CN103197560A - Design method for wide adaptability of aircraft three-dimensional aviating area controller - Google Patents

Abstract

The invention provides a design method for wide adaptability of an aircraft three-dimensional aviating area controller so as to overcome the defect that an existing controller design method can not ensure stable and safe aviation of an aircraft in a given aviating area. According to the method, an aircraft motion phase plane equation is built, an aircraft stable level aviation flow angle of attack and a trim control surface are obtained in a given control target height and mach number through an aerodynamic force equation and a moment equation, a feedback controller of states such as the flow angle of attack and a sideslip angle is introduced, regional stability of a system is confirmed by adopting a phase plane analyzing model, and parameters of the feedback controller are confirmed based on regional stability. Three-dimensional motion of the aircraft is controlled directly, so that the defect that incorrect approximation such as an aerodynamic force effect is ignored in the moment equation is avoided, stability of the aircraft can be ensured by the controller in the whole designed area, and occurrence of problems such as unstable and unsafe aviation caused by the analyzing model is reduced or even avoided.

Description

The wide adaptability design method of the three-dimensional flight range controller of aircraft

Technical field

The present invention relates to a kind of controller of aircraft method for designing, particularly the wide adaptability design method of the three-dimensional flight range controller of a kind of aircraft.

Background technology

The basic purpose of flight control is to improve stability and the maneuverability of aircraft, thereby improves the ability of executing the task; In decades recently, along with improving constantly of aeroplane performance, very big variation has taken place in flight control technology, advanced flight control technology such as active control technology, Comprehensive Control Technology, autonomous flight control technology occurred, the trend of high integrityization has appearred in flight control system and avionics system.The modern high performance aircraft is had higher requirement to flight control system, uses classic control theory advanced design aircraft flight controlling system more and more difficult; In order to obtain better flight quality, many modern control method are applied in the design of aircraft flight control system, recover (LQR/LQG/LTR) method, Quantitative Feedback method, dynamic inversion, feedback linearization method, contragradience control method, sliding mode variable structure control method etc. as linear quadratic type regulator/linear quadratic type Gaussian function/circuit transmission; These methods need aircraft mathematical model accurately, yet dummy vehicle is a very complicated non-linear differential equation, and people are difficult to obtain mathematical model accurately; On the engineering, model aircraft is all obtaining by wind tunnel experiment and flight test, also will consider following problem in the practical flight Control System Design: when (1) changed or exists structure uncertain at the aircraft parameter of setting up mathematical model, flight control system should have little sensitivity response; (2) because the controller frequency band is wideer, the influence that makes aeroplane performance changed by aircaft configuration and topworks's dynamic property relatively has little sensitivity response greatly; (3) though the design of feedback controller can obtain comparatively ideal response to pilot's instruction, may be destructive for the response of external disturbance; (4) there are fabrication tolerance in execution unit and control element, also have aging, wearing and tearing and phenomenons such as environment and service condition deterioration in system's operational process; (5) in actual engineering problem, to simplify artificially mathematical model usually, remove some complicated factors; For this reason, non-linear methods for designing such as non-linear H ∞ and the comprehensive robust control of μ also obtain extensive concern in the flight controller design; Said method, can access the control law structure and the parameter that only are suitable for certain basic flight reference, on this basis, need one by one the control law under the different flight state in the whole flight envelope to be designed, obtain being suitable for the control law structure and parameter of different flight state, and the adjustment parameter rule of utilizing diverse ways to carry out control law parameter and structure designs, and obtains a complete Flight Control Law that is suitable for whole envelope curve at last; Rely on above controller design method, the designer can not directly determine the stability at given flight range; Document " Hsien-Keng Chenand Ching-I Lee, Anti-control of chaos in rigid body motion, Chaos, Solitons ﹠amp; Fractals, 2004, Vol.21 (4): 957 – 965 " directly carried out phase plane analysis according to the general aerodynamic force of aircraft, moment expression formula, neither consider the aircraft type, do not consider aerodynamic derivative again; It is too far away that the paper method departs from reality, and the result who provides is not approved by people.

Summary of the invention

Can not guarantee deficiency in the flight of given flight range scope aircraft stability and safety in order to overcome the existing controller method for designing, the invention provides the wide adaptability design method of the three-dimensional flight range controller of a kind of aircraft, this method has been set up aircraft movements phase plane equation, this method is passed through aerodynamic force, momental equation obtains given control object height, aircraft during Mach number is the flat air-flow angle of attack and the trim rudder face of flying steadily, introduce the air-flow angle of attack, state feedback controllers such as yaw angle, adopt the phase plane analysis model to determine the Domain Stability of system, determine the parameter of feedback controller on this basis, directly three-dimensional motion is controlled to aircraft, incorrect being similar to such as aerodynamic force effect have been avoided ignoring in the momental equation, make controller can both guarantee the stability of aircraft, the instability that reduces even avoided analytical model to cause at whole design section, problems such as dangerous flight take place.

The technical solution adopted for the present invention to solve the technical problems: the wide adaptability design method of the three-dimensional flight range controller of a kind of aircraft is characterized in may further comprise the steps:

(1) according to the aircraft movements equation:

And aerodynamic moment equation:

$\left\{\begin{array}{c}\stackrel{\·}{p}=\frac{1}{I_x{I}_z-I_{\mathrm{zx}}^2}[I_z{C}_L(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})+I_{\mathrm{zx}}{C}_N(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})\\ +I_{\mathrm{zx}}(I_z+I_x-I_y)\mathrm{pq}+(I_y{I}_z-I_z^2-I_{\mathrm{zx}}^2)\mathrm{qr}]\\ \stackrel{\·}{q}=\frac{C_M(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β},\mathrm{\δ}})+(I_z-I_x)\mathrm{pr}+I_{\mathrm{zx}}(r^2-p^2)}{I_{\mathrm{yf}}}\\ \stackrel{\·}{r}=\frac{1}{I_x{I}_z-I_{\mathrm{zx}}^2}[I_{\mathrm{zx}}{C}_L(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})+I_x{C}_N(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})\\ +(I_x^2-I_x{I}_y+I_{\mathrm{zx}}^2)\mathrm{pq}+I_{\mathrm{zx}}(I_y-I_z-I_x)\mathrm{qr}]\end{array}\right.---\left(2\right)$

Wherein:

$+\left[\begin{array}{c}{L}_e(\mathrm{\α},\mathrm{\β}\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})\\ N_e(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})\\ M_e(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})\end{array}\right]$

Derived by Eulerian equation;

Obtain:

Wherein: $f_{\mathrm{\αq}}=1-\frac{\mathrm{QS}}{{\mathrm{mV}}_T}{f}_{q-\mathrm{\α}}(\mathrm{\α},\mathrm{\β},\mathrm{\δ})\sec \mathrm{\β}$

α is the air-flow angle of attack, and β is yaw angle, Be the angle of pitch,

Be roll angle, p is angular velocity in roll, and q is rate of pitch, and r is yaw rate, and g is acceleration of gravity, and δ comprises yaw rudder, aileron, elevating rudder, accelerator open degree, canard etc. at interior input vector, I _xBe the moment of inertia around axle x, I _yBe the moment of inertia around axle y, I _zBe the moment of inertia around axle z, I _Zx=I _XzBe product moment of inertia, V _TBe air speed,

$M_{\mathrm{p\α}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $M_{\mathrm{r\α}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $M_{\mathrm{q\α}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $M_e(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ})$ Be relevant longitudinal moment function expression, $L_{\mathrm{p\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $L_{\mathrm{r\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $L_{\mathrm{q\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $L_e(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $N_{\mathrm{p\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $N_{\mathrm{r\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $N_{\mathrm{q\β}}(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ $N_e(\mathrm{\α},\mathrm{\β},\stackrel{\·}{\mathrm{\α}},\stackrel{\·}{\mathrm{\β}},\mathrm{\δ}),$ Be relevant side force moment function expression formula, f _Q-α(α, β δ) are the longitudinal force function, f _P-β(α, β, δ), f _R-β(α, β δ) are the relevant function of side force, C _x(α, β, δ), C _y(α, β, δ), C _x(α, β δ) are respectively vertically, side direction, normal direction aerodynamic force, and Q, S, m represent aircraft dynamic pressure, wing area and quality respectively;

The phase plane equation is:

(4)

Will

Bring (4) formula into, and arrangement can get

In the formula:

I, j=1,2,3 is to exist according to (4), (5) formula

Cancellation p in the expression formula, capable, the j column element of i of the matrix function that q, r obtain; ;

At p=0, r=0, q=0,

The equilibrium point δ of the yaw angle of the trim rudder face when determining control object height, Mach number under the condition, the air-flow angle of attack, given radius of turn sustained turn _s, α _s, β _s

(2) choosing the feedback controller expression formula is:

δ=δ ₀+k(α,β,p,r,q)

Satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _s

Wherein: δ ₀Be the constant value of rudder face input, and k (α, β, p, r q) is the FEEDBACK CONTROL function;

(3) in given flight range, adopt following phase plane analysis model:

The analytic system convergence obtains the constraint condition away from saddle point:

$\left[\begin{array}{ccc}{f}_{11}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{12}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{13}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{21}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{22}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{23}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{31}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{32}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{33}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\end{array}\right]<0,$

f _αa(·)<0，f _βa(·)<0

According to convergence index and equilibrium point condition: satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _sThe common parameter of determining feedback controller.

The invention has the beneficial effects as follows: the equilibrium point when obtaining given control object height and Mach number by aerodynamic force, momental equation, adopt the phase plane analysis model to determine the Domain Stability of system, determine the parameter of feedback controller on this basis, directly three-dimensional motion is controlled to aircraft, incorrect being similar to such as aerodynamic force effect have been avoided ignoring in the momental equation, make controller can both guarantee the stability of aircraft at whole design section, reduce even avoided problems such as the instability that analytical model causes, dangerous flight and take place.

Elaborate below in conjunction with the present invention of embodiment.

Embodiment

Be example with certain aircraft three-dimensional model.

(1) according to the aircraft movements equation:

Reach aerodynamic force, momental equation:

$\stackrel{\&CenterDot;}{p}=-1.02p-0.02322r-0.01859521\mathrm{\&beta;}+0.002145291{\mathrm{\&beta;}}^3-0.2232{\mathrm{\&delta;}}_x$

$\stackrel{\&CenterDot;}{r}=-0.02336p-0.92r-0.0323\mathrm{\&beta;}-0.1335{\mathrm{\&delta;}}_r$

$\stackrel{\&CenterDot;}{q}=-1.396q-4.208\mathrm{\&alpha;}-0.47{\mathrm{\&alpha;}}^2-3.564{\mathrm{\&alpha;}}^3-20.967{\mathrm{\&delta;}}_e+6.265{\mathrm{\&alpha;}}^2{\mathrm{\&delta;}}_e$

gn _y/V ₀=-0.01r-0.40226β+0.0236β ²-0.010221β ³-0.035δ _r

gn _z/V ₀=-0.877α+0.47α ²+3.846α ³-0.215δ _e

Obtain:

Wherein: $f_{\mathrm{\&alpha;q}}=1-\frac{\mathrm{QS}}{{\mathrm{mV}}_T}{f}_{q-\mathrm{\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\mathrm{\&delta;})\sec \mathrm{\&beta;}$

α is the air-flow angle of attack, and β is yaw angle,

Be the angle of pitch,

Be roll angle, p is angular velocity in roll, and q is rate of pitch, and r is yaw rate, and g is acceleration of gravity, and δ comprises yaw rudder, aileron, elevating rudder, accelerator open degree, canard etc. at interior input vector, I _xBe the moment of inertia around axle x, I _yBe the moment of inertia around axle y, I _zBe the moment of inertia around axle z, I _Zx=I _XzBe product moment of inertia, V _TBe air speed,

$M_{\mathrm{p\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_{\mathrm{r\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_{\mathrm{q\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})$ Be relevant longitudinal moment function expression, $L_{\mathrm{p\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_{\mathrm{r\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_{\mathrm{q\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{p\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{r\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{q\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})$ Be relevant side force moment function expression formula, f _Q-α(α, β δ) are the longitudinal force function, f _P-β(α, β, δ), f _R-β(α, β δ) are the relevant function of side force, C _x(α, β, δ), C _y(α, β, δ), C _x(α, β δ) are respectively vertically, side direction, normal direction aerodynamic force, and Q, S, m represent aircraft dynamic pressure, wing area and quality respectively;

The phase plane equation is:

(10)

Will

$\left[\begin{array}{c}\stackrel{\&CenterDot;}{p}\\ \stackrel{\&CenterDot;}{q}\\ \stackrel{\&CenterDot;}{r}\end{array}\right]=\left[\begin{array}{ccc}-1.02& -0.02322& 0\\ -0.02336& -0.92& 0\\ 0& 0& -1.396\end{array}\right]\left[\begin{array}{c}p\\ q\\ r\end{array}\right]+\left[\begin{array}{c}-0.01859521\mathrm{\&beta;}+0.002145291{\mathrm{\&beta;}}^3-0.2232{\mathrm{\&delta;}}_x\\ -0.0323\mathrm{\&beta;}-0.1335{\mathrm{\&delta;}}_r\\ -4.208\mathrm{\&alpha;}-0.47{\mathrm{\&alpha;}}^2-3.564{\mathrm{\&alpha;}}^3-20.967{\mathrm{\&delta;}}_e+6.265{\mathrm{\&alpha;}}^2{\mathrm{\&delta;}}_e\end{array}\right]---\left(11\right)$

And

Bring (10) formula into,, and arrangement can get

In the formula:

I, j=1,2,3 is to exist according to (4), (5) formula

Cancellation p in the expression formula, capable, the j column element of i of the matrix function that q, r obtain;

At p=0, r=0, q=0,

The equilibrium point δ of the yaw angle of the trim rudder face when determining control object height, Mach number under the condition, the air-flow angle of attack, given radius of turn sustained turn _s, α _s, β _s

(2) choosing the feedback controller expression formula is:

δ=δ ₀+k(α,β,p,r,q)

Satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _s

Wherein: δ ₀Be the constant value of rudder face input, and k (α, β, p, r q) is the FEEDBACK CONTROL function;

At p=0, r=0, q=0,

The equilibrium point δ of the yaw angle of the trim rudder face when determining control object height, Mach number under the condition, the air-flow angle of attack, given radius of turn sustained turn _s, α _s, β _s

Satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time,

$\begin{array}{c}-0.01859521\mathrm{\&beta;}+0.002145291{\mathrm{\&beta;}}^3-0.2232{\mathrm{\&delta;}}_x=0\\ -0.0323\mathrm{\&beta;}-0.1335{\mathrm{\&delta;}}_r=0\\ -4.208\mathrm{\&alpha;}-0.47{\mathrm{\&alpha;}}^2-3.564{\mathrm{\&alpha;}}^3-20.967{\mathrm{\&delta;}}_e+6.265{\mathrm{\&alpha;}}^2{\mathrm{\&delta;}}_e=0\end{array};$

(3) at given flight range -30 °≤α≤60 °, adopt following phase plane analysis model:

The analytic system convergence obtains the constraint condition away from saddle point:

$\left[\begin{array}{ccc}{f}_{11}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{12}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{13}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{21}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{22}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{23}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{31}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{32}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{33}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\end{array}\right]<0,$ f _αa(·)<0，f _βa(·)<0

According to convergence index and equilibrium point condition: satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, the analytic system convergence, according to convergence index and equilibrium point condition: satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _sThe parameter of common definite feedback controller is: δ _x=0.0961 β ³, δ _r=0, δ _e=-α ³/ (5.883-1.758 α ²), make whole flight range stable, guaranteed flight safety.

Claims (1)

1. the wide adaptability design method of the three-dimensional flight range controller of an aircraft is characterized in may further comprise the steps:

(1) according to the aircraft movements equation:

And aerodynamic moment equation:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{p}=\frac{1}{I_x{I}_z-I_{\mathrm{zx}}^2}[I_z{C}_L(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})+I_{\mathrm{zx}}{C}_N(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ +I_{\mathrm{zx}}(I_z+I_x-I_y)\mathrm{pq}+(I_y{I}_z-I_z^2-I_{\mathrm{zx}}^2)\mathrm{qr}]\\ \stackrel{\&CenterDot;}{q}=\frac{C_M(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;},\mathrm{\&delta;}})+(I_z-I_x)\mathrm{pr}+I_{\mathrm{zx}}(r^2-p^2)}{I_{\mathrm{yf}}}\\ \stackrel{\&CenterDot;}{r}=\frac{1}{I_x{I}_z-I_{\mathrm{zx}}^2}[I_{\mathrm{zx}}{C}_L(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})+I_x{C}_N(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ +(I_x^2-I_x{I}_y+I_{\mathrm{zx}}^2)\mathrm{pq}+I_{\mathrm{zx}}(I_y-I_z-I_x)\mathrm{qr}]\end{array}\right.---\left(2\right)$

Wherein:

$+\left[\begin{array}{c}{L}_e(\mathrm{\&alpha;},\mathrm{\&beta;}\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ N_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ M_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\end{array}\right]$

Derived by Eulerian equation;

Obtain:

Wherein: $f_{\mathrm{\&alpha;q}}=1-\frac{\mathrm{QS}}{{\mathrm{mV}}_T}{f}_{q-\mathrm{\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\mathrm{\&delta;})\sec \mathrm{\&beta;}$

α is the air-flow angle of attack, and β is yaw angle,

Be the angle of pitch,

Be roll angle, p is angular velocity in roll, and q is rate of pitch, and r is yaw rate, and g is acceleration of gravity, and δ comprises yaw rudder, aileron, elevating rudder, accelerator open degree, canard etc. at interior input vector, I _xBe the moment of inertia around axle x, I _yBe the moment of inertia around axle y, I _zBe the moment of inertia around axle z, I _Zx=I _XzBe product moment of inertia, V _TBe air speed,

$M_{\mathrm{p\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_{\mathrm{r\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_{\mathrm{q\&alpha;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $M_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})$ Be relevant longitudinal moment function expression, $L_{\mathrm{p\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_{\mathrm{r\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_{\mathrm{q\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $L_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{p\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{r\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_{\mathrm{q\&beta;}}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;}),$ $N_e(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})$ Be relevant side force moment function expression formula, f _Q-α(α, β δ) are the longitudinal force function, f _P-β(α, β, δ), f _R-β(α, β δ) are the relevant function of side force, C _x(α, β, δ), C _y(α, β, δ), C _x(α, β δ) are respectively vertically, side direction, normal direction aerodynamic force, and Q, S, m represent aircraft dynamic pressure, wing area and quality respectively;

The phase plane equation is:

(4)

Will

Bring (4) formula into, and arrangement can get

In the formula:

I, j=1,2,3 is to exist according to (4), (5) formula

Cancellation p in the expression formula, capable, the j column element of i of the matrix function that q, r obtain; ;

At p=0, r=0, q=0,

The equilibrium point δ of the yaw angle of the trim rudder face when determining control object height, Mach number under the condition, the air-flow angle of attack, given radius of turn sustained turn _s, α _s, β _s

(2) choosing the feedback controller expression formula is:

δ=δ ₀+k(α,β,p,r,q)

Satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _s

Wherein: δ ₀Be the constant value of rudder face input, and k (α, β, p, r q) is the FEEDBACK CONTROL function;

(3) in given flight range, adopt following phase plane analysis model:

The analytic system convergence obtains the constraint condition away from saddle point:

$\left[\begin{array}{ccc}{f}_{11}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{12}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{13}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{21}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{22}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{23}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\\ f_{31}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{32}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})& f_{33}(\mathrm{\&alpha;},\mathrm{\&beta;},\stackrel{\&CenterDot;}{\mathrm{\&alpha;}},\stackrel{\&CenterDot;}{\mathrm{\&beta;}},\mathrm{\&delta;})\end{array}\right]<0,$

f _αa(·)<0，f _βa(·)<0

According to convergence index and equilibrium point condition: satisfy condition: p=0, r=0, q=0,

α=α _s, β=β _sThe time, δ=δ _sThe common parameter of determining feedback controller.