adaptive feedforward control for uncertain linear...
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Adaptive Feedforward Control for Uncertain Linear System
Yang WangSupervisor: Prof. T. Parisini
Imperial College London
UKACC PhD Presentation Showcase
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
PlantInput Output
Reference
• LTI• Stable• Uncertain
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
Plant
Disturbances
Input Output
• LTI• Stable• Uncertain
Reference
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
Plant
Disturbances
Input Output
• LTI• Stable• Uncertain
• Periodic• Source unknown• Not measurable
Reference
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
Plant
Disturbances
Input Output
• LTI• Stable• Uncertain
• Periodic• Source unknown• Not measurable
Reference
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
Plant
Disturbances
Input Output
• LTI• Stable• Uncertain
• Periodic• Source unknown• Not measurable
Reference
1. Engine Noise
2. Wind Noise
3. Tire (Break) Noise
Problem Formulation
UKACC PhD Presentation Showcase Slide 2
Plant
Disturbances
Input Output
• LTI• Stable• Uncertain
• Periodic• Source unknown• Not measurable
Reference
Goal: Minimize the influence of the disturbances
Problem Formulation
UKACC PhD Presentation Showcase Slide 3
Plant
Disturbances
Input OutputReference
Goal: Minimize the influence of the disturbances
lim𝑡𝑡→∞
(𝑦𝑦 𝑡𝑡 − 𝑟𝑟 𝑡𝑡 ) = 0
𝑑𝑑(𝑡𝑡)
𝑟𝑟(𝑡𝑡)
𝑑𝑑(𝑡𝑡) = 𝑎𝑎 sin(𝜔𝜔∗𝑡𝑡 + 𝜙𝜙)
�̇�𝑥 = 𝐴𝐴 𝜇𝜇 𝑥𝑥 + 𝐵𝐵 𝜇𝜇 (𝑑𝑑 + 𝑟𝑟)
𝑦𝑦(𝑡𝑡) = 𝐶𝐶 𝜇𝜇 𝑥𝑥(𝑡𝑡)
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
Reference 𝑦𝑦(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
𝑦𝑦(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
𝑦𝑦(𝑡𝑡)
DisturbancesCopy
�̂�𝑑(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
FeedForward Control
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
𝑦𝑦(𝑡𝑡)
DisturbancesCopy
�̂�𝑑(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
FeedForward Control
𝜔𝜔𝑎𝑎𝜙𝜙
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
𝑦𝑦(𝑡𝑡)
DisturbancesCopy
�̂�𝑑(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
FeedForward Control
𝜔𝜔∗
𝑎𝑎𝜙𝜙
Key Point: 𝑑𝑑(𝑡𝑡) not available
𝑦𝑦 𝑡𝑡 = 𝑎𝑎 𝑊𝑊 𝑗𝑗𝜔𝜔∗ sin 𝜔𝜔∗𝑡𝑡 + 𝜙𝜙 + ∠𝑊𝑊 𝑗𝑗𝜔𝜔∗
unknown unknown
Solution: Adaptive Forward Control
UKACC PhD Presentation Showcase Slide 4
Plant
Disturbances
𝑦𝑦(𝑡𝑡)
DisturbancesCopy
�̂�𝑑(𝑡𝑡)
𝑑𝑑(𝑡𝑡)
FeedForward Control
𝜔𝜔∗
�𝑎𝑎(𝑡𝑡)�Φ(𝑡𝑡)
Key Point: 𝑑𝑑(𝑡𝑡) not available
𝑦𝑦 𝑡𝑡 = 𝑎𝑎 𝑊𝑊 𝑗𝑗𝜔𝜔∗ sin 𝜔𝜔∗𝑡𝑡 + 𝜙𝜙 + ∠𝑊𝑊 𝑗𝑗𝜔𝜔∗
unknown unknown
Estimator
Adaptive Observer
Estimator
UKACC PhD Presentation Showcase Slide 5
�𝜃𝜃(1)𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
Estimator
UKACC PhD Presentation Showcase Slide 5
�𝜃𝜃(1)𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
Estimator
UKACC PhD Presentation Showcase Slide 5
�𝜃𝜃(1)𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
Estimator
UKACC PhD Presentation Showcase Slide 5
�𝜃𝜃(1)𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]Price:
• Computation burden
• Slower convergence
Estimator
UKACC PhD Presentation Showcase Slide 5
�𝜃𝜃(1)𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]Price:
• Computation burden
• Slower convergence
Achievements:
• Time-varying system
• Time-varying disturbance
Simulation Results
UKACC PhD Presentation Showcase Slide 6
Plant :𝑊𝑊 𝑠𝑠 = 2(𝑠𝑠−1)𝑠𝑠2+2𝑠𝑠+5
1) 𝜔𝜔1∗ = 1 , 𝑑𝑑(𝑡𝑡) = 2 sin(𝑡𝑡)
𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝑊𝑊 𝑗𝑗𝜔𝜔1∗
Simulation Results
UKACC PhD Presentation Showcase Slide 6
Plant :𝑊𝑊 𝑠𝑠 = 2(𝑠𝑠−1)𝑠𝑠2+2𝑠𝑠+5
1) 𝜔𝜔1∗ = 1 , 𝑑𝑑(𝑡𝑡) = 2 sin(𝑡𝑡) 2) 𝜔𝜔2∗ = 3 , 𝑑𝑑(𝑡𝑡) = 2 sin(3𝑡𝑡)
𝑅𝑅𝑅𝑅[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝐼𝐼𝐼𝐼[𝑊𝑊 𝑗𝑗𝜔𝜔∗ ]
𝑊𝑊 𝑗𝑗𝜔𝜔1∗
𝑊𝑊 𝑗𝑗𝜔𝜔2∗
Results
UKACC PhD Presentation Showcase Slide 7
Plant :𝑊𝑊 𝑠𝑠 = 2(𝑠𝑠−1)𝑠𝑠2+2𝑠𝑠+5
0 50 100 150
-3
-2
-1
0
1
2
0 50 100 150
-3
-2
-1
0
1
2
1) 𝜔𝜔1∗ = 1 , 𝑑𝑑(𝑡𝑡) = 2 sin(𝑡𝑡) 2) 𝜔𝜔2∗ = 3 , 𝑑𝑑(𝑡𝑡) = 2 sin(3𝑡𝑡)
Intermediate Results and Further Plans
Simplify controller
Extend to MIMO system
Combine controller with frequency estimator
UKACC PhD Presentation Showcase Slide 8
Remove the SPR-like conditions in AFC of uncertain system
Current results:
Plans: