iii. attitude hold autopilots. - cvut.cz · iii. attitude hold autopilots. ... alpha is...

III. Attitude hold autopilots.

Stabilization of aircraft pitch, roll and yaw angles. Multiloop SISO design approach. Proporional and integrating control laws.

Control

& aerospace applications

Stabilization of attitude angles: attitude hold autopilots

-

attitude-hold autopilots (stabilizers / reference trackers of pitch, roll

and yaw angles) are essential first-level automatic control (i.e. “lost pilot’s authority”

–

-

compare with dampers) loops of any FCS -

basic functionality of autopilots for piloted aircraft (for almost a century ☺)

as well as control systems for UAV’s

-

if the attitude-hold circuits (codes) work properly, all subsequent loops (VOR / GPS navigation, ILS, altitude select, vertical speed, ...) are easy to design

-

careful design of the autopilots is therefore essential (transients, rise times, robustness w.r.t. parameter changes and flight envelope variables, ...)

-

design approaches: nested SISO loops (with pre-designed separate dampers), or MIMO design (with integrated dampers functionality –

LQ control to be

discussed later, H2/Hinf synthesis etc.)

http://en.wikipedia.org/wiki/File:FMS_B747-cockpit.jpg


Pitch autopilot: signal diagram

A/C LONG

v

alpha

theta

q

K_damp

delta_TH

delta_EL fligh

t va

riabl

es

flight model

–K_AP–

pitch angle reference (by pilot

or higher-level controls – - vertical speed, altitude select, ...

K_alpha_limiter

Dead Zone

–

K_AP ... is just a gain (proportional controller) sufficient? How about PI controller ...


A remark on alpha feedback and statically unstable aircraft ...

-

the effect of decreasing stability margin of the LONG equations

can be illustrated by artificially introduced positive feedback alpha -> EL

-

simulates statically-unstable A/C: stabilization effect of the A/C (tail surfaces mainly) with alpha is insufficient. pitching moment curve has positive slope (for some alpha range). note the exponentially-unstable mode + 3rd

mode oscillation (“as fast as PHUG, as damped as SP”):

-

adversely: alpha-feedback is used to stabilize statically-unstable A/C (nowadays just fighters but who knows for future ... ☺). Reference: Stevens, Lewis, Aircraft control and


K_AP ... is just a gain (proportional controller) sufficient? How about PI controller ...

-

P controller (K = 2) green, PI controller ( K = 2*(1+0.1/s) ) blue. Step response.

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4From: In(1) To: theta

Step Response

Time (sec)

Ampl

itude

0 50 100 1500

0.2

0.4

0.6

0.8

1

1.2


Step Response

Time (sec)

Ampl

itude

-

similar situation for constant disturbance (try step to thrust input, simulating front/rear wind)

Pitch autopilot: proportional vs. PI control law


-

P controller (K = 2) green, PI controller ( K = 2*(1+0.1/s) ) blue. Step response

in thrust.

-

similar situation for constant disturbance (try step to thrust input, simulating front/rear wind)

0 20 40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25

0.3


Step Response

Time (sec)

Ampl

itude

Pitch autopilot: proportional vs. PI control law


-

pre-designed

pitch damper pre-determines, to considerble extent, achievable performance of the pitch-angle stabilizer (pitch autopilot) –

overshoot, settling time, gain/phase margins, ...

-

tedious re-designs of already computed controllers (pitch damper, in this case) are often required, during this loop-by-loop procedure, in order to achieve acceptable performance

-

K_damp = 0.5

K_damp = 1 (... well, best results I got ☺, for comparable maximum EL deflection and gain / phase margins)

-

this trouble can be avoided / reduced if advanced MIMO design procedures are used (e.g. LQ control)

Pitch autopilot: interaction with pitch damper


Bank (roll) autopilot: signal diagram

K_AP–

bank angle reference (by pilot

or higher-level controls – - turn / heading select, NAV / VOR / ILS, ...

K_AP ... is just a gain (proportional controller) sufficient? How about PI controller ... the same story ...

A/C LAT

K

delta_AIL

delta_RUD

flight model

–

beta

phi

psi

p

r

KWO

–


Bank (roll) autopilot: step response (in reference bank angle), P controller


Bank (roll) autopilot: step response (in reference bank angle), PI controller

Saturation


Yaw autopilot –

heading select: signal diagram

K_AP–

A/C LAT

K

delta_AIL

delta_RUD

flight model

–

beta

phi

psi

p

r

KWO

–K_AP

K


Yaw autopilot –

heading select

- two loops added on top of bank autopilot for coordinated (correct) turn

-

yaw-angle (heading) loop, giving setpoint for bank autopilot (mind the artificially added saturation to avoid excessive bank angles

for large yaw angle setpoint changes

-

beta stabilization –

for turn coordination (beta should be zero, assuring zero on-board side acceleration)

- roll angle and yaw rate are given for coordinated turn by the equation

(independent of A/C physical parameters competely ...)

-

the beta stabilizer has also other purposes –

landing at side-wind, OEI (one engine inoperative) flight, ...


Yaw autopilot: step response (in reference bank angle), PI controller

0 5 10 15 20 25 30 35 40 45 50-200

-150

-100

-50

0

50

time (s)

angl

e ( °

)

Stabilizace kurzu

φψβ

-

yaw-angle (heading) loop, giving setpoint for bank autopilot

-

artificially added saturation to avoid excessive bank angles for large yaw angle setpoint changes

- beta stabilization

-

P or PI ontrol? A bit tricky. -

REF vs. DIST ...

-

mind ainti-windup ...

iii. attitude hold autopilots. - cvut.cz · iii. attitude hold autopilots. ... alpha is...

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