CN102707624B - Design method of longitudinal controller region based on conventional aircraft model - Google Patents

Abstract

The invention discloses a design method of a longitudinal controller region based on a conventional aircraft model. The design method solves the technical problem that the traditional design method of the controller can not be used for directly determining overall integrity of a given flying region. According to the design method of the longitudinal controller region based on the conventional aircraft model, a balance point is obtained by using aerodynamic force and moment equation when height and Mach number of a control target are given; a regional stability of a system is determined by using a phase plane analysis model, parameters of a feedback controller are determined on the basis, and the longitudinal motion of an aircraft is controlled directly; incorrect approximations are avoided in the moment equation due to the neglects of aerodynamic action and lateral-directional flying influence, so that the controller can guarantee the stability of the aircraft in the whole design region and can be used for reducing and even avoiding the occurrences of problems of unstable and unsafe flying caused by the analysis model.

Description

Longitudinal controller zone design method based on aircraft conventional model

Technical field

The present invention relates to a kind of aircraft longitudinal controller method for designing, particularly a kind of longitudinal controller zone design method based on aircraft conventional model.

Background technology

The basic object that flight is controlled is to improve the stability and control of aircraft, thereby improves the ability of executing the task; In decades recently, along with improving constantly of aeroplane performance, flight control technology has a very large change, having occurred the advanced flight control technology such as active control technology, Comprehensive Control Technology, autonomous flight control technology, there is the trend of high integrity in flight control system and avionics system.Modern high performance aircraft is had higher requirement to flight control system, uses the flight control system of Classical control Theoretical Design Advanced Aircraft 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, as Linear-Quadratic Problem regulator/Linear-Quadratic-Gauss function/loop transfer recovery (LQR/LQG/LTR) method, Quantitative Feedback method, dynamic inversion, feedback linearization method, contragradience control method, sliding mode variable structure control method etc.; These methods all need aircraft mathematical model accurately, but dummy vehicle is a very complicated non-linear differential equation, and people are difficult to obtain mathematical model accurately; In engineering, model aircraft is all obtaining by wind tunnel experiment and flight test, in practical flight Control System Design, also to consider following problem: (1), in the time that the aircraft parameter of setting up mathematical model changes or exists structure uncertain, flight control system should have little sensitivity response; (2), because controller frequency band is wider, the impact that makes aeroplane performance changed by aircaft configuration and topworks's dynamic property relatively has little sensitivity response greatly; (3) although the design of feedback controller obtains comparatively ideal response to pilot's instruction meeting, may be destructive for the response of external disturbance; (4) there is fabrication tolerance in execution unit and control element, also has aging, wearing and tearing and the phenomenon such as environment and service condition deterioration in system operational process; (5) in Practical Project problem, conventionally to simplify artificially mathematical model, remove some complicated factors; For this reason, the Nonlinear Design method such as non-linear H ∞ and the comprehensive robust control of μ also obtains extensive concern in Flight Controller Design; Said method, can be only suitable for the control law structure and parameters of certain basic flight reference, on this basis, need to be successively to the design of control law under different flight state in whole flight envelope, 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, finally obtain a complete Flight Control Law that is suitable for whole envelope curve; Rely on above controller design method, 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; litons & Fractals; 2004; Vol.21 (4): 957-965 " has directly carried out phase plane analysis according to the general aerodynamic force of aircraft, moment expression formula, neither considers aircraft type, does not consider aerodynamic derivative again; It is too far away that paper method departs from reality, and the result providing is not approved by people.

Summary of the invention

Can not directly determine the deficiency of given flight range resistance to overturning in order to overcome existing controller method for designing, the invention provides a kind of longitudinal controller zone design method based on aircraft conventional model, the method is passed through aerodynamic force, momental equation obtains given control object height, aircraft when Mach number is the flat air-flow angle of attack and the trim rudder face of flying steadily, introduce the state feedback controllers such as the air-flow angle of attack, adopt the Domain Stability of phase plane analysis model determination system, determine on this basis the parameter of feedback controller, directly Flight Altitude Moving is controlled, Aerodynamic force action and the impact of horizontal course etc. are avoided ignoring in momental equation incorrect approximate, make controller can ensure the stability of aircraft at whole design section, reduce even avoided analytical model to cause unstable, the problems such as dangerous flight occur.

The technical solution adopted for the present invention to solve the technical problems: a kind of longitudinal controller zone design method based on aircraft conventional model, is characterized in comprising the following steps:

1, according to aerodynamic force, momental equation:

At q=0, equilibrium point δ while determining given control object height and Mach number _s, α _s;

In formula: q is rate of pitch, α is the air-flow angle of attack, and β is yaw angle, and υ is the angle of pitch, for roll angle, p is angular velocity in roll, and r is yaw rate, and δ comprises elevating rudder, accelerator open degree, canard etc. at interior input vector, and g is acceleration of gravity, I _xfor the moment of inertia around axle x, I _yfor the moment of inertia around axle y, I _xzfor product moment of inertia, V ₀for air speed, M _q, Z _q, f _q, f _αfor relevant function expression, δ _s, α _sthe flat peaceful air-flow angle of attack that flies of trim rudder face that flies while being respectively corresponding control object height, Mach number;

2, choosing feedback controller expression formula is:

δ=δ ₀+k(α，q，υ)

Satisfy condition: α=α _swhen q=0, δ=δ _s;

Wherein: δ ₀for the constant value of rudder face input, k (α, q, υ) is FEEDBACK CONTROL function to be determined;

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

Analytic system convergence, according to convergence index and equilibrium point condition: α=α _sq=0 and δ=δ _stime, δ=δ _sthe common parameter of determining feedback controller;

Wherein:

The invention has the beneficial effects as follows: the equilibrium point while obtaining given control object height and Mach number by aerodynamic force, momental equation, adopt the Domain Stability of phase plane analysis model determination system, determine on this basis the parameter of feedback controller, directly Flight Altitude Moving is controlled, Aerodynamic force action and the impact of horizontal course etc. are avoided ignoring in momental equation incorrect approximate, make controller can ensure the stability of aircraft at whole design section, reduce the problems such as even avoided that analytical model causes unstable, dangerous flight and occur.

Below in conjunction with embodiment, the present invention is elaborated.

Brief description of the drawings

Fig. 1 is the phase-plane diagram example of the inventive method, and in Fig. 1, horizontal ordinate is α, and unit is radian, and ordinate is unit is radian per second.

Embodiment

As an example of F-8 aircraft example, embodiment is described.

1, according to aerodynamic force, momental equation:

$\stackrel{\·}{\mathrm{\α}}=(1-0.088\mathrm{\α}-{\mathrm{\α}}^2)q-0.877\mathrm{\α}+0.47{\mathrm{\α}}^2+3.846{\mathrm{\α}}^3-0.215{\mathrm{\δ}}_e+0.28{\mathrm{\α}}^2{\mathrm{\δ}}_e+0.47{\mathrm{\δ}}_e^2\mathrm{\α}+0.63{\mathrm{\δ}}_e^3$

$\stackrel{\·}{q}=-0.396q-4.208\mathrm{\α}-0.47{\mathrm{\α}}^2-3.564{\mathrm{\α}}^3-20.967{\mathrm{\δ}}_e+6.265{\mathrm{\α}}^2{\mathrm{\δ}}_e+46{\mathrm{\δ}}_e^2+61.4{\mathrm{\δ}}_e^3$

Get q=0, time, can obtain non-linear algebraic equation group:

$0=-0.877\mathrm{\α}+0.47{\mathrm{\α}}^2+3.846{\mathrm{\α}}^3-0.215{\mathrm{\δ}}_e+0.28{\mathrm{\α}}^2{\mathrm{\δ}}_e+0.47{\mathrm{\δ}}_e^2\mathrm{\α}+0.63{\mathrm{\δ}}_e^3$

$0=-4.208\mathrm{\α}-0.47{\mathrm{\α}}^2-3.564{\mathrm{\α}}^3-20.967{\mathrm{\δ}}_e+6.265{\mathrm{\α}}^2{\mathrm{\δ}}_e+46{\mathrm{\δ}}_e^2+61.4{\mathrm{\δ}}_e^3$

Can determine the equilibrium point δ in the time that control target is current height and Mach number by this equation _es=0, α _s=0;

Wherein: δ _es, α _sthe flat peaceful air-flow angle of attack that flies in trim elevating rudder drift angle that flies while being respectively corresponding control object height, Mach number;

2, choosing feedback controller expression formula is:

δ _e=k ₀+k ₁α

Satisfy condition: α=α _swhen q=0, δ _e=δ _es;

3, at the initial value-0.5≤α of the given air-flow angle of attack and angle of attack derivative ₀≤ 0.5 radian, in flight range corresponding to radian per second, adopt following phase plane analysis model

$\frac{d^2\mathrm{\α}}{{\mathrm{dt}}^2}=d_0(-4.208\mathrm{\α}-0.47{\mathrm{\α}}^2-3.564{\mathrm{\α}}^3-20.967{\mathrm{\δ}}_e+6.265{\mathrm{\α}}^2{\mathrm{\δ}}_e+46{\mathrm{\δ}}_e^2+61.4{\mathrm{\δ}}_e^3)$

$-d_1(\stackrel{\·}{\mathrm{\α}}+0.877\mathrm{\α}-0.47{\mathrm{\α}}^2-3.846{\mathrm{\α}}^3+0.215{\mathrm{\δ}}_e-0.28{\mathrm{\α}}^2{\mathrm{\δ}}_e-0.47{\mathrm{\δ}}_e^2\mathrm{\α}-0.63{\mathrm{\δ}}_e^3)-0.877\stackrel{\·}{\mathrm{\α}}$ Analyze system

$+0.94\mathrm{\α}\stackrel{\·}{\mathrm{\α}}+11.538{\mathrm{\α}}^2\stackrel{.}{\mathrm{\α}}-0.215{\stackrel{\·}{\mathrm{\δ}}}_e+0.28{\mathrm{\α}}^2{\stackrel{\·}{\mathrm{\δ}}}_e+0.56\mathrm{\α}\stackrel{\·}{\mathrm{\α}}{\mathrm{\δ}}_e+0.47{\mathrm{\δ}}_e^2\stackrel{\·}{\mathrm{\α}}+0.94{\mathrm{\δ}}_e{\stackrel{\·}{\mathrm{\δ}}}_e\mathrm{\α}+1.89{\mathrm{\δ}}_e^2{\stackrel{\·}{\mathrm{\δ}}}_e$

System convergence, according to convergence index and equilibrium point condition: α=α _sq=0 and δ _e=δ _estime, the parameter of determining feedback controller is k ₀=0, k ₁=1/4.9826521, corresponding phase-plane diagram as shown in Figure 1; Wherein d ₀=1-0.088 α-α ², $d_1=0.396+\left[(0.088+2\mathrm{\α})\stackrel{\·}{\mathrm{\α}}\right]/(1-0.088\mathrm{\α}-{\mathrm{\α}}^2).$

From the phase-plane diagram of Fig. 1, at initial value-0.5≤α ₀≤ 0.5 radian, in the thru-flight region of radian per second, it is asymptotically stable that designed controller makes system, has reached the stable control effect of full flight range.

Claims (1)

1. the longitudinal controller zone design method based on aircraft conventional model, is characterized in that comprising the following steps:

(a) according to aerodynamic force, momental equation:

? equilibrium point δ while determining given control object height and Mach number _s, α _s;

In formula: q is rate of pitch, α is the air-flow angle of attack, and β is yaw angle, for the angle of pitch, for roll angle, p is angular velocity in roll, and r is yaw rate, and δ comprises elevating rudder, accelerator open degree, canard at interior input vector, and g is acceleration of gravity, I _xfor the moment of inertia around axle x, I _yfor the moment of inertia around axle y, I _xzfor product moment of inertia, V ₀for air speed, M _q, Z _q, f _q, f _αfor relevant function expression, δ _s, α _sthe flat peaceful air-flow angle of attack that flies of trim rudder face that flies while being respectively corresponding control object height, Mach number;

(b) choosing feedback controller expression formula is:

Satisfy condition: α=α _swhen q=0, δ=δ _s;

Wherein: δ ₀for the constant value of rudder face input, for FEEDBACK CONTROL function to be determined;

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

Analytic system convergence, according to convergence index and equilibrium point condition: α=α _sq=0 and δ=δ _stime, δ=δ _sthe common parameter of determining feedback controller;

Wherein: