, after carrying out mathematical modeling to each part, using programming language Speech Fortran builds basic tiltrotor nonlinear mathematical model.

On this basis, pilot control rod volume information is introduced, is set up and is applied to XV-15 tiltrotor thru-flight moulds The mixing of formula manipulates equation：

Wherein δ_colIt is driver's stayed mast (from bottom to top 0~1), δ_lonIt is driver's longitudinal rod (from back to front -1~1), δ_latIt is driver's transverse bar (from left to right -1~1), δ_pedIt is driver's pedal (from left to right -1~1), δ_inIt is driver's thumb Refer to roller (0 °~95 °)；Each coefficient of manipulated variableWith compensation rate θ_gWith δ_B1Set by consulting XV-15 tiltrotor parameters Meter table is obtained；Mixing manipulates equation and 10 manipulated variables in former base this flight dynamics model is reduced to 5, so both reduces Manipulating variable, the operation information of the driver that gets back.

The controlled quentity controlled variable differential equation：

Limitation in view of steerable system characteristic to manipulated variable pace of change, while in order to avoid manipulated variable is in optimization process It is middle jump occur discontinuously or the form of bang-bang types control, use δ_col、δ_lon、δ_lat、δ_pedAnd δ_inFirst derivative make It is controlled quentity controlled variable, and δ_col、δ_lon、δ_lat、δ_pedAnd δ_inAs new state variable：

By basic nonlinear flight dynamics model, mixing manipulates equation and the controlled quentity controlled variable differential equation is whole in Fortran Close, you can obtain being applied to and calculate tiltrotor and vert the flight dynamics model of transient process；Tiltrotor has edge Longitudinally asymmetric configuration, transient process of verting all in fore-and-aft plane, in order to improve the computational efficiency of method for solving, without crosswind condition Lower quantity of state and controlled quentity controlled variable by model further simplifies, and its state space form is：

Quantity of state x and controlled quentity controlled variable u are respectively in formula：

X=[u, w, q, θ, x, h, δ_col,δ_lon,i_n]^T

U=[u_c,u_s,u_n]^T。

To verify the accurate fixed of built XV-15 tiltrotor Mathematical Modelings, trim checking is carried out to it, from accompanying drawing Result of calculation is can be seen that in 2a-2e, 3a-3e, 4a-4e and similarly configure the test flight data of lower XV-15 tiltrotors It coincide preferable, illustrate that the flight dynamics model of foundation is more accurate, can be used to study the optimal of tiltrotor and verted Transient.

In the present embodiment tiltrotor proceed by vert transition when, aircraft be in stabilized flight condition, therefore The poised state of calculating can provide initial value for the transition optimization of verting of tiltrotor.

Tiltrotor is described as in the problem of verting of transient process of verting：From the transition Handling Strategy that verts that a class is allowed In find out an optimal Handling Strategy, make tiltrotor the Handling Strategy effect under finger is tilted to by initiation state mode While fixed dbjective state pattern, the performance indications that it evaluates motion process quality are optimal.In whole process of verting In, the motion of aircraft, Handling Strategy and performance indications are the function in time and space, therefore tiltrotor was verted The problem of crossing can be attributed to a kind of Nonlinear Dynamic optimal control problem containing state and control constraint.Nonlinear Dynamic is optimal Control problem includes performance indications, three parts of boundary condition and path constraint.

Performance indications are specially：Tiltrotor in transient process of verting, the direction of pull of rotor and full machine center of gravity Can change, cause pitch attitude to change greatly, it is necessary to driver is held position by appropriate manipulation, therefore performance refers to Mark needs to consider the control to pitch attitude；Additionally, it should also be taken into account that the work of vert transient process required time and driver Make load, therefore performance indications are set to：

Wherein,

W in formula_t,w₁,w₂,w₃,w₄,w₅It is the constant-weight factor, weight coefficient is bigger, and respective items are more important；Verting In transient, driver allows engine nacelle to be verted with fixed angular speed by thumb roller, and be absorbed in always away from The control of bar and longitudinal rod；In addition, the change of pitch rate and the angle of pitch is also paid close attention in transient process of verting, because This every proportion is different, and weight coefficient is set to：w_t=1.0, w₁=2.0, w₂=2.0, w₃=1.0, w₄=1.5, w₅= 1.5。

In order to allow driver to focus on the manipulation for holding position, so as to reduce operating difficulty, performance indications wouldn't be examined Consider the control to track (for height is controlled in fore-and-aft plane).As for the height change in transient process of verting, can be in path Required into row constraint according to different aerial missions in constraint, kept it in acceptable scope.

Boundary condition：Handling Strategy optimization initial boundary conditions are aircraft current flight state；Study for convenience, will End boundaries condition is set as target tilt angle and forward flight speed, i.e.,：

Wherein i_ntIt is target engine nacelle tilt angle,It is target forward flight speed, concrete numerical value is according to aerial mission It is required that determining.

Path constraint：In order to allow height to keep within the acceptable range, can be flown according to different in path constraint Row mission requirements has carried out certain limitation to height change；Additionally, to pitch attitude angle and angular speed in path constraint Limited；

Determine path constraint using tiltrotor nacelle tilt angle-speed envelope analysis method, make transient process of verting It is maintained in nacelle tilt angle-speed envelope curve；

When low speed verts, the lift that wing is provided is limited by the critical stalling angle of wing, therefore is inclined in low speed segment When subcontracting line, the wing angle of attack is in the wing critical angle of attack, now meets following relation：

α_w=α_wc=i_w+α_f

Wherein α_wIt is the wing angle of attack, α_wcIt is the wing critical angle of attack, i_wIt is the true angle of incidence, α_fIt is the fuselage angle of attack；By low speed segment The inequality path constraint that engine nacelle tilt angle-speed envelope curve determines is：

α_wcmin≤α_w≤α_wcmax

α_wcminWith α_wcmaxObtained by the blowing data of tiltrotor, with XV-15 as model machine in embodiment, respectively- 20 ° and 12 °.

Maximum forward flight speed during verting is by rotor advancing blade compressibility and retreating blade stall effect and rotation The limitation such as wing available horsepower and kinetic stability, the limitation of wherein rotor available horsepower is that most basic and most important limitation will Element.Be thus in high regime vert envelope curve when, total required horsepower of rotor reaches the rated power of engine output.

Rotor required horsepower coefficient C_PFor：

Wherein C_TIt is rotor thrust coefficient, is obtained by flight dynamics model, K_indIt is induced velocity modifying factor (1.15), f_GIt is the ground effect factor (1.0), v_iIt is dimensionless induced velocity, is obtained by flight dynamics model, σ is rotor reality Degree (XV-15 is 0.089), c_dIt is rotor blade resistance coefficient (0.015)；Then the total required horsepower of tiltrotor is expressed as：

Wherein η_pIt is transmission power loss (0.95).

The inequality path constraint determined by high regime engine nacelle tilt angle-speed envelope curve is：

0≤P_r≤P_cr

Wherein P_crIt is the rated power (volume of XV-15 tiltrotors engine output of tiltrotor engine output Power is determined for 1737.5kw)；In order to further ensure that the flight safety of transient process of verting, high regime is verted and start on envelope curve Used as cessation speed, the process flying speed of verting can not be more than cessation speed V to 45 ° of corresponding speed of machine nacelle tilt angle_stop, The cessation speed of XV-15 tiltrotors is 88m/s.

V_max≤V_stop

In whole transient process of verting, the manipulation speed of driver can be according to the booster of XV-15 tiltrotors speed Rate limitation determines：

The numerical optimisation algorithms of design are specially：Tiltrotor is verted the transient process optimal control of corresponding Nonlinear Dynamic The state and control variables of problem processed are numerous, and constraint and object function are extremely complex, therefore Analytical Solution is infeasible, it is necessary to pass through number Value optimized algorithm is solved；Solved using direct transformation approach and sequential quadratic programming algorithm；

When numerical computations are carried out, dimensionless scaling is carried out to the parameter in flight dynamics model first；

Define constant k₁, k₂, k₃, k₄Dimensionless scaling is carried out to quantity of state, controlled quentity controlled variable and time：

The dimensionless scaling of length, quality, aerodynamic force and aerodynamic moment is as follows：

In order that the state variable and control variables size after dimensionless scaling take k close to 1₁=k₂=100, k₃=1, k₄ =0.01；

Flight dynamics state equation after dimensionless scaling is expressed as：

The dimensionless τ of time is divided into N-1 time period：

The state variable and control variables under continuous space are carried out using direct transformation approach discrete, obtain Non-Linear Programming The design variable of problem, its principle is as shown in Figure 5；

Design variable after then discrete is：

Wherein：

τ_mk=(τ_k+τ_k+1)/2

The differential equation in Nonlinear Dynamic optimal control problem is carried out using Hermite-Simpson methods it is discrete, Obtain following defect equality constraint equation：

Wherein：

Discrete obtaining is carried out to performance indications：

Boundary condition acts on last node：

Path constraint acts on each time period node and intermediate node：

After Nonlinear Dynamic optimal control problem is converted into nonlinear programming problem, application sequence Novel Algorithm is asked Solve the nonlinear programming problem and can obtain optimal solution；Sequential quadratic programming algorithm can be very good solution a large amount of design variables With the nonlinear programming problem of constraint equation；Finally the state variable and control variables at all nodes in optimal solution are divided 3 Hermite interpolation of section, obtain more smooth rod volume change, rule of verting and flight path.

The tiltrotor provided using the present invention vert transient process method for solving carry out tiltrotor it is positive with And the emulation of reverse transient process of most verting, and emulate Data Comparison, wherein pilot flying's emulation data with pilot flying Obtained by driver's transition flight simulated experiment that carries out verting in XV-15 tiltrotor flight simulation equipment, driven Member can decide optimal Handling Strategy and corresponding flight path in transient process of verting in its sole discretion according to current flight task, and The predetermined flight path and manipulation schemes of tracking need not be gone, thus be adapted to be carried out with the transient process of verting for obtaining of the invention it is right Than.Driver's emulation type parameter used is consistent with the model machine that the present embodiment is used.

Forward direction is verted transition

So that XV-15 tiltrotors are verted from helicopter mode to fixed wing aircraft mode continuous forward direction as an example, using this The method for solving of invention carries out Handling Strategy optimization, and is contrasted with pilot flying's simulation result.Driver carries out forward direction Vert transition when original state it is as follows：Speed 32m/s, height 88m, 7 ° of flight-path angle, now aircraft is in stabilized flight shape State.Aerial mission requirement driver decides optimal Handling Strategy in its sole discretion, it is allowed to height change, and speed is remained after end of verting 65m/s。

According to current flight task, target engine nacelle tilt angle i_ntIt is 0 °, target forward flight speedIt is 65m/s, Altitude range is set in path constraint：

80m≤h(t)≤150m

As shown in accompanying drawing 6a-6g, it can be seen that engine nacelle is directly verted to fixed-wing with the angular speed of 6.5 °/s and flown Machine pattern, period driver slowly increases collective-pitch lever displacement and forward push rod, forward flight speed increase, the stabilization that then takes back appearance State.The vert Handling Strategy of transient process of whole forward direction is relatively easy to realize, and the change of state of flight amount is steady.Invention calculates knot Fruit is closer to pilot flying's simulation result, and angle of pitch change is more steady.

Reverse transition of verting

So that XV-15 tiltrotors are continuously inversely verted from fixed wing aircraft pattern to helicopter mode as an example, using this The method for solving of invention carries out Handling Strategy optimization, and is contrasted with pilot flying's simulation result.Driver is carried out inversely Vert transition when original state it is as follows：Speed 62m/s, height 120m, -2 ° of flight-path angle, in stabilized flight condition, flight is appointed Business requires that driver decides optimal Handling Strategy and flight path in its sole discretion, finally needs to land.

Reverse transition of verting generally relates to the deceleration landing mission of tiltrotor, in order to meet air worthiness regulation on peace The full requirement landed to the end boundaries condition and path constraint of Nonlinear Dynamic optimal control problem, it is necessary to make following repairing Change：

As shown in accompanying drawing 7a-7g, it can be seen that engine nacelle is directly verted to helicopter with the angular speed of -6.5 °/s Airplane-mode, rotor thrust gradually increases, and driver's increase collective-pitch lever simultaneously takes back, and the angle of pitch rises, and forward flight speed is gradually Reduce；Vert to helicopter mode, driver continues manipulation collective-pitch lever and longitudinal cyclic makes aircraft security land. Compared with pilot flying's simulation result, the time history of state of flight amount that the present invention is calculated and document coincide compared with It is good, and rate of descent and angle of pitch change are more steady, collective-pitch lever change is softer.

By more than contrast as can be seen that method for solving of the invention can be used for study verting for tiltrotor tide over Journey, and corresponding optimal Handling Strategy and flight path are obtained, provide certain reference to driver and designer.

Concrete application approach of the present invention is a lot, and the above is only the preferred embodiment of the present invention, it is noted that for For those skilled in the art, under the premise without departing from the principles of the invention, some improvement can also be made, this A little improvement also should be regarded as protection scope of the present invention.

Claims (9)

1. a kind of tiltrotor is verted the method for solving of transient process, it is characterised in that as follows including step：

1) flight dynamics model of transient process of being verted suitable for calculating tiltrotor is set up；

2) suitable boundary condition, path constraint and performance indications are set up according to different aerial missions, by tiltrotor Transient process of verting is converted into Nonlinear Dynamic optimal control problem；

3) design value optimized algorithm is to step 2) in Nonlinear Dynamic optimal control problem solve, obtain tilting rotor The transient process of verting of machine.

2. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 1) in model in transition solution procedure of verting it is contemplated that limitation of the steerable system characteristic to manipulated variable pace of change, moreover it is possible to Avoid occurring during numerical solution jump discontinuously.

3. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 1) model includes in：Basic nonlinear flight dynamics model, mixing manipulates equation and the controlled quentity controlled variable differential equation.

4. tiltrotor according to claim 3 is verted the method for solving of transient process, it is characterised in that above-mentioned is mixed Closing manipulation equation is：

$\left\{\begin{array}{c}{\mathrm{\θ}}_{0,r}=\∂{\mathrm{\θ}}_0/\∂{\mathrm{\δ}}_{col}\·{\mathrm{\δ}}_{col}-\∂{\mathrm{\θ}}_0/\∂{\mathrm{\δ}}_{lat}\·{\mathrm{\δ}}_{lat}+{\mathrm{\θ}}_g\\ {\mathrm{\θ}}_{0,l}=\∂{\mathrm{\θ}}_0/\∂{\mathrm{\δ}}_{col}\·{\mathrm{\δ}}_{col}+\∂{\mathrm{\θ}}_0/\∂{\mathrm{\δ}}_{lat}\·{\mathrm{\δ}}_{lat}+{\mathrm{\θ}}_g\\ {\mathrm{\θ}}_{c,r}=\∂{\mathrm{\θ}}_c/\∂{\mathrm{\δ}}_{lat}\·{\mathrm{\δ}}_{lat}\\ {\mathrm{\θ}}_{c,l}=\∂{\mathrm{\θ}}_c/\∂{\mathrm{\δ}}_{lat}\·{\mathrm{\δ}}_{lat}\\ {\mathrm{\θ}}_{s,r}=\∂{\mathrm{\θ}}_s/\∂{\mathrm{\δ}}_{lon}\·{\mathrm{\δ}}_{lon}-\∂{\mathrm{\θ}}_s/\∂{\mathrm{\δ}}_{ped}\·{\mathrm{\δ}}_{ped}+{\mathrm{\δ}}_{B1}\left(1-\sin i_n\right)\\ {\mathrm{\θ}}_{s,l}=\∂{\mathrm{\θ}}_s/\∂{\mathrm{\δ}}_{lon}\·{\mathrm{\δ}}_{lon}+\∂{\mathrm{\θ}}_s/\∂{\mathrm{\δ}}_{ped}\·{\mathrm{\δ}}_{ped}+{\mathrm{\δ}}_{B1}\left(1-\sin i_n\right)\\ {\mathrm{\θ}}_e=\∂{\mathrm{\θ}}_e/\∂{\mathrm{\δ}}_{lon}\·{\mathrm{\δ}}_{lon}\\ {\mathrm{\θ}}_a=-\∂{\mathrm{\θ}}_a/\∂{\mathrm{\δ}}_{lat}\·{\mathrm{\δ}}_{lat}\\ {\mathrm{\θ}}_r=\∂{\mathrm{\θ}}_r/\∂{\mathrm{\δ}}_{ped}\·{\mathrm{\δ}}_{ped}\\ i_n={\mathrm{\δ}}_{in}\end{array}\right..$

5. tiltrotor according to claim 3 is verted the method for solving of transient process, it is characterised in that above-mentioned control The amount differential equation processed is：

Limitation in view of steerable system characteristic to manipulated variable pace of change, while in order to avoid manipulated variable goes out in optimization process The form that the discontinuous or bang-bang types that now jump are controlled, uses δ_col、δ_lon、δ_lat、δ_pedAnd δ_inFirst derivative as control Amount processed, and δ_col、δ_lon、δ_lat、δ_pedAnd δ_inAs new state variable：

$\left\{\begin{array}{c}{\stackrel{\·}{\mathrm{\δ}}}_{col}=u_c\\ {\stackrel{\·}{\mathrm{\δ}}}_{lon}=u_s\\ {\stackrel{\·}{\mathrm{\δ}}}_{lat}=u_a\\ {\stackrel{\·}{\mathrm{\δ}}}_{ped}=u_p\\ {\stackrel{\·}{\mathrm{\δ}}}_{in}=u_n\end{array}\right..$

6. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 2) performance indications in are specially：

$\min J=w_t{t}_f+\frac{1}{t_f-t_0}{\∫}_{t_0}^{t_f}L\left(q\right(t),\mathrm{\θ}(t),u(t\left)\right)dt$

Wherein,

$L(q,\mathrm{\θ},u)=w_1{u}_c^2/u_{c\max }^2+w_2{u}_s^2/u_{s\max }^2+w_3{u}_n^2/u_{n\max }^2+w_4{\stackrel{\‾}{q}}^2/{\stackrel{\‾}{q}}_{\max }^2+w_5{\mathrm{\θ}}^2/{\mathrm{\θ}}_{\max }^2$

W in formula_t,w₁,w₂,w₃,w₄,w₅It is the constant-weight factor, weight coefficient is bigger, and respective items are more important；Tided over verting Cheng Zhong, driver allows engine nacelle to be verted with fixed angular speed by thumb roller, and be absorbed in collective-pitch lever and The control of longitudinal rod；Additionally, the change of pitch rate and the angle of pitch is also paid close attention in transient process of verting, therefore every ratio Weight is different, and weight coefficient is set to：w_t=1.0, w₁=2.0, w₂=2.0, w₃=1.0, w₄=1.5, w₅=1.5.

7. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 2) path constraint in is specially：In order to allow height to keep within the acceptable range, flown according to different in path constraint Row mission requirements has carried out certain limitation to height change；Additionally, to pitch attitude angle and angular speed in path constraint Limited：

Determine path constraint using tiltrotor nacelle tilt angle-speed envelope analysis method, make transient process holding of verting In nacelle tilt angle-speed envelope curve；

In whole transient process of verting, the manipulation speed of driver is limited according to the booster speed of the tiltrotor of correspondence model System determines：

$\left\{\begin{array}{c}{u}_{cmin}\≤u_c\≤u_{cmax}\\ u_{s\min }\≤u_s\≤u_{s\max }\\ u_{n\min }\≤u_n\≤u_{nmax}\end{array}\right..$

8. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 2) boundary condition in is specially：Handling Strategy optimization initial boundary conditions are aircraft current flight state；By end boundaries Condition is set as target tilt angle and forward flight speed, i.e.,：

$\left\{\begin{array}{c}{i}_{nt}\≤i_n\left(t_f\right)\≤i_{nt}\\ 0\≤u_n\left(t_f\right)\≤0\\ {\stackrel{\·}{x}}_t\≤\stackrel{\·}{x}\left(t_f\right)\≤{\stackrel{\·}{x}}_t\end{array}\right.$

Wherein i_ntIt is target engine nacelle tilt angle,It is target forward flight speed, concrete numerical value is true according to aerial mission requirement It is fixed.

9. tiltrotor according to claim 1 is verted the method for solving of transient process, it is characterised in that above-mentioned steps 3) numerical optimisation algorithms in are specially：Solved using direct transformation approach and sequential quadratic programming algorithm；

When numerical computations are carried out, dimensionless scaling is carried out to the parameter in flight dynamics model first；

Define constant k₁, k₂, k₃, k₄Dimensionless scaling is carried out to quantity of state, controlled quentity controlled variable and time：

$\left\{\begin{array}{c}\begin{array}{cccc}\stackrel{\‾}{w}=\frac{k_{1}w}{{\mathrm{\Ω}}_{0}R}& \stackrel{\‾}{u}=\frac{k_{1}w}{{\mathrm{\Ω}}_{0}R}& \stackrel{\‾}{q}=\frac{k_{2}q}{{\mathrm{\Ω}}_0}& \stackrel{\‾}{h}=\frac{k_{3}h}{R}\end{array}\\ \begin{array}{ccc}\stackrel{\‾}{x}=\frac{k_{3}x}{R}& {\stackrel{\‾}{P}}_a=\frac{1}{k_4}\frac{P_a}{I_R{{\mathrm{\Ω}}_0}^3}& \stackrel{\‾}{\mathrm{\Ω}}=\frac{\mathrm{\Ω}}{{\mathrm{\Ω}}_0}\end{array}\\ \begin{array}{cc}\mathrm{\τ}=k_4{\mathrm{\Ω}}_{0}t& \stackrel{\‾}{u}=\frac{u}{k_4{\mathrm{\Ω}}_0}\end{array}\end{array}\right.$

The dimensionless scaling of length, quality, aerodynamic force and aerodynamic moment is as follows：

$\left\{\begin{array}{c}\stackrel{\‾}{l}=\frac{k_1}{k_2}\frac{l}{R},m_0=\frac{k_4}{k_1}\frac{m}{{\mathrm{\ρ\πR}}^3},\\ {\stackrel{\‾}{M}}_A=\frac{k_2}{k_4}\frac{M_A}{{{\mathrm{\Ω}}_0}^2{I}_{yy}},{\stackrel{\‾}{A}}_z=\frac{k_1}{k_4}\frac{A_z}{{{\mathrm{m\Ω}}_0}^{2}R}\end{array}\right.$

In order that the state variable and control variables size after dimensionless scaling take k close to 1₁=k₂=100, k₃=1, k₄= 0.01；

Flight dynamics state equation after dimensionless scaling is expressed as：

$\frac{d\stackrel{\‾}{x}}{d\mathrm{\τ}}=f(\stackrel{\‾}{x},\stackrel{\‾}{u},\mathrm{\τ})$

The dimensionless τ of time is divided into N-1 time period：

$\left\{\begin{array}{c}{\mathrm{\&tau;}}_0={\mathrm{\&tau;}}_1<{\mathrm{\&tau;}}_2...<{\mathrm{\&tau;}}_k...<{\mathrm{\&tau;}}_N={\mathrm{\&tau;}}_f\\ {\mathrm{\&tau;}}_k={\mathrm{\&tau;}}_{k-1}+\mathrm{\&Delta;}\mathrm{\&tau;}\\ \mathrm{\&Delta;}\mathrm{\&tau;}=({\mathrm{\&tau;}}_f-{\mathrm{\&tau;}}_0)/(N-1)\end{array}\right.$

The state variable and control variables under continuous space are carried out using direct transformation approach discrete, obtain nonlinear programming problem Design variable；

Design variable after then discrete is：

$Y=\&lsqb;{(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{u},{\stackrel{\&OverBar;}{u}}_m)}_1,{(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{u},{\stackrel{\&OverBar;}{u}}_m)}_2,{(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{u},{\stackrel{\&OverBar;}{u}}_m)}_k,...,{(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{u})}_N,{\mathrm{\&tau;}}_f\&rsqb;$

Wherein：

${\stackrel{\&OverBar;}{u}}_{mk}=\stackrel{\&OverBar;}{u}\left({\mathrm{\&tau;}}_{mk}\right)$

τ_mk=(τ_k+τ_k+1)/2

The differential equation in Nonlinear Dynamic optimal control problem is carried out discrete, obtain following defect equality constraint equation：

$0\&le;{\stackrel{\&OverBar;}{x}}_{k+1}-{\stackrel{\&OverBar;}{x}}_k-\frac{1}{6}\mathrm{\&Delta;}\mathrm{\&tau;}\&lsqb;f({\stackrel{\&OverBar;}{x}}_k,{\stackrel{\&OverBar;}{u}}_k,{\mathrm{\&tau;}}_k)+4f({\stackrel{\&OverBar;}{x}}_{mk},{\stackrel{\&OverBar;}{u}}_{mk},{\mathrm{\&tau;}}_{mk})+f({\stackrel{\&OverBar;}{x}}_{k+1},{\stackrel{\&OverBar;}{u}}_{k+1},{\mathrm{\&tau;}}_{k+1})\&rsqb;\&le;0$

Wherein：

${\stackrel{\&OverBar;}{x}}_{mk}=\frac{1}{2}({\stackrel{\&OverBar;}{x}}_k+{\stackrel{\&OverBar;}{x}}_{k+1})+\frac{1}{8}\mathrm{\&Delta;}\mathrm{\&tau;}\left(f\right({\stackrel{\&OverBar;}{x}}_k,{\stackrel{\&OverBar;}{u}}_k,{\mathrm{\&tau;}}_k)-f({\stackrel{\&OverBar;}{x}}_{k+1},{\stackrel{\&OverBar;}{u}}_{k+1},{\mathrm{\&tau;}}_{k+1}\left)\right)$

Discrete obtaining is carried out to performance indications：

$\underset{u}{min}J=w_t{\mathrm{\&tau;}}_N+\frac{1}{6}\underset{k=1}{\overset{N-1}{\&Sigma;}}\frac{1}{N-1}\&lsqb;L({\stackrel{\&OverBar;}{q}}_k,{\mathrm{\&theta;}}_k,{\stackrel{\&OverBar;}{u}}_k)+4L({\stackrel{\&OverBar;}{q}}_{mk},{\mathrm{\&theta;}}_{mk},{\stackrel{\&OverBar;}{u}}_{mk})+L({\stackrel{\&OverBar;}{q}}_{k+1},{\mathrm{\&theta;}}_{k+1},{\stackrel{\&OverBar;}{u}}_{k+1})\&rsqb;$

Boundary condition acts on last node：

$\left\{\begin{array}{c}{i}_{nt}\&le;i_{n\left(N\right)}\&le;i_{nt}\\ 0\&le;u_{n\left(N\right)}\&le;0\\ {\stackrel{\&CenterDot;}{x}}_t\&le;{\stackrel{\&CenterDot;}{x}}_{\left(N\right)}\&le;{\stackrel{\&CenterDot;}{x}}_t\end{array}\right.$

Path constraint acts on each time period node and intermediate node：

After Nonlinear Dynamic optimal control problem is converted into nonlinear programming problem, application sequence Novel Algorithm is solved should Nonlinear programming problem is that can obtain optimal solution；And the state variable and control variables at all nodes in optimal solution are divided 3 Hermite interpolation of section, obtain rod volume change, rule of verting and flight path.