飞行控制系统设计.docx
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飞行控制系统设计
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一、对最简单的角位移系统的评价
1、某低速飞机本身具有较好的短周期阻尼,采用这种简单的控制规律是可行的。
它的传递函数为:
openp3_6
系统根轨迹为:
nem1=-12.5;
den1=[112.5];
sys1=tf(nem1,den1);
nem2=[-1-3.1];
den2=[12.83.240];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
随着k的增大,该系统的一对闭环复极点的震荡阻尼逐渐减小。
但由于飞机本身的阻尼较大,所以当k增大致1.34时,系统的震荡阻尼比仍有0.6。
k增大到6.2时系统才开始不稳定。
2、现代高速飞机的短周期运动自然阻尼不足,若仍采用上述单回路控制系统则不能胜任自动控制飞机的要求。
openp3_10
系统根轨迹为:
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.30];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
随着k增大,系统阻尼迅速下降。
当k=1.06时,处于临界稳定。
所以无法选择合适的k值以满足系统动静态性能。
为了使系统在选取较大的k值基础上仍有良好的动态阻尼,引入俯仰角速度反馈。
二、具有俯仰角速率反馈的角位移自动驾驶仪参数设计
openp3_16
1、系统内回路根轨迹为:
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
按物理概念似乎速率陀螺的作用越强,阻尼效果越显著。
但根轨迹分析告诉我们,只有在一定范围内这种概念才是正确的,否则会得到相反的效果。
这种现象是由舵回路的惯性造成的。
舵回路具有不同时间常数时的内回路根轨迹图:
Tδ=0
sys1=-1;
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
Tδ=0.1
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
Tδ=0.25
nem1=-4;
den1=[14];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
rlocus(sys)
结论:
1)、为了确保角稳定回路的性能,不能单纯地增加速率陀螺信号强度,必须同时设法减小舵回路的惯性,使舵回路具有足够宽的通频带。
2)、一般舵回路时间常数限制在0.03~0.1秒内,接近飞机自然频率的5倍。
这就是舵回路频带一般比飞行器的频带宽3至5倍的理由。
2、角稳定回路的设计
系统角稳定回路根轨迹为:
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0);
sys3=tf([1],[10]);
sys=series(sys,sys3);
figure
rlocus(sys)
holdon
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0.4);
sys3=tf([1],[10]);
sys=series(sys,sys3);
rlocus(sys)
holdon
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0.7);
sys3=tf([1],[10]);
sys=series(sys,sys3);
rlocus(sys)
holdon
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,1.3);
sys3=tf([1],[10]);
sys=series(sys,sys3);
rlocus(sys)
holdon
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,1.56);
sys3=tf([1],[10]);
sys=series(sys,sys3);
rlocus(sys)
比较:
与的选值关系。
=0
=0.4
=0.7
=1.3
=1.56
0.6
无
0.14
1.08
1.9
无
0
1.06
5.2
8.7
11.6
17.3
系统选不同的与值时的阶跃响应图:
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0);
sys3=tf([1],[10]);
sys4=tf([1.06]);
sys=series(sys,sys3);
sys=series(sys,sys4);
sys13=feedback(sys,1);
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0.4);
sys3=tf([1],[10]);
sys4=tf([0.14]);
sys=series(sys,sys3);
sys=series(sys,sys4);
sys14=feedback(sys,1);
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,0.7);
sys3=tf([1],[10]);
sys4=tf([1.08]);
sys=series(sys,sys3);
sys=series(sys,sys4);
sys12=feedback(sys,1);
nem1=-10;
den1=[110];
sys1=tf(nem1,den1);
nem2=[-4.3-4.3*0.33];
den2=[10.613.3];
sys2=tf(nem2,den2);
sys=series(sys1,sys2);
sys=feedback(sys,1.3);
sys3=tf([1],[10]);
sys4=tf([1.9]);
sys=series(sys,sys3);
sys=series(sys,sys4);
sys11=feedback(sys,1);
step(sys11,sys12,sys13,sys14);
3、自动驾驶仪参数与飞机特性的关系:
用根轨迹法选择参数时,若要求一定的振荡阻尼比,参数与之间有这样的规律:
当所选择的较大时,才能得到较大的值,它们之间的比值存在一定的规律:
当参数与选得比较合理时,比值ωAP=/总是落在飞机短周期运动自然频率ωd的附近。
三、
ControlDesignUsingSimulink®
ThisdemonstrationillustrateshowtousetheControlSystemToolbox™andSimulink®ControlDesign™tointeractwithSimulinktodesignadigitalpitchcontrolfortheU.S.Navy'sF-14Tomcataircraft.Inthisexample,wewilldesignthecontrollertopermittheaircrafttooperateatahighangleofattackwithminimalpilotworkload.
Ourexampletakesyouthroughthefirstpassatdesigningadigitalautopilotforahighangleofattackcontroller.ToruneverythinginthisdemoyoumusthavetheControlSystemToolbox,SimulinkControlDesign,Simulink,andReal-TimeWorkshop®.Ifyoudon'thavealloftheseproducts,youcanstillrunportionsofthedemousingcellexecutionmodeoftheMATLAB®editor.
BelowisaSimulinkmodeloftheF-14.ThecontrolsystemsintheControllersblockcanbeswitchedinthemodeltoallowyoutoseetheanalogresponseandthentoswitchtoadesigncreatedusingtheControlSystemToolbox'sLinearTimeInvariant(LTI)objects.Acontrollerisalsoincludedthatisadiscreteimplementationoftheanalogdesignthatissimilartothealgorithmthatwouldgointoanon-boardflightcomputer.Takeafewmomentstoexplorethemodel.
Openthef14_digitalmodel
f14dat_digital;
f14_digital
sim('f14_digital');
Figure1:
SimulinkmodeloftheF-14flightcontrolsystem.
TrimandLinearization
ThemodelcanbelinearizedintheControlandEstimationToolsManagerlaunchedfromf14autopilotSimulinkmodel.IntheToolsmenu,selectControlDesign>LinearAnalysis.
WhentheControlandEstimationToolsManageropens,selectanoperatingpointandclicktheLinearizeModelbutton.AnLTIViewercanbecreatedshowingastepplotofthelinearization.TobrowsearoundtheLTIViewer,rightclickonthegraphwindowtoseeyouroptions.
ForhelptypehelpslcontrolorhelpltivieworlookattheControlSystemToolboxandSimulinkControlDesignproductdocumentation.
Openthef14autopilotmodel
apmdl='f14autopilot';
open_system(apmdl)
op=operpoint(apmdl);
io=getlinio(apmdl);
contap=linearize(apmdl,op,io)
a=
Alpha-sensorPitchRateLProportionalStickPrefil
Alpha-sensor-2.526000
PitchRateL0-4.14400
Proportional-1.710.9567010
StickPrefil000-10
b=
Stick(pt.1AlphaSensedqSensed(pt
Alpha-sensor010
PitchRateL001
Proportional00-0.8156
StickPrefil100
c=
Alpha-sensorPitchRateLProportionalStickPrefil
Sum(pt.1)2.986-1.67-3.864-17.46
d=
Stick(pt.1AlphaSensedqSensed(pt
Sum(pt.1)001.424
Continuous-timemodel.
Figure2:
Originalanalogautopilot.
LinearTime-Invariant(LTI)Systems
TherearethreetypesofLTIobjectsyoucanusetodevelopalinearmodel:
StateSpace(SS),TransferFunction(TF),andZero-Pole-Gain(ZPG)objects.
ThevariablecontapisaStateSpaceobject.Youcanthengetoneoftheothertypeswiththeothercommands.WhenyoucreatetheobjectinMATLAB,youcanmanipulateitusingoperationssuchas*,+,-,etc.Thisiscalled"overloading"theMATLABoperators.Trycreatinganobjectofyourownandseewhathappenswhenadding,multiplying,etc.withthecontapobject.
ToseeexactlywhatisstoredintheLTIobject,typeget(contap)orcontap.InputNameforexample.
contap=tf(contap);
contap=zpk(contap)
Zero/pole/gainfrominput"Stick(pt.1)"tooutput"Sum(pt.1)":
-17.46(s+2.213)
s(s+10)
Zero/pole/gainfrominput"AlphaSensed(pt.1)"tooutput"Sum(pt.1)":
2.9857(s+2.213)
s(s+2.526)
Zero/pole/gainfrominput"qSensed(pt.1)"tooutput"Sum(pt.1)":
1.424(s+2.971)(s+2.213)
s(s+4.144)
DiscretizedControllerUsingZero-OrderHold
NowtheLTIobjectwillbeusedtodesignthedigitalautopilotthatwillreplacetheanalogautopilot.TheanalogsystemiscodedintotheLTIobjectcalledcontap(CONtinuousAutoPilot).
Thefirstattemptatcreatingadigitalautopilotwilluseazero-orderholdwithasampletimeof0.1seconds.Notethatthediscreteobjectmaintainsthetype(ss,tf,orzpk).
ItisclearfromBodeplotbelowthatthesystemsdonotmatchinphasefrom3rad/sectothehalfsamplefrequency(theverticalblackline)forthepilotstickinputandtheangleofattacksensor.Thisdesignhaspoorerresponsethantheanalogsystem.GototheSimulinkmodelandstartthesimulation(makesureyoucanseethescopewindows).Whilethesimulationisrunning,double-clickthemanualswitchlabeledAnalogorDigital.
DoesthesimulationverifytheconclusionreachedbyinterpretingtheBodediagram?
discap=c2d(contap,0.1,'zoh');
get(discap)
bode(contap,discap)
z:
{1x3cell}
p:
{1x3cell}
k:
[-1.250.2941.42]
ioDelay:
[000]
DisplayFormat:
'roots'
Variable:
'z'
Ts:
0.1
InputDelay:
[3x1double]
OutputDelay:
0
InputName:
{3x1cell}
OutputName:
{'Sum(pt.1)'}
InputGroup:
[1x1struct]
OutputGroup:
[1x1struct]
Name:
''
Notes:
{}
UserData:
[]
Figure3:
BodediagramcomparinganalogandZOHcontrollers.
Tustin(Bilinear)Discretization
Nowtrydifferentconversiontechniques.YoucanusetheTustintransformation.Inthecommandwindowtypethecommandsabove.
Itshouldbeclearthatthesystemsstilldonotmatchinphasefrom3rad/sectothehalfsamplefrequency,theTustintransformationdoesbetter.ThesimulationusestheLTIobjectasitisdesigned.ToseehowtheobjectisusedlookintheControllerssubsystembyusingthebrowserorbydoubleclickingtheicon.TheLTIblockpicksupanLTIobjectfromtheworkspace.YoucanchangetheobjectnameusedintheblocktoanyLTIobjectintheworkspace.Tryusing"discap1",theTustindiscretizationoftheanalogdesign:
discap1=c2d(contap,0.1,'tustin');
bode(contap,discap,discap1)
Figure4:
Bodediagramcomparinganalo