CN103558843A

CN103558843A - Automatic amplitude modulation frequency scanning method for airplane servo elasticity frequency response test

Info

Publication number: CN103558843A
Application number: CN201310544419.9A
Authority: CN
Inventors: 蒲利东; 洪兆贵; 高怡宁
Original assignee: Xian Aircraft Design and Research Institute of AVIC
Current assignee: Xian Aircraft Design and Research Institute of AVIC
Priority date: 2013-11-05
Filing date: 2013-11-05
Publication date: 2014-02-05
Anticipated expiration: 2033-11-05
Also published as: CN103558843B

Abstract

The invention belongs to the field of airplane aeroelasticity tests, and relates to an airplane ground test scope, in particular to an automatic amplitude modulation frequency scanning method for an airplane servo elasticity frequency response test. Control plane overloads are fed back to automatically adjust a frequency scanning amplitude value, on the premise that safety of a control pane structure is guaranteed, control plane deflection exciting force of all frequency scanning points is kept maximum so that sufficiently large airplane structure response can be excited, the signal to noise ratio of a response signal of an airplane-flight control combined circuit is improved, test errors are reduced, and reliability of a test result is improved. Meanwhile, the adjusting process of an excitation signal amplitude value is controlled through construction of a hyperbolic tangent-exponent function, violent response of a control plane caused by sudden changes of the excitation signal amplitude value is prevented from happening in the process of frequency scanning, and safety of the control plane structure is ensured. In addition, the advantages of a real-time simulation system of a computer are brought into full play, in the process of the test, people only need to slightly click a mouse, so that parameters such as control limit overloads and excitation signal cycles can be adjusted, and the automatic amplitude modulation frequency scanning method is high in practicability.

Description

Automatic amplitude modulation frequency sweeping method is tested in the servo elasticity frequency response of a kind of aircraft

Technical field:

The invention belongs to aircraft aeroelastic effect test field, relate to airplane ground test category, relate in particular to the servo elasticity frequency response of a kind of aircraft and test automatic amplitude modulation frequency sweeping method.

Background technology

When carrying out the servo elasticity frequency response test of aircraft floor, conventionally before actuator, inject constant amplitude frequency conversion sinusoidal excitation signal and drive control surface deflection, rely on the caused inertial force exciting of control surface deflection aircraft, airbornely fly to control sensor (accelerometer, angular rate gyroscope etc.) perception body vibration information by resolved output rudder inclined to one side instruction by control law, by measuring the inclined to one side instruction of flight control computer output rudder, obtain aircraft-fly to control the open loop Frequency Response of combined loop, the servo elastic stability nargin of aircraft is assessed.

For improving aircraft-fly to control response signal (the inclined to one side instruction output signal of the rudder) signal to noise ratio (S/N ratio) of combined loop, require to fly to control sensor on machine and produce enough large output, to guarantee that the inclined to one side instruction of rudder that feedback signal is generated after control law resolves is not fallen into oblivion by noise.Therefore in whole frequency sweep process, should remain that the inclined to one side exciting force of rudder is enough large.

Yet due to square being directly proportional of the inclined to one side inertial force of rudder and rudder face gyro frequency, while adopting constant amplitude swept-frequency signal, for guaranteeing that rudder face does not destroy near its intrinsic revolving mode frequency, in process of the test, to strictly limit swept-frequency signal amplitude, frequency sweep instruction is sometimes shortly past actuator instruction dead band.Therefore, in process of the test, part frequency sweep point rudder face exciting force is not enough, flies to control sensor output little on machine, tests resulting aircraft-fly to control combined loop response output signal-to-noise ratio poor, and test result error is large.

Summary of the invention

The object of the invention is to solve in the servo elasticity frequency response test of existing aircraft floor, adopt constant amplitude frequency conversion frequency sweeping method cannot guarantee rudder face structural safety and loop response Signal-to-Noise, the technical matters that error of test data is large simultaneously.

Technical solution of the present invention is as follows

At aircraft rudder surface trailing edge, arrange acceleration transducer, the flight control system backfeed loop of aircraft is disconnected between the inclined to one side instruction output end of flight control computer rudder and the comprehensive end of actuator forward direction instruction, and seal in real-time emulation system, in real-time emulation system, build automatic amplitude modulation frequency sweep realistic model, amplitude modulation frequency sweep realistic model comprises constant amplitude stepping sinusoidal excitation signal systematic function module, automatic amplitude-modulated signal systematic function module, loop dynamic property calculation functional module automatically; After constant amplitude stepping sinusoidal excitation signal generation module output signal I (t) multiplies each other with the signal w (t) that amplitude-modulated signal generation module is exported automatically, obtain amplitude modulation stepping sinusoidal excitation signal u (t), amplitude modulation stepping sinusoidal excitation signal u (t) road enters loop dynamic property calculation module, the comprehensive port of aircraft rudder surface actuator forward direction instruction is inputted, the acceleration sensor outputs signals a on aircraft rudder surface in another road after D/A conversion _δ(t) after A/D conversion, be transferred to automatic amplitude-modulated signal generation module, the inclined to one side command signal y of rudder (t) of the flight control computer output of aircraft is after A/D conversion, transfer to loop dynamic property calculation module, loop dynamic property calculation module is calculated the inclined to one side command signal y of rudder (t) of the amplitude modulation stepping sinusoidal excitation signal u (t) of input and flight control computer output, and by result of calculation output display; Wherein,

Constant amplitude stepping sinusoidal excitation signal generation module, at each frequency sweep point f _ithe cycle N of the pumping signal I (t) that place generates is not less than 10, that is:

I (t) = \{\begin{matrix} \sin 2 π f_{i} (t - T_{i}) & T_{i} \leq t \leq T_{i} + t_{i} \\ 0 & T_{i} + t_{i} < t < T_{i} + t_{i} + Δt \end{matrix}, i = 0,1,2 \cdot \cdot \cdot n

Wherein:

T_{0} = 0; T_{i} = i \cdot Δt + Σ_{j = 1}^{i} \frac{N}{f_{0} + (j - 1) \cdot Δf}, i = 1,2,3 \cdot \cdot \cdot n

t_{i} = \frac{N}{f_{0} + i \cdot Δf}, i = 0,1,2 \cdot \cdot \cdot n; f_{i} = f_{0} + i \cdot Δf, i = 0,1,2 \cdot \cdot \cdot n

F ₀for frequency sweep initial frequency, Δ f is frequency step, and n is that frequency sweep is counted, and N>=10 are the excitation signal cycle number at each frequency sweep point place, and Δ t is frequency sweep point f _icorresponding pumping signal end time and next frequency sweep point f _i+1pumping signal start time poor;

Amplitude-modulated signal w (t):

w (t) = \{\begin{matrix} {\bar{A}}_{0} \cdot th (\frac{5 f_{i} \cdot t}{2}) \cdot th (\frac{3 f_{i} \cdot t}{2}) \cdot {(\frac{f_{i} \cdot t}{2})}^{0.15} & T_{i} \leq t \leq T_{t} + \frac{2}{f_{i}} \\ {\bar{A}}_{0} & T_{i} + \frac{2}{f_{i}} < t \leq T_{i} + \frac{4}{f_{i}} \\ (A_{i} - {\bar{A}}_{0}) \cdot th (\frac{5 f_{i} \cdot t}{3}) \cdot {th (\frac{3 f_{i} \cdot t}{3}) \cdot (\frac{f_{i} \cdot t}{3})}^{0.15} + {\bar{A}}_{0} & T_{i} + \frac{4}{f_{i}} < t \leq T_{i} + \frac{7}{f_{i}} \\ A_{i} & T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}} \end{matrix}

i＝0,1,2…n

Wherein:

{\bar{A}}_{0} = 1.15 δ_{D}

A_{i} = \{\begin{matrix} {\bar{A}}_{0} & a_{i}^{{1.15 δ}_{D}} &GreaterEqual; a_{δ}^{L} \\ \min (\frac{a_{δ}^{L}}{a_{i}^{{1.15 δ}_{D}}} {\bar{A}}_{0}, \frac{δ_{\max}}{k_{δ}}) & a_{i}^{{1.15 δ}_{D}} < a_{δ}^{L} \end{matrix}

K in formula _δfor the conversion coefficient between actuator input instruction and rudder face drift angle, δ _dactuator instruction dead band threshold value,

for ground surface servo elasticity test rudder face restriction drift angle,

to take frequency as f _i, amplitude is

sinusoidal signal drive the caused rudder face maximum overload of control surface deflection;

For each frequency sweep point f _i, within 1st～2 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t), with tanh-exponential function form, increases to from zero

within 3rd～4 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t) keeps

constant; Within 5th～7 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t) is with tanh-exponential function form, from increase to A _i; Wherein, if interior rudder face maximum overload of 3rd～4 cycles

be greater than rudder face limiting overload

?

if rudder face maximum overload in 3rd～4 cycles

be less than rudder face limiting overload

and

be less than rudder face restriction drift angle

corresponding actuator instruction

?

otherwise

at the 8th～N of pumping signal, in the cycle, the amplitude of amplitude-modulated signal w (t) keeps A _iconstant;

Constant amplitude stepping sinusoidal excitation signal I (t) and amplitude-modulated signal w (t) multiply each other, and obtain amplitude modulation stepping sinusoidal excitation signal u (t),

\begin{matrix} u (t) = I (t) \cdot w (t) \\ = \{\begin{matrix} {\bar{A}}_{0} \cdot th (\frac{5 f_{i} \cdot t}{2}) \cdot th (\frac{3 f_{i} \cdot t}{2}) \cdot {(\frac{f_{i} \cdot t}{2})}^{0.15} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} < t \leq T_{i} + \frac{2}{f_{i}} \\ {\bar{A}}_{0} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{2}{f_{i}} < t \leq T_{i} + \frac{4}{f_{i}} \\ [(A_{i} - {\bar{A}}_{0}) \cdot th (\frac{5 f_{i} \cdot t}{3}) \cdot th (\frac{3 f_{i} \cdot t}{3}) \cdot {(\frac{f_{i} \cdot t}{3})}^{0.15} + {\bar{A}}_{0}] \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{4}{f_{i}} < t \leq T_{i} + \frac{7}{f_{i}} \\ A_{i} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}} \\ 0 & T_{i} + \frac{N}{f_{i}} < t < T_{i} + \frac{N}{f_{i}} + Δt \end{matrix} \end{matrix}

i＝0,1,2…n

To each frequency sweep point f _ithe inclined to one side command signal y of rudder (t) of the amplitude modulation stepping sinusoidal excitation signal u (t) after loop dynamic property calculation module synchronous acquisition in N-7 time cycle and flight control computer output, respectively the inclined to one side command signal y of rudder (t) of amplitude modulation stepping sinusoidal excitation signal u (t) and flight control computer output is carried out to Fourier transform, the inclined to one side command signal F[y of rudder (t) after Fourier transform] with pumping signal F[u (t)] be divided by, obtain aircraft-fly to control combined loop to put f in frequency sweep _idynamic perfromance G (the i ω at place _i)

G ({iω}_{i}) = \frac{F [y (t)]}{F [u (t)]}, T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}}, i = 0,1,2 \cdot \cdot \cdot n

And by G (i ω _i) output display.

Advantage and beneficial effect that the present invention has are: by feedback rudder face overload, automatically adjust frequency sweep amplitude, guaranteeing under the prerequisite of rudder face structural safety, make the extreme force retaining maximum of shaking of rudder at all frequency sweep points place, to have encouraged enough large aircaft configuration response, improve aircraft-fly to control combined loop response signal signal to noise ratio (S/N ratio), reduce test error, the reliability of lifting test result; Meanwhile, by structure tanh-exponential function, control excitation signal amplitude adjustment process, avoid because excitation signal amplitude suddenlys change, causing that rudder face acutely responds in frequency sweep process, guarantee rudder face structural safety; In addition, give full play to the advantage of Computer real time simulation system, the just parameter such as capable of regulating rudder face limiting overload and excitation signal cycle of only need clicking the mouse slightly, strong adaptability in process of the test.

Accompanying drawing explanation

Fig. 1 is constant amplitude stepping sinusoidal excitation signal I of the present invention (t);

Fig. 2 is the automatic amplitude-modulated signal w of the present invention (t);

Fig. 3 is amplitude modulation stepping sinusoidal excitation signal u of the present invention (t);

Fig. 4 is the automatic amplitude modulation frequency sweep of the present invention theory diagram.

Embodiment

1, at aircraft rudder surface trailing edge, arrange acceleration transducer;

2, the flight control system backfeed loop of aircraft is disconnected between the inclined to one side instruction output end of flight control computer rudder and the comprehensive end of actuator forward direction instruction, and seal in real-time emulation system;

3, in real-time emulation system, build automatic amplitude modulation frequency sweep realistic model, amplitude modulation frequency sweep realistic model comprises constant amplitude stepping sinusoidal excitation signal systematic function module, automatic amplitude-modulated signal systematic function module, loop dynamic property calculation functional module automatically;

With reference to Fig. 1, constant amplitude stepping sinusoidal excitation signal module, at each frequency sweep point f _ithe cycle N of the pumping signal I (t) that place generates is not less than 10, that is:

I (t) = \{\begin{matrix} \sin 2 π f_{i} (t - T_{i}) & T_{i} \leq t \leq T_{i} + t_{i} \\ 0 & T_{i} + t_{i} < t < T_{i} + t_{i} + Δt \end{matrix}, i = 0,1,2 \cdot \cdot \cdot n

Wherein:

T_{0} = 0; T_{i} = i \cdot Δt + Σ_{j = 1}^{i} \frac{N}{f_{0} + (j - 1) \cdot Δf}, i = 1,2,3 \cdot \cdot \cdot n

t_{i} = \frac{N}{f_{0} + i \cdot Δf}, i = 0,1,2 \cdot \cdot \cdot n; f_{i} = f_{0} + i \cdot Δf, i = 0,1,2 \cdot \cdot \cdot n

With reference to Fig. 2 and Fig. 4, the acceleration sensor outputs signals a on aircraft rudder surface _δ(t) after A/D conversion, be transferred to automatic amplitude-modulated signal generation module, amplitude-modulated signal generation module is adjusted signal amplitude at each frequency sweep point place automatically according to rudder face overload automatically, generates automatic amplitude-modulated signal w (t):

w (t) = \{\begin{matrix} {\bar{A}}_{0} \cdot th (\frac{5 f_{i} \cdot t}{2}) \cdot th (\frac{3 f_{i} \cdot t}{2}) \cdot {(\frac{f_{i} \cdot t}{2})}^{0.15} & T_{i} \leq t \leq T_{t} + \frac{2}{f_{i}} \\ {\bar{A}}_{0} & T_{i} + \frac{2}{f_{i}} < t \leq T_{i} + \frac{4}{f_{i}} \\ (A_{i} - {\bar{A}}_{0}) \cdot th (\frac{5 f_{i} \cdot t}{3}) \cdot {th (\frac{3 f_{i} \cdot t}{3}) \cdot (\frac{f_{i} \cdot t}{3})}^{0.15} + {\bar{A}}_{0} & T_{i} + \frac{4}{f_{i}} < t \leq T_{i} + \frac{7}{f_{i}} \\ A_{i} & T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}} \end{matrix}

i＝0,1,2…n

{\bar{A}}_{0} = 1.15 δ_{D}

A_{i} = \{\begin{matrix} {\bar{A}}_{0} & a_{i}^{{1.15 δ}_{D}} &GreaterEqual; a_{δ}^{L} \\ \min (\frac{a_{δ}^{L}}{a_{i}^{{1.15 δ}_{D}}} {\bar{A}}_{0}, \frac{δ_{\max}}{k_{δ}}) & a_{i}^{{1.15 δ}_{D}} < a_{δ}^{L} \end{matrix}

In formula:

K _δfor the conversion coefficient between actuator input instruction and rudder face drift angle,

δ _dactuator instruction dead band threshold value,

for ground surface servo elasticity test rudder face restriction drift angle,

rudder face limiting overload,

to take frequency as f _i, amplitude is

constant; Within 5th～7 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t) is with tanh-exponential function form, from

increase to A _i; Wherein, if interior rudder face maximum overload of 3rd～4 cycles

be greater than rudder face limiting overload ?

if rudder face maximum overload in 3rd～4 cycles

be less than rudder face limiting overload

and be less than rudder face restriction drift angle corresponding actuator instruction

? otherwise

4,, with reference to Fig. 3 and Fig. 4, constant amplitude stepping sinusoidal excitation signal generation module output signal I (t) obtains amplitude modulation stepping sinusoidal excitation signal u (t), that is: after multiplying each other with automatic amplitude-modulated signal generation module output signal w (t)

\begin{matrix} u (t) = I (t) \cdot w (t) \\ = \{\begin{matrix} {\bar{A}}_{0} \cdot th (\frac{5 f_{i} \cdot t}{2}) \cdot th (\frac{3 f_{i} \cdot t}{2}) \cdot {(\frac{f_{i} \cdot t}{2})}^{0.15} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} < t \leq T_{i} + \frac{2}{f_{i}} \\ {\bar{A}}_{0} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{2}{f_{i}} < t \leq T_{i} + \frac{4}{f_{i}} \\ [(A_{i} - {\bar{A}}_{0}) \cdot th (\frac{5 f_{i} \cdot t}{3}) \cdot th (\frac{3 f_{i} \cdot t}{3}) \cdot {(\frac{f_{i} \cdot t}{3})}^{0.15} + {\bar{A}}_{0}] \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{4}{f_{i}} < t \leq T_{i} + \frac{7}{f_{i}} \\ A_{i} \cdot \sin 2 π f_{i} (t - T_{i}) & T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}} \\ 0 & T_{i} + \frac{N}{f_{i}} < t < T_{i} + \frac{N}{f_{i}} + Δt \end{matrix} \end{matrix}

i＝0,1,2…n

5, with reference to Fig. 3 and Fig. 4, amplitude modulation stepping sinusoidal excitation signal u (t) road enters loop dynamic property calculation module, and another road is inputted the instruction of aircraft rudder surface actuator forward direction and comprehensively held after D/A conversion

6, the inclined to one side command signal y of rudder (t) of the flight control computer of aircraft output, after A/D conversion, transfers to loop dynamic property calculation module

7, to each frequency sweep point f _ithe inclined to one side command signal y of rudder (t) of the amplitude modulation stepping sinusoidal excitation signal u (t) after loop dynamic property calculation module synchronous acquisition in N-7 time cycle and flight control computer output, respectively the inclined to one side command signal y of rudder (t) of amplitude modulation stepping sinusoidal excitation signal u (t) and flight control computer output is carried out to Fourier transform, the inclined to one side command signal F[y of rudder (t) after Fourier transform] with pumping signal F[u (t)] be divided by, obtain aircraft-fly to control combined loop to put f in frequency sweep _idynamic perfromance G (the i ω at place _i), that is:

G ({iω}_{i}) = \frac{F [y (t)]}{F [u (t)]}, T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}}, i = 0,1,2 \dots n

8, loop dynamic property calculation module is by aircraft-fly to control combined loop to put f in frequency sweep _idynamic perfromance result of calculation G (the i ω at place _i) output display.

Embodiment

1, at aircraft rudder surface trailing edge, arrange acceleration transducer;

2,, with reference to Fig. 4, the flight control system backfeed loop of aircraft is disconnected between the inclined to one side instruction output end of flight control computer rudder and the comprehensive end of actuator forward direction instruction, and seal in real-time emulation system;

4, consult Fig. 4, the word content in contrast figure is described, and completes constant amplitude stepping sinusoidal excitation signal generation module, the transmission of the signal between amplitude-modulated signal generation module, loop dynamic property calculation module connection automatically;

5, consult Fig. 4, the word content of contrast in figure described, and completes that real-time emulation system is comprehensively held with the inclined to one side instruction output end of flight control computer rudder, the instruction of actuator forward direction, the signal between rudder face accelerometer transmits and be connected;

6, complete parameter setting: original frequency f ₀=1Hz, frequency step Δ f=0.1Hz, the frequency sweep n=90 that counts, the excitation signal cycle at each frequency sweep point place is counted N=10, above sweeps frequency f _icorresponding pumping signal end time and next frequency sweep point f _i+1corresponding pumping signal start time interval of delta t=2s; Conversion coefficient k between actuator input instruction and rudder face drift angle _δ=2.5, rudder face limiting overload

rudder face restriction drift angle

actuator instruction dead band threshold voltage value δ _d=0.04V;

7, start frequency sweep, for frequency sweep point f ₀, the amplitude of pumping signal u (t) within 3rd～4 cycles is

rudder face trailing edge maximum overload

due to the rudder face trailing edge maximum overload in 3rd～4 cycles

therefore the amplitude of pumping signal u (t) within 5th～7 cycles by

with tanh-exponential function form, increase to

the amplitude of pumping signal u (t) within 8th～10 cycles keeps A ₀=5.111V is constant; The inclined to one side command signal y of rudder (t) of the amplitude modulation stepping sinusoidal excitation signal u (t) after loop dynamic property calculation module synchronous acquisition in 3 time cycles and flight control computer output, calculates frequency sweep point f ₀aircraft-fly to control combined loop dynamic perfromance G (the i ω at place ₀)

8, successively to frequency sweep point f _i(f _i=f ₀+ i Δ f=1.0+0.1i, i=1,2,3 ... 90) carry out frequency sweep, obtain loop dynamic performance data G (the i ω at corresponding frequency sweep point place _i)

9, record and analysis circuit dynamic characteristic test result, as required, reset correlation parameter, revision test.

Claims

1. automatic amplitude modulation frequency sweeping method is tested in the servo elasticity frequency response of aircraft, it is characterized in that, at aircraft rudder surface trailing edge, arrange acceleration transducer, the flight control system backfeed loop of aircraft is disconnected between the inclined to one side instruction output end of flight control computer rudder and the comprehensive end of actuator forward direction instruction, and seal in real-time emulation system, in real-time emulation system, build automatic amplitude modulation frequency sweep realistic model, amplitude modulation frequency sweep realistic model comprises constant amplitude stepping sinusoidal excitation signal systematic function module, automatic amplitude-modulated signal systematic function module, loop dynamic property calculation functional module automatically; After constant amplitude stepping sinusoidal excitation signal generation module output signal I (t) multiplies each other with the signal w (t) that amplitude-modulated signal generation module is exported automatically, obtain amplitude modulation stepping sinusoidal excitation signal u (t), amplitude modulation stepping sinusoidal excitation signal u (t) road enters loop dynamic property calculation module, the comprehensive port of aircraft rudder surface actuator forward direction instruction is inputted, the acceleration sensor outputs signals a on aircraft rudder surface in another road after D/A conversion _δ(t) after A/D conversion, be transferred to automatic amplitude-modulated signal generation module, the inclined to one side command signal y of rudder (t) of the flight control computer output of aircraft is after A/D conversion, transfer to loop dynamic property calculation module, loop dynamic property calculation module is calculated the inclined to one side command signal y of rudder (t) of the amplitude modulation stepping sinusoidal excitation signal u (t) of input and flight control computer output, and by result of calculation output display; Wherein,

I (t) = \{\begin{matrix} \sin 2 π f_{i} (t - T_{i}) & T_{i} \leq t \leq T_{i} + t_{i} \\ 0 & T_{i} + t_{i} < t < T_{i} + t_{i} + Δt \end{matrix}, i = 0,1,2 \cdot \cdot \cdot n

Wherein:

T_{0} = 0; T_{i} = i \cdot Δt + Σ_{j = 1}^{i} \frac{N}{f_{0} + (j - 1) \cdot Δf}, i = 1,2,3 \cdot \cdot \cdot n

t_{i} = \frac{N}{f_{0} + i \cdot Δf}, i = 0,1,2 \cdot \cdot \cdot n; f_{i} = f_{0} + i \cdot Δf, i = 0,1,2 \cdot \cdot \cdot n

Amplitude-modulated signal w (t):

w (t) = \{\begin{matrix} {\bar{A}}_{0} \cdot th (\frac{5 f_{i} \cdot t}{2}) \cdot th (\frac{3 f_{i} \cdot t}{2}) \cdot {(\frac{f_{i} \cdot t}{2})}^{0.15} & T_{i} \leq t \leq T_{t} + \frac{2}{f_{i}} \\ {\bar{A}}_{0} & T_{i} + \frac{2}{f_{i}} < t \leq T_{i} + \frac{4}{f_{i}} \\ (A_{i} - {\bar{A}}_{0}) \cdot th (\frac{5 f_{i} \cdot t}{3}) \cdot {th (\frac{3 f_{i} \cdot t}{3}) \cdot (\frac{f_{i} \cdot t}{3})}^{0.15} + {\bar{A}}_{0} & T_{i} + \frac{4}{f_{i}} < t \leq T_{i} + \frac{7}{f_{i}} \\ A_{i} & T_{i} + \frac{7}{f_{i}} < t \leq T_{i} + \frac{N}{f_{i}} \end{matrix}

i＝0,1,2…n

Wherein:

{\bar{A}}_{0} = 1.15 δ_{D}

A_{i} = \{\begin{matrix} {\bar{A}}_{0} & a_{i}^{{1.15 δ}_{D}} &GreaterEqual; a_{δ}^{L} \\ \min (\frac{a_{δ}^{L}}{a_{i}^{{1.15 δ}_{D}}} {\bar{A}}_{0}, \frac{δ_{\max}}{k_{δ}}) & a_{i}^{{1.15 δ}_{D}} < a_{δ}^{L} \end{matrix}

for ground surface servo elasticity test rudder face restriction drift angle,

to take frequency as f _i, amplitude is sinusoidal signal drive the caused rudder face maximum overload of control surface deflection;

within 3rd～4 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t) keeps constant; Within 5th～7 cycles of pumping signal, the amplitude of amplitude-modulated signal w (t) is with tanh-exponential function form, from