Lecture #12 Aircraft Lateral Autopilots Multi-loop closure Heading Control: linear Heading control: nonlinear
Lecture # 12 Aircraft Lateral Autopilots • Multiloop closure • • Heading Control: linear Heading Control: nonlinear
Fa2004 16.33310-1 Lateral Autopilots We can stabilize/ modify the lateral dynamics using a variety of dif- ferent feedback architectures o Look for good sensor/ actuator pairings to achieve desired behavior e Example: Yaw damper Can improve the damping on the dutch-roll mode by adding a feedback on r to the rudder df=kr(rc-r) Servo dynamics Hr=3. 32added to rudder 8a=H. c 1618s3+0.7761s2+0.03007s+0.1883 +3.967s4+3.06s3+3.642s2+1.71s+0.01223 Lateral autopilot: r to rudder 050340.16 × Per Ave Figure 2: Lateral pole-zero map gser
Fall 2004 16.333 10–1 Lateral Autopilots • We can stabilize/modify the lateral dynamics using a variety of different feedback architectures. δa - -p 1 - φ s δr - Glat(s) -r 1 - ψ s • Look for good sensor/actuator pairings to achieve desired behavior. • Example: Yaw damper – Can improve the damping on the Dutchroll mode by adding a feedback on r to the rudder: δc = kr(rc − r) r 3.33 – Servo dynamics Hr = s+3.33 added to rudder δa = Hrδc r r – System: 1.618s3 + 0.7761s2 + 0.03007s + 0.1883 Gδr cr = −s5 + 3.967s4 + 3.06s3 + 3.642s2 + 1.71s + 0.01223 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0.94 0.86 0.76 0.64 0.5 0.34 0.16 3.5 0.76 0.985 0.64 0.5 0.34 0.16 1 0.86 0.94 0.985 3 2.5 2 1.5 0.5 Lateral autopilot: r to rudder Real Axis Imaginary Axis c r Figure 2: Lateral polezero map Gδ r
Fa2004 16.33310-2 Note that the gain of the plant is negative(Kplant<0), so if kr < 0, then K= kplanthr >0, so must draw a 180 locus(neg feedback ateral autopilot: r to8 with k>0 Lateral autopilot: r to 8 with k<0 Figure 3: Lateral pole-zero map. Definitely need kr <0 Root locus with hr <0 looks pretty good as we have authority over the four poles kr=-1.6 results in a large increase in the dutch-roll damping and spiral/roll modes have combined into a damped oscillation Yaw damper looks great, but this implementation has a problem There are various flight modes that require a steady yaw rate (ssf). For example, steady turning flight Our current yaw damper would not allow this to happen -it would create the rudder inputs necessary to cancel out the motion Exact opposite of what we want to have happen, which is to damp out any oscillations about the steady turn
� Fall 2004 16.333 10–2 • Note that the gain of the plant is negative (Kplant < 0), so if kr < 0, then K = Kplantkr > 0, so must draw a 180◦ locus (neg feedback) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 1 0.5 0.25 0.25 0.25 0.75 0.5 0.5 1 0.75 0.25 0.5 Lateral autopilot: r to δ r with k>0 Real Axis Imaginary Axis −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 1 0.25 0.5 0.25 0.5 0.75 0.25 0.5 0.75 Lateral autopilot: r to δ r with k<0 Real Axis Imaginary Axis Figure 3: Lateral polezero map. Definitely need kr < 0 • Root locus with kr < 0 looks pretty good as we have authority over the four poles. – kr = −1.6 results in a large increase in the Dutchroll damping and spiral/roll modes have combined into a damped oscillation. • Yaw damper looks great, but this implementation has a problem. – There are various flight modes that require a steady yaw rate (rss = 0). For example, steady turning flight. – Our current yaw damper would not allow this to happen – it would create the rudder inputs necessary to cancel out the motion !! – Exact opposite of what we want to have happen, which is to damp out any oscillations about the steady turn
Fa2004 16.33310-3 Yaw Damper Part 2 Can avoid this problem to some extent by filtering the feed back signal Feedback only a high pass version of the r signal High pass cuts out the low frequency content in the signal steady state value of r would not be fed back to the controller New yaw damper: 8c=kr(rc- Hu(sr)where Hu(s)=Tsi is the washout filt Washout filter with a4_2 Figure 4: Washout filter with T= 4. 2 New control picture k H2(s)
Fall 2004 16.333 10–3 Yaw Damper: Part 2 • Can avoid this problem to some extent by filtering the feedback signal. – Feedback only a high pass version of the r signal. – High pass cuts out the low frequency content in the signal ⇒ steady state value of r would not be fed back to the controller. • New yaw damper: δc = kr(rc − Hw(s)r) where Hw(s) = τs is the r τs+1 “washout” filter. 10−2 10−1 100 101 10−2 10−1 100 Washout filter with τ=4.2 |H w(s)| Freq (rad/sec) Figure 4: Washout filter with τ = 4.2 • New control picture δa p 1 φ - - - s Glat(s) δc rc r r 1 ψ - - H - - - kr r(s) – 6 s H w(s)
Fa2004 16.33310-4 Lateral autopilot: r to rudder WITH washout filter 025 0.75 O}0 0.5 Figure 5: Root Locus with the washout filter included Zero in Hu(s) traps a pole near the origin, but it is slow enough that it can be controlled by the pilot · Obviously has changed the closed loop pole locations(◆→√),but kr=-1.6 still seems to give a well damped response
Fall 2004 16.333 10–4 −2 −1.5 −1 −0.5 0 0.5 1 −1.5 −1 −0.5 0 0.5 1 1.5 0.5 0.25 0.5 0.75 0.75 0.25 1 0.5 0.25 Lateral autopilot: r to rudder WITH washout filter Real Axis Imaginary Axis Figure 5: Root Locus with the washout filter included. • Zero in Hw(s) traps a pole near the origin, but it is slow enough that it can be controlled by the pilot. • Obviously has changed the closed loop pole locations (� ⇒ �), but kr = −1.6 still seems to give a well damped response