advances in iterative learning control with application to response reconstruction ·...
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Advances in Iterative learning Control with Application to Response Reconstruction
J.J.A. EksteenDept. of Mechanical and Aeronautical Engineering, University of Pretoria
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Introduction (1)
• Final validation of structural integrity is done experimentally (testing)
• Testing:
– Actual operation (accelerated)
– Laboratory (accelerated)
• In laboratory: recreate realistic structural responses
• At UP this is called response reconstruction.
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Road Simulator Research Test Rig
INPUTS: u(t) = drive signals to actuators applied to test specimen
OUTPUTS:y(t) = response signals in sensors on specimen
Introduction (2)
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Response reconstruction is used to
recreate desired histories in response sensors
desired histories = yd(t)
Is used when (most generally)• structure is dynamically excited• excitation is multi‐axis • cross‐coupling between axes
Thus, inverse problem (output is known, input is unknown)
Introduction (3)
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• Response reconstruction can be used for:
• These are examples of environmental testing, other types include:
• Humidity
• Temperature
• Pressure
• Acoustic noise, etc.
Introduction (4)
TEST TYPE Source of yd(t)
Fatigue tests Field measurements (usually)
Vibration tests Standards
Shocks tests Standards
Example: Fatigue test (Autocar)
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Example: Shock and vibration test (Airbus/Aerosud)
Cargo hold panels on A400M
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Missile system vibration and shock testing
Example: Shock and vibration test (Thales)
AIM Domain
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Response Reconstruction Procedure (1)
• Need test rig (T) in lab with
– Test specimen
– Inputs, u(t) = drive signals to actuators
– Outputs, y(t) = response sensors on test specimen
– Realistic boundary conditions
• Need desired response histories (output) ‐ yd• Need inverse model of entire test system ‐ L
• Need reconstruction algorithm to
– reconstruct desired outputs (responses)
– by calculating required inputs (actuator drive signals)
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Response Reconstruction Procedure (2)
• Desired response histories (output) (yd) typically obtained by field measurements (full‐scale fatigue tests)
• Inverse model (L) obtained by
– System identification on test rig in lab to get model
– Inversion of the model to get inverse model
• The reconstruction algorithm is an iterative off‐line control algorithm called Iterative Learning Control (ILC)
How is ILC done? (1)
• Have nonlinear test system = T, input = u, output = y: y = T(u)
• Have desired response, yd ; need desired input ud• Have L = Inverse model of T (may be very approximate)
• For i‐th iteration do test with u(i): y(i) = T(u(i))
• Conventional ILC algorithm:
u(i+1) = Q(u(i) + L(yd) ‐ L(y(i)))
u(0) = [0], y(0) = [0]
• Q = Optional low pass filter12
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How is ILC done? (2)
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• Convergence exact tracking (seldom over whole frequency band)
• Advantages of accurate inverse model (L)
• Reduced number and width of divergent frequency bands
• Increased width of convergent frequency band
• Control over rate of convergence
Thus gives better results before divergence (if ILC not convergent)
How is ILC done? (3)
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In research at UP we propose
• Nonlinear inverse model (L) instead of (usual) linear L (using NARX models)
• Using different models to model different frequency ranges separately instead of one model for whole frequency range
• Modifications to the ILC algorithm that may potentially give more accurate results
Response Reconstruction Research at UP (1)
• Swingarm monoshockmotorcycle rear suspension
• High speed electrohydraulicactuator
• PID controller• AD/DA interface of test with computer
• Hydraulic pumps• Strain gauges:
– A: near bracket– B: near pivot
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Response Reconstruction Research at UP (2)