Towards robust control design for active flow control on wind turbine - - PowerPoint PPT Presentation

Towards robust control design for active flow control on wind turbine blades first results based on numerical simulations Dimitri Peaucelle Caroline Braud, Emmanuel Guilmineau Active flow control on wind turbine blades session - 29 August - 12 :00-12 :25

Objectives

■ Robust control tools for active feedback control of the air flow on turbine blades

• Linear transfer functions representing approximately some dynamics
• Heuristic (or better) design of low order controllers
• Robust analysis of the feedback loop with respect to modeling uncertainties

■ Cooperation with Caroline Braud & Emmanuel Guilmineau

• Choice of a blade profile & actuators/sensors
• Discussion about expected phenomena and objectives
• 1st tests on numerical simulations of the flow
• 2nd tests on a physical benchmark
• D. Peaucelle

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Blade profile & sensors/actuators & numerical measurement

• D. Peaucelle

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Numerical experiments without and with constant air blowing

Cµ = 0 Cµ = 0.055 fCµ=0 = 97.3408Hz fCµ=0.055 = 102.7487Hz

Increased steady-state and amplitude

• D. Peaucelle

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Proposed linear model

Oscillator at fCµ Hz + + Cµ upstream air flow kCµ k0p

kp τps+1 ˆ kp ˆ τps+1

+ + + air pressure at point p V0 actuation Pp wake

• Choice of 1st order transfer functions coherent with experiments by Braud&Jaunet
• Model takes into account only dynamics at low frequencies (from 0 to fCµ ≃ 100Hz)
• Blue part is repeated for each points where air pressure is measured

▲ kCµ and k0p identified using steady-state values ▲ τp identified using phase shift of sinusoids at frequency fCµ ▲ τp ≃ ˆ τp assumed similar because almost colocated ▲ kp and ˆ kp identified using amplitude of sinusoids at frequency fCµ ▼ All parameters should be considered as uncertain (modeling and identification errors) ▼ Model at one operating point (eg. one pitch angle α = 0)

Linear parameter-varying (LPV) could be considered to go further

• D. Peaucelle

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Proposed control problem

Oscillator at fCµ Hz + + Cµ upstream air flow kCµ k0

k τs+1 ˆ k ˆ τs+1

+ + + P vector of measured air pressures at several points V0 actuation wake + + fluctuation in air flow ∆V0 W1 weighted sum of pressures ≃ lift W2(s) band limited filter around fCµ Hz z performance y measurements + + white noise

0.055

u control signal H +

• yc requested value

ǫ error

■ Goal 1 : Make the system asymptotically stable (wake will converge to zero)

• Could be achieved by appropriate feedback control : u(t) = H(y(t))

■ Goal 2 : Keep lift at prescribed achievable level

• Control should contain integrator

■ Goal 3 : Attenuate influences of ∆V0 and wake on lift

• Can be evaluated by the H∞ norm of the transfer from ∆V0 to z

■ Properties should be robust to modeling, uncertainties, noise & saturation

• D. Peaucelle

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Choice of a simple control structure

■ y : sum of 2 measures, upstream + close to wake y = P131683 + P168671

• upstream : contains mostly information about ∆V0
• downstream : contains mostly information about wake

■ PI control u(t) = KP ˆ ǫ(t) + KI ∞ ˆ ǫ(τ)dτ ■ with Anti-Windup ˆ ǫ = ǫ − ka τas + 1(Cµ − u)

• Hand-tuned parameters

Kp = 10−2, KI = −200, ka = 10, τa = 10−5

PI +

• ka

τas+1

0.055

+

• ǫ

u ˆ ǫ

• D. Peaucelle

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Open loop simulations with linear model

■ OFF/ON actuator Cµ(t ∈ [0 , 0.25]) = 0 Cµ(t ∈ [0.25 , 0.5]) = 0.055 ■ ∆V0 periodic positive and negative steps (5% variation of V0) Pp(t) y(t)

wake

• D. Peaucelle

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Closed loop simulations with linear model

■ Requested ’lift’ yc(t ∈ [0 , 0.25]) = −1.04 yc(t ∈ [0.25 , 0.5]) = −1.46 ■ Same ∆V0, noise=0 u(t) y(t)

wake

• D. Peaucelle

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Closed loop simulations with linear model

■ Requested ’lift’ yc(t ∈ [0 , 0.25]) = −1.04 yc(t ∈ [0.25 , 0.5]) = −1.46 ■ Same ∆V0, noise = 0 u(t) y(t)

wake

• D. Peaucelle

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Robustness of closed-loop

■ γ = H∞ performance of transfert ∆V0 → z

• (A) If no uncertainties on parameters
• (B) Constant uncertainties : 10% on τ, 5% on fCµ, 20% on kCµ
• (C) Time varying uncertainties : 10% on τ, 5% on fCµ, 20% on kCµ

Oscillator at fCµ Hz + + Cµ upstream air flow kCµ k0

k τs+1 ˆ k ˆ τs+1

+ + + P vector of measured air pressures at several points V0 actuation wake + + fluctuation in air flow ∆V0 W1 weighted sum of pressures ≃ lift W2(s) band limited filter around fCµ Hz z performance y measurements + + white noise

0.055

u control signal H +

• yc requested value

ǫ error

γ(A) = 0.4153 , γ(B) ≤ 0.4279 , γ(C) ≤ 0.4563

• Values computed using R-Romuloc toolbox
• D. Peaucelle

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Conclusions

▲ Simple control strategy based on existing actuators/sensors ▲ Data obtained from numerical experiments ▲ Encouraging simulations and robustness assessments ▼ Need for validation on closed-loop numerical experiments ▼ Need for validation on physical experiments ▼ Physical sensors may not be efficient enough (noise +?) ▼ Actuators may not be efficient enough (saturation + PWM +?) ■ Easily hand-tuned control

• Structured control tools (Hifoo, hinfstruct,...) could do better

■ Current study for one operating point (α = 0, one wind speed, etc.)

• Need for parameter-varying control, or adaptive control
• D. Peaucelle

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