Department of Engineering, Control & Instrumentation Research Group 22 – Mar – 2006 Optimisation Based Clearance of Nonlinear Flight Control Laws Prathyush P. Menon Jongrae Kim Declan G. Bates Ian Postlethwaite Control & Instrumentation Research Group, Department of Engineering, University of Leicester, Leicester LE1 7RH, UK.
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Department of Engineering, Control & Instrumentation Research Group 22 – Mar – 2006 Optimisation Based Clearance of Nonlinear Flight Control Laws Prathyush.
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Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Optimisation Based Clearance of
Nonlinear Flight Control Laws
Prathyush P. MenonJongrae Kim
Declan G. BatesIan Postlethwaite
Control & Instrumentation Research Group,Department of Engineering,
University of Leicester,Leicester LE1 7RH, UK.
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
•Nonlinear flight clearance
•A general optimisation framework
•Worst case uncertainty evaluation
•Clearance over regions of the flight envelope
•Worst case input identification
•Summary
Overview
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Nonlinear flight clearance
• Control algorithms usually designed based on linear models
• Robust performance over the whole flight envelope
• Controller gains are scheduled for the whole envelope
• How can we effectively
“clear” the controller
over the whole envelope?
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Nonlinear flight clearance
• Nonlinear flight clearance criterion – Based on time response, peak overshoot– AoA limit exceedance
• SecttJ 10));(max(
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Nonlinear flight clearance
•The uncertain parameters define a
multidimensional (dimension ‘l’) hyper box
•The worst case need not be at the vertices (max or min
values)
•Industry needs efficient, reliable and easily portable
methods
lΔ
• Problem becomes extremely computationally expensive
• Need efficient search methods to find “worst - case”
uncertain parameter combinations
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
ADMIRE model
• Dynamics …(1)
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
ADMIRE model
•Control algorithm …(2)
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
• ADMIRE
– Simulink model
– Long. controller scheduled over the flight envelope
– SAAB phase compensation rate limiter active
– Nonlinear stick shaping elements present
– Reference inputs limited to ±40 N (for this study)
– Uncertain parameters are bounded
ADMIRE model
AIRCRAFT MATHEMATICAL MODEL
u(t))h(x(t),y(t)
)w(t),u(t),f(x(t),(t)x
)Δ̂(t),yg(x(t),u(t) REF
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
General optimisation framework
The philosophy
JMax
Reference inputs Uncertain parameters
Mach AltitudeLevel Trim
Finite time history Optimisation
Algorithm
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Global Optimisation Schemes
•Several algorithms evaluated:
– Genetic algorithms (GA)
– Differential evolution (DE)
– Hybrid GA / Hybrid DE
– Dividing Rectangles (DIRECT)
Department of Engineering, Control & Instrumentation Research Group
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Flight envelope clearance
Mach [ 0.4 - 0.5 ]
Altitude [ 1000 - 4000 ]
Uncertainties same
as discussed earlier
Stick input now to 80N.
We apply Hybrid DE
scheme over the region
of flight envelope
Optimisation based clearance over a continuous region offlight envelope:
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Optimisation Performance
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Clearance Results
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Clearance Results
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Clearance Results
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Clearance Results
Worst case
Flight condition
P. P. Menon, J. Kim, D.G. Bates and I. Postlethwaite, ``Clearance of nonlinear flight control laws using hybrid evolutionary optimisation”, to appear in IEEE Transactions on Evolutionary Computation 2006
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Deterministic global optimisation
• Disadvantages of stochastic optimisation for flight clearance:
No guaranteed proof of convergence
Require statistical analysis of performance
Non-repeatability of results
• DIviding RECTangles (DIRECT) is a deterministic global
optimisation algorithm with a proof of convergence
• Initial results of application of this method for flight clearance
are very promising: P. P. Menon, D.G. Bates and I. Postlethwaite, ``A Hybrid Deterministic Optimisation Algorithm for Nonlinear Flight Clearance”, to appear in the proceedings of the American Control Conference, Boston, 2006
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Computation of worst-case pilot inputs
•Klonk inputs:
deg16.0038αmax
]t[tt,(t)y f0REF
Global Optimisation 12Xx(t)
Δ(t),yREF
FULL NONLINEAR AIRCRAFT SIMULATION MODEL
u(t))h(x(t),y(t)
)w(t),u(t),f(x(t),(t)x
)Δ̂(t),yg(x(t),u(t) REF
Mach AltitudeLevel Trim
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Computation of worst-case pilot inputs•Worst-case inputs: deg66.4316αmax
0.0611 0.0648 -0.0020 -0.0022 0.0418 66.4316
cgx mass
emC
alC
mC
max
Time: 3hrs. 5mins.
deg58.0721αIIAnalysis max
deg16.0038αKlonk max
deg27.066α:IAnalysis max
P. P. Menon, D. G. Bates and I. Postlethwaite, ``Computation of Worst-Case Pilot Inputs for Nonlinear Flight Control System Analysis'', AIAA Journal of Guidance, Control and Dynamics, 29(1), 2006.
Department of Engineering, Control & Instrumentation Research Group
22 – Mar – 2006
Computation of worst-case pilot inputs
Rudder
Input of Rate LimiterOutput of Rate Limiter
•What’s the problem?
Department of Engineering, Control & Instrumentation Research Group