Speed funnel control with disturbance observer for wind turbine systems with elastic shaft

Transcription

1 Speed funnel control with disturbance observer for wind turbine systems with elastic shaft Christoph Hackl (TUM) Munich School of Engineering (MSE) Research group Control of Renewable Energy Systems (CRES) Session Power Systems I Conference on Decision and Control (CDC 215), Japan Christoph Hackl: Speed funnel control with disturbance observer for WTS with elastic shaft Seite 1/14

2 Outline 1 Motivation and problem statement 2 Funnel control 3 Speed funnel control with disturbance observer (DO) of WTS with elastic shaft 4 Conclusion Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 2/14

3 Outline 1 Motivation and problem statement Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 2/14

4 Motivation and problem statement Regimes of operation of wind turbine systems v w r t ω t r t ω m gr A t πr 2 t p t,nom I II III IV ω t γ r t β p t rws v cut in v nom v cut out v w m s Regime I: Standstill p t Regime II: Variable oper. ď p t ă p t,nom (Goal: Maximum power point tracking) Regime III: Nominal oper. p t p t,nom Regime IV: Standstill p t Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 3/14

5 Motivation and problem statement Turbine power & torque, power coefficient and control objective (in regime II) p t c p pv w, β, ω m q 1 2 ϱr2 t πvw 3 g r c p pv w, β, ω m qp w ùñ m t pv w, β, ω m q (1) loooomoooon ω m : p w c p pλ, βq c p p, βq λ λ ùñ Control objective: MPPT, i.e. λ r tω t v w r tω m v w g r Ñ λ for β β ě Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 4/14

6 Munich School of Engineering Motivation and problem statement Wind turbine system with elastic shaft ( reference tracking ωt p q Ñ ωt,ref p q vw p q rt λ d ` cs Θm ` active damping of natural frequency ω Θt 2 gr Θm Θt only ωm available for feedback Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 5/14

7 Outline 2 Funnel control Control objective and controller Admissible system class Properties of the closed-loop system Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 5/14

8 Outline 2 Funnel control Control objective and controller Admissible system class Properties of the closed-loop system Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 5/14

9 Funnel control Control objective and controller control objective: tracking with prescribed transient accuracy ψpq epq ψptq eptq ψp q ep q λ t time t rss performance funnel ψpq funnel controller: uptq kptq` yloooooomoooooon ref ptq yptq :eptq where kptq ςptq ψptq eptq (FC) gain scaling ςp q P CpR ě ; R ą q (e.g. such that kptq ě ςptq ψptq for all t ě ) Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 6/14

10 Outline 2 Funnel control Control objective and controller Admissible system class Properties of the closed-loop system Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 6/14

11 Funnel control Admissible system class S 1 : System description and structural properties 9xptq Axptq ` b`uptq ` u d ptq ` B T dpt, xptqq ` ptxqptq yptq c J xptq, + (2) (sp 1 ) γ : c J b and signpγ q known; j sin A b (sp 2 s P C with Rpsq ě : det c J ; (sp 3 ) T P T (see Def. 1 in [1]) and M T : sup t ptξqptq t ě, ξp q P Cpr h, 8q, R n quă8; (sp 4 ) dpt, q P CpR n ; R m q; (sp 5 ) u d p q P L 8 pr h, 8q; Rq and dp, q P L 8 pr h, 8q ˆ R n ; R m q Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 7/14

12 Outline 2 Funnel control Control objective and controller Admissible system class Properties of the closed-loop system Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 7/14

13 Funnel control Properties of the closed-loop system u d y ref (FC) u 9x Ax ` b`u ` u d `B T d ` Tx y c J x, y system of class S 1 y ` n y n y (i) there exists a solution x: r h, T q Ñ R n which can be maximally extended and T P p, 8s; (ii) the solution does not have finite escape time, i.e. T 8; (iii) the tracking error is uniformly bounded away from the funnel boundary, i.e. Dε ą : eptq ă ψptq for all t ě ; (iv) gain & input are bounded, i.e. kp q, up q P L 8 pr ą ; Rq Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 8/14

14 Outline 3 Speed funnel control with disturbance observer (DO) of WTS with elastic shaft Model of WTS with elastic shaft Closed-loop system with disturbance observer (DO, based on [2]) Simulation results Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 8/14

15 Outline 3 Speed funnel control with disturbance observer (DO) of WTS with elastic shaft Model of WTS with elastic shaft Closed-loop system with disturbance observer (DO, based on [2]) Simulation results Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 8/14

16 Speed funnel control with DO of WTS with elastic shaft Model of WTS with elastic shaft P S 1 (see Prop. IV.1) d dt x Sptq A S x S ptq ` b S`uptq ` ua ptq ` B S yptq c J S x S ptq, x S pq x S P R 3 where m t p,, q is as in (1) and bounded (see Lem. III.1), and» A S ds`g 2 r ν m g 2 r Θ m cs g r Θ m d s g r Θ m 1 g r 1 d s g r Θ t Θ m, Θ t ą, c s ą, d s ą, g r ě 1, ν m, ν t ą, k a ą, c s Θ t ds`ν t Θ t fi ffi ffi fl, b S pf g ω m qptq m t`vw ptq, βptq, ω t ptq pf t ω t qptq k a Θ m», B S 1 Θ m 1 Θ t u a p q, v w p q, βp q P L 8 pr ą ; i P tg, tu: F i P T ^ M Fi : sup pf i ξqptq ˇˇ t ě, ξp q P CpRą, Rq ( ă8. fi fl, c S 1, Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 9/14

17 Outline 3 Speed funnel control with disturbance observer (DO) of WTS with elastic shaft Model of WTS with elastic shaft Closed-loop system with disturbance observer (DO, based on [2]) Simulation results Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 9/14

18 Speed funnel control with DO of WTS with elastic shaft Closed-loop system with disturbance observer (DO) elastic WTS 1{g r m t ν m ω m `F m ω m d s ν t ω t `F t ω t observer actuator ω m g k k Ăm r T f Θ a 1{Θ m 1{g r c s 1{Θ t ω t,ref y ref e u u m m φ (FC) s u a v w β ω t y m do (DO) n ω sensor extended system of class S 1 (see Prop. IV.1) 9x do ptq 1 T x do do ptq ` uptq ` pθ, m ω m ptq. pk a T do m do ptq p1 k do q`x do ptq pθ m ω m ptq, xdo pq. - pk a T do d Active damping for k do ą 1: ω 1 pk do q c s`θ m` Θt g 2 k do r Θ m Θ t (DO) ^ ζ 1 pk do q ω pk do q d s 2 c. s Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 1/14

19 Outline 3 Speed funnel control with disturbance observer (DO) of WTS with elastic shaft Model of WTS with elastic shaft Closed-loop system with disturbance observer (DO, based on [2]) Simulation results Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 1/14

20 Speed funnel control with DO of WTS with elastic shaft Simulation results: (FC), (FC)+(DO) 1 vw [ m s ] ωt [ rad s ] λ [1] cp [1] φs [rad] 5 2 ω t,ref time t [s] λ c p Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 11/14

21 Speed funnel control with DO of WTS with elastic shaft Simulation results: (FC), (FC)+(DO) 2 y [ rad s ] 1 4 y ref ψ e [ rad s ] 2 k [ 1 3 Nms rad ] time t [s] Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 12/14

22 Outline 4 Conclusion Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 12/14

23 Conclusion To take home: Speed funnel control of wind turbine systems with disturbance observer... is simple is robust (λ and g r must be known; p Θ m and p k a rough estimates) achieves active damping (for all k do ą 1) only ω m required for feedback (not ω t ) no problems due to non-ideal torque control [3] faster dynamics and more efficient than nonlinear controller k pω 2 m [4] Current drawbacks: ω t,ref ω t ă ψ g r (and λ ă λ ε) only in steady state wind speed measurement required (for ω t,ref p q v wp q r t λ ) Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 13/14

24 References I [1] A. Ilchmann, E. P. Ryan, and C. J. Sangwin, Tracking with prescribed transient behaviour, ESAIM: Control, Optimisation and Calculus of Variations, vol. 7, pp , 22. [2] Y. Hori, H. Sawada, and Y. Chun, Slow resonance ratio control for vibration suppression and disturbance rejection in torsional system, IEEE Transactions on Industrial Electronics, vol. 46, no. 1, pp , [3] C. M. Hackl and K. Schechner, Non-ideal torque control of wind turbine systems: Impacts on annual energy production, in Proceedings of the IEEE International Energy Conference (submitted), 216. [4] C. M. Hackl, Funnel control for wind turbine systems, in Proceedings of the 214 IEEE International Conference on Control Applications, pp , Speed funnel control with disturbance observer for WTS with elastic shaft, C. Hackl 14/14