Modelling and Optimal Control of Tethered Airfoils for Wind by murplelake83

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									Modelling and Optimal Control of Tethered
  Airfoils for Wind Power Generation


                             Moritz Diehl
         Optimization in Engineering Center (OPTEC) & ESAT
                         K.U. Leuven, Belgium


   Symposium on Control and Modelling of Alternative Energy Systems,
                 Urbana-Champaign, April 2-3, 2009
 Optimization in Engineering Center OPTEC
Center of Excellence of K.U. Leuven, since 2005
About 25 professors, 10 postdocs, and 50 PhD students involved in OPTEC
  research

Promoted by four departments:
   Electrical Engineering
   Mechanical Engineering
   Chemical Engineering
   Computer Science



Many real world applications at OPTEC...
Aim: Connect Optimization Methods and Applications
                                   Applications: Smart
                                   problem formulations allow
                                   efficient solution (e.g.
                                   convexity)




Methods: New developments
are inspired and driven by
application needs
Overview



 Idea: Wind Power Generation by Fast Flying Kites

 Optimal Periodic Orbits

 Stabilization by Nonlinear Model Predictive Control (NMPC)

 Do Open-Loop Stable Periodic Orbits exist?

 Status of Real-World Implementation
Conventional Wind Turbines


                      Due to high speed, wing tips are most
                      efficient part of wing
                      High torques at wings and mast limit size
                      and height of wind turbines
                      But best winds are in high altitudes!




                   Could we construct a wind turbine
                   with only wing tips and generator?
Conventional Wind Turbines


                      Due to high speed, wing tips are most
                      efficient part of wing
                      High torques at wings and mast limit size
                      and height of wind turbines
                      But best winds are in high altitudes!




                   Could we construct a wind turbine
                   with only wing tips and generator?
Crosswind Kite Power (Loyd 1980)

                      Fly kite fast in crosswind direction
                      Very strong force (100x higher than static
                      kite)




                   But where could a generator be driven?
Variant 1: On-Board Generator
                       attach small wind turbines to kite
                       due to high relative wind speed, can be
                       small
                       optimally increase system drag by 50%
                       lines must transmit power



                    Pros: fast spinning generators
                    Cons: heavy, moving parts on board,
                       electric cables, conversion losses
Variant 2: New Pumping Cycle
                  New cycle consists of two phases:
                    Power generation phase:
                     • Fly kite fast, have high force
                     • unwind cable (!!)
                     • generate power

                     Retraction phase:
                      • Slow down kite, reduce force
                      • pull back line

                     Cycle produces same power as (gigantic)
                     windmill of same wing area
Variant 2: New Pumping Cycle
                  New cycle consists of two phases:
                    Power generation phase:
                     • Fly kite fast, have high force
                     • unwind cable (!!)
                     • generate power

                     Retraction phase:
                      • Slow down kite, reduce force
                      • pull back line

                  Pros: all heavy and electric parts on ground



                  Can generate same power as (gigantic) wind
                    turbine of same wing area
Can stack kites, can use on sea
High Altitude Wind Power investigated by many groups


 TU Delft: Wubbo Ockels, …
 U Sussex: Allister Furrey
 K.U. Leuven: MD, J. Swevers, …

 AmpyxPower: R. Ruiterkamp, B. Lansdorp
 KiteGen: M. Milanese, M. Ippolito, …
 SkySails
 NTS
 makani
 JobyEnergy
 …
Many Important Questions:

  Cable length? 100 m, 1 km, 10 km ?

  Cable strength? (drag vs. elastic losses)

  Shall kites fly high, or close to ground?

  How long should each phase be?

  How fast to roll in and out cable?

  What are the optimal flight figures?

  How to control?                             (old illustration of TU Delft‘s „laddermill“)
Five Claims [Kite Workshop, January 2007]

The future kite power plants will look as follows:

   Kite lines will be far from vertical, kites fly at low angles
   Lift control will play crucial role
   Kites will be “pumping” rather than turning a carousel
   Plants will be built rather on sea than on land
   Connection to ground by only one line, not two or more
Overview



 Idea: Wind Power Generation by Fast Flying Kites

 Optimal Periodic Orbits

 Stabilization by Nonlinear Model Predictive Control (NMPC)

 Do Open-Loop Stable Periodic Orbits exist?

 Status of Real-World Implementation
 Kite Model for Optimal Control (Boris Houska)
                        Have to regard also cable elasticity



                        ODE Model with 12 states and 3 controls




forces at kite (here:                Control inputs:
   500 m2)                             line length
                                       roll angle (as for toy kites)
                                       lift coefficient (pitch angle)
Some Kite Parameters
                       e.g. 10 m x 50 m,
                       like Boeing wing,
                       but much lighter
                       material

                       standard wind velocity for
                       nominal power of wind
                       turbines
 Periodic Optimization Problem
Maximize mean power production:




by varying line thickness, period duration,
controls,    subject to periodicity and other
constraints:
Solve by Bock’s Direct Multiple Shooting Method [Bock&Plitt,’84]
implemented in MUSCOD-II[Leineweber‘99] or ACADO[Ferreau, Houska’09]
 Solution of Periodic Optimization Problem
Maximize mean power production:




by varying line thickness, period duration,
controls,    subject to periodicity and other
constraints:




                                         Cable length 1.3km, thickness 7 cm
Periodic Orbit: 5 MW mean power production
What about ‚dancing‘ kites ?
2 x 500 m2 airfoils
Optimal ‚Dancing‘ Kites: 14 MW possible




    2 x 500 m2 airfoils
    kevlar line 1500 m, diameter 8 cm
    wind speed 10 m/s
Overview



 Idea: Wind Power Generation by Fast Flying Kites

 Optimal Periodic Orbits

 Stabilization by Nonlinear Model Predictive Control (NMPC)

 Do Open-Loop Stable Periodic Orbits exist?

 Status of Real-World Implementation
Problem: kite orbits unstable. What to do?
Feedback by Nonlinear Model Predictive Control (NMPC)

           Always look a bit into the future!




                             Controller predicts and optimizes:
                             e.g. slow down before curve
  Principle of Optimal Feedback Model Predictive Control (MPC)
Computations in Control / Nonlinear MPC:




                         x0

                              u0

                                   x0




                         u0

     Main challenge for MPC: fast and reliable real-time optimization
Fast MPC Group Leuven -
Software and Applications
Our aim: make fastest possible online optimization codes



    Our two open source MPC “products”:

      qpOASES for linear MPC
      ACADO for nonlinear MPC
 qpOASES: Tailored QP Solver

Solve p-QP via „Online Active Set Strategy“:


   go on straight line in parameter space
   from old to new problem data

   solve each QP on path exactly (keep
   primal-dual feasibility)

   Update matrix factorization at boundaries
   of critical regions

   Up to 10 x faster than standard QP


                   qpOASES: open source C++ code by Hans Joachim Ferreau
The Predictive Prefilter: a 100 Hz Application
                           Quarter car: oscillating spring
                           damper system
                           MPC Aim: settle at any new
                           setpoint in in minimal time
                           Re-Formulate with L1-slacks as
                           p-QP:
                               6 online data
                               30 variables
                               180 constraints (in-&output)
                           use qpOASES on dSPACE
                           CPU time: 0.5 – 2.9 ms


                         Lieboud Van den Broeck in front of
                         quarter car experiment
Slow Motion Video of qpOASES content
qpOASES running on Industrial Control Hardware (20 ms)




Project manager (Dec. 2008): “…we had NO problem at all
with the qpOASES code. Your Software has throughout the
whole project shown reliable and robust performance.”
ACADO Toolkit

 A Toolkit for „Automatic Control and Dynamic Optimization“




 C++ code along with user-friendly Matlab interfaces
 Open-source software (LGPL 3)
 Since mid 2008 developed at OPTEC by
 Boris Houska and Hans Joachim Ferreau
ACADO Toolkit – Main Features

 Problem Classes:                 Discretization Methods:
 • Optimal control                 • Single shooting
 • State & parameter estimation    • Multiple shooting
 • Robust optimization             • Collocation
 • Model predictive control
                                  Integrators:
                                   • RKF and BDF methods
 Dynamic Optimization:
                                   • Efficient sensitivity generation
 • Linear and Nonlinear
                                   • Second order sensitivities
 • ODE and DAE
 • Continuous and discrete time   NLP solvers:
 • Automatic differentiation       • Adjoint-based SQP
 • Convexity detection             • Interior point methods
NMPC of Wind Power Generating Kites
              (with Boris Houska, A. Ilzhoefer, K. Evers, B. Struyven...)
NMPC of Large Kite Systems (Andreas Ilzhoefer)

  Track Reference. Predict 20 secs. Sample time: 1 sec
  Use real-time iteration scheme within MUSCOD-II
  Combine with Moving Horizon Estimator (MHE)
Computation always < 1s:            Closed-loop simulation:
Kite NMPC Problem solved with ACADO

   9 states, 3 controls
   Penalize deviation from “lying eight”
   Predict half period
   zero terminal constraint
   10 multiple shooting intervals

Solve with SQP real-time iterations
Kite NMPC: CPU Time per RTI below 50 ms

    Initial-Value Embedding            : 0.03 ms
    QP solution (qpOASES)               : 2.23 ms
-----------------------------------------------------------
Feedback Phase:                               3 ms
(QP after condensing: 30 vars. / 240 constr.)



    Expansion of the QP                : 0.10 ms
    Simulation and Sensitivities : 44.17 ms
    Condensing (Phase I)               : 2.83 ms
-----------------------------------------------------------
Preparation Phase:                         47 ms

(on Intel Core 2 Duo CPU T7250, 2 GHz)
NMPC Control with large turn of wind direction
Overview



 Idea: Wind Power Generation by Fast Flying Kites

 Optimal Periodic Orbits

 Stabilization by Nonlinear Model Predictive Control (NMPC)

 Do Open-Loop Stable Periodic Orbits exist?

 Status of Real-World Implementation
Question: Could kite also fly WITHOUT feedback?




Stability just by smart choice of open-loop controls?
Monodromy Matrix determines stability

„Monodromy matrix“ = Jacobian of Poincare map.




 Stability   Spectral radius of monodromy matrix smaller one


 Disadvantages of spectral radius:
    nonsmooth criterion, difficult for optimization
    constraints and uncertainty of parameters not taken into account
Alternative Approach (Houska, D. 2007)

Regard linearized propagation of noise:


Compute covariance matrix P by
Lyapunov Equation:


Infinitely long time: covariance blows up, or
becomes periodic

THEOREM: If periodic Lyapunov solution
exists (with     ), system is stable.
New robust stability optimization problem




Allows to robustly satisfy inequality constraints!

Numerical challenges: higher order sensitivities, large scale ODEs,
non-smooth constraints, relaxations for infeasible initializations, ...
 Orbit optimized for power and robust stability




                                         Kite never touches
                                         ground: inequalities
                                         robustly satisfied


We have GENERATED a stable attractor!
Only possible due to nonlinearity
Overview



 Idea: Wind Power Generation by Fast Flying Kites

 Optimal Periodic Orbits

 Stabilization by Nonlinear Model Predictive Control (NMPC)

 Do Open-Loop Stable Periodic Orbits exist?

 Status of Real-World Implementation
Prototypes built in Hamburg, Delft, Torino, California, …
The groups known to the speaker


 TU Delft: Wubbo Ockels, …
 U Sussex: Allister Furrey
 K.U. Leuven: MD, J. Swevers, …

 AmpyxPower: R. Ruiterkamp, B. Lansdorp
 KiteGen: M. Milanese, M. Ippolito, …
 SkySails
 NTS
 makani
 JobyEnergy
 …
Leuven Kite Power Group

    Build toy prototypes to validate
    mathematical predictions
    Investigate rather rigid than flexible
    airfoils (kite power grows
    quadratically with gliding number)
    Involved groups: Diehl, Swevers,
    Vandepitte
    Good contacts with AmpyxPower,
    TU Delft, KiteGen
Makani power

   Financed by google with 15 MDollar
   In “stealth” mode, but seems to bet on “generator on board” variant
   Like everyone else, first builds pumping kite wind generator




   Nice recent video (google “TED kite griffith”)
KiteGen

   Financed by small investors and local government subsidies
   Believes in “carousel” variant
   Like everyone, first builds pumping kite wind generator (two lines)
KiteGen Test Flight in 2006
TU Delft Team headed by Wubbo Ockels

    Financed by sponsors and local companies (port of rotterdam)
    Group working longest experimentally on kite power
    Calls its concept “Laddermill”
    Has built pumping wind generator with single line
Kite Demo in Groningen August 28, 2007
AmpyxPower, Delft

    Founded by ex-members of TU Delft team
    Financed by seed investors and subsidies
    Is building pumping wind generator with rigid airfoils
AmpyxPower Test Flight in Dec 2008
AmpyxPower Test Flight in Dec 2008
Summary: Optimal Control for Kites

  Open-Loop Optimization
  (finds optimal designs, unstable, non-robust)




Model Predictive Control          Open-Loop Robustness and Stability
(powerful feedback by fast        (no sensor feedback needed, simple)
online optimization)
Job Announcements – Join the OPTEC team!




               Join the OPTEC team!




Open PhD positions:
 •   Optimal Control of Power Generating Kite Systems
 •   Distributed Optimization for MPC
 •   Nonlinear State and Parameter Estimation
Thank you!

								
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