2011/12/25

Transcription

1 Outline [] Control Technologies for Ocean Engineering Control technologies as the second axis Kyushu University Prof. H.Kajiwara (.8,at PNU) LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine Double Inverted Pendulum (979) [] Inverted Pendulum (IP) [] [5] Inverted Pendulum Under-actuated System SISO (Single-Input Single-Output) System [6] -input -output MIMO (Multi-Input Multi-Output) System m-inputs p-outputs Under-actuated System m<p Under-actuated System controlled variables as many as manipulated m-variables based on measured p-variables If you chase after two rabbits, you won't catch either.

2 Andersen s Approach [7] Position Control of a Cart [8] SISO# SISO# Unity feedback is used to correct the error between given command and current position. How to Regulate the Oscillation? Step Response (small dumping) [9] PID Control of a Cart (Motor/Ship) I-Action [0] Step Response (desired) P-Action D-Action identified Which action regulates the oscillation? Andersen s Approach (Step ) [] Which is easier to control? [] Type Type Position Controlled Cart

3 Andersen s Approach (Step ) [] The Same Period of Pendulums [] Simple Pendulum Rigid Pendulum Pinching the point, Adjust a control gain to stop the oscillation. Find the length ell to realize the same period as the rigid pendulum. [5] The Same Period of Pendulums Center of Impact [6] move quickly move quickly Center of impact The controlled variable should be such a physically unmovable point, what we call, a node. Examples of Center of Impact [7] Finding a Controlled Variable [8] nonminimum phase minimum phase Hit a ball to get the minimum impact on hands.

4 Velocity Input Model [9] [0] Double Inverted Pendulum velocity input This model is obtained as a sub-product. But the usefulness will be noticed later. Under-actuated System Andersen s Approach SISO# [] [] Control System for DIP SISO# SISO# [] LTI Model for DIP [6] LTI Control by LQI Design Method

5 [7] OBC with an I-Action [8] Steady State Analysis [9] LQI Design Method () [0] LQI Design Method () Double Inverted Pendulum (979) [] Outline [] LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control 5

6 [] Spinning Body [] LPV Model varying parameter Under the z-angular velocity variation, regulate the disturbed x&y-angular velocities. LPV Control [5] [8] Design Specification Vertex# Vertex# # # Vertex# # # Vertex# The interpolation of two vertex controllers doesn t guarantee the closed-loop stability. [9] CLPS by LPV SF [0] LMI-Based Design of LPV SF 6

7 LMIs for SF [] No Control [] LTI Control (SF) [] LPV Control (SF) [] Quasi-LPV Control (SF) [5] Arm-Driven IP (ADIP,997) [6] 7

8 Equilibrium States for ADIP [7] Wide-range Stabilization of ADIP [8] The horizontal movement is reduced. Under-actuated System LTI Model for ADIP [9] Velocity Controlled Actuator [50] LPV Model for ADIP [5] Control System for ADIP [5] # # varying parameter velocity input # # 8

9 Arm-Driven IP (997) [5] Outline [5] LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine Underwater Vehicle: DELTA [55] [56] Underwater Vehicle (DELTA) Wide-area survey: Towing mode for wide scanning Self-propulsive mode for local investigation Control System for DELTA [57] Exp# (LQI Control, 99) [58] 9

10 Exp# (Manual and LQI Controls) [59] Diving by Linear Control [60] Decreasing thrust Pitching proportional to the target depth Increasing thrust Diving by Scheduling Control [6] Physical Parameters of DELTA [6] Pitching independent of the target depth Decreasing thrust Increasing thrust L=,. d= 085,. = 0, g= 9. 8 = 5. / 000, xt=l ( ), zt=l ( ) xb= , zb=- 05 m= (58. +w +w )/ 9. 8, dm= 5 L d 0 xg** = ( w- 68w ) / ( w +w ) xg= ( m-dm) /m xg** +dm/m xdm, zg= ( w+ 075w ) / (58. +w +w ) I xx= ( w +w )/ 9. 8 I yy* = (( ) w + ( ) w )/ 9. 8, I yy= I yy* +dm xdm I zz* = ( 787 w + 68 w )/ 9. 8, I zz= I zz* +dm xdm, I xz= 0 A= 5 L d 078,. A= 5 L d 0, A= 5 L d 598 A= 5 L d 08, A55= 5 L d 99, A66= 5 L d 0 X uu= 5 Ld ( - 06), X uuk= 5 Ld ( )), X v= 5 ULd 9, X ww= 5 Ld 07 Y v= 5 ULd ( ), Yvv= 5 Ld 7. 88, Yp= 5 UL d 68, Y r= 5 UL d. 769, Yrr= 5 L d Z w= 5 ULd ( ) 9, Zq= 5 UL d Zq* K v= 5 UL d ( - 5), K p= 5 UL d ( - 6), K r= 5 UL d M w= 5 UL d ( - 88), M q= 5 UL d M q* N v= 5 UL d 999, Nvv= 5 L d ( ), N r= 5 UL d ( - 708), Nrww= 0 pthy= 06, z=l ( -0),. k=l ( -059),. zth=l 0896, pthx=l ( -009),. yth= 06 b=- t 5, c t= 98, e t= 866, ft=-005. ; Hydrodynamic Coefficients [6] Parameter Sensitivities [6] Parameter Uncertainties 0

11 Control System for DELTA [66] Exp# (LTI Control, m to m) [67] # # # # # # # # Exp# (Q-LPV Control, m to m) [68] Exp#5 (LTI Control, m to m) [69] Exp#6 (Q-LPV Control, m to m) [70] Exp#7 (LTI Control, 5m to m) [7]

12 Exp#8 (Q-LPV Control, 5m to m) [7] Exp#9 (Q-LPV Control) [7] Outline [7] CHIKYU: Deep-sea Drilling Vessel [75] LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine (C)JAMSTEC/CDEX by revealing the system of major Length : 0m Breadth : 8m Gross tonnage : 57,087tons Open the new frontier of earth and life science for future of mankind earthquakes, global changes, origin of life CHIKYU: Riser Pipe Units & BOP [76] [77] CHIKYU: DPS & Azimuth Thrusters Length :7m Diameter :.m (C)JAMSTEC/CDEX (C)JAMSTEC/CDEX (C)JAMSTEC/CDEX (C)JAMSTEC/CDEX

13 [78] CHIKYU: Drill House [79] CHIKYU: Operations CHIKYU: Landing Operation [80] CHIKYU: Reentry Operation [8] 0m 0m Drill House 00m Wind Wave Current Drill House 00m Wind Wave Current DPS 000m.m DPS 000m.m VIV unknown deviation VIV unknown deviation ROV BOP Entry Corn ROV LMRP LowerMarine RiserPackage Lower BOP [8] CHIKYU: Reentry Control System Why the reentry op is difficult? [8] Command DPS Control 推力配分 Allocation THR Current Vessel Position moving vessel moving vessel Automatic Controller Upper-End Inclined Angle Lower-End Position Riser CAMERA entry point entry point Center of impact

14 Reentry Control Problem [8] [85] Control System for a Riser How to realize the stability and the performance of reentry control under no wind, no current and surface current DPS not to be modified [86] State Variables q,q, [87] Motion Equation Velocity Input Model [88] Experimental Set Up (5m) [89] varying parameter velocity input.5m Current kt.5m.5m Stereo Camera

15 Riser Pipe Unit Model (5m) [90] Exp# (No Control for Riser) [9] CHIKYU: 0 m length Vessel Model:.8 m length Scaling factor : /55 Riser: 500 m length Riser Model:.8 m length Scaling factor : / mm Current st nd rd th period Dynamic Similarity 0mm /55 deviation Geometric Similarity Exp# (No Control with Current) [9] Exp# (Unity Feedback) [9] Exp# (LQI Control) [9] Exp#5 (LQI Control with Current) [95] 5

16 Exp#6 (Overview) [96] Experimental Set Up (m) [97] Current kt m Riser Pipe Unit Model (m) [98] Experiments by m riser model [99] CHIKYU: 0 m length Assumed Vessel Model: m length Scaling factor : /000 Riser: 500 m length Riser Model: m length Scaling factor : /500 Current.5 mm st nd rd th period Dynamic Similarity 0mm /000 deviation Geometric Similarity Concluding Remark [00] Outline [0] Control Tech. Ocean Eng. Having control technologies as the second axis will expand your engineering ability. Thank you for your attention. LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine 6

17 [0] Thrust Components and Moment 5 [0] CA Equation 5 [0] CA Problem 5 General Solution of CA Eq. [05] 5 Command DPS Control 推力配分 Allocation THR Vessel Position arbitrary (n-)-vector Conventional Method [06] 5 CA with Rotated Angle Constraints [07] 5 By norm minimization, each THR is apt to play the same role with the same thrust & direction. Conventional Compensation Proposal Therefore for the small sign change under the weak disturbance, each THR must always rotate for the forward and backward commands. Forward Backward

18 No. No. No. Toy Problem on CA [08] 5 CA Simulation of Toy Problem T [09] 5 X T T Y N Θ Θ Θ CA Experiment () [0] 5 CA Experiment () [] 5 Outline [] [] MOMOTO Model 6 LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine Time lag Parameter Uncertainty Velocity Variation 8

19 [] Scheduled MOMOTO Model 6 [5] Scheduled MOMOTO Model 6 [6] Sate Equation 6 [7] LPV Model with Vertexes 6 [8] LPV Control System 6 [9] Design Specification 6 # # # # # # 9

20 [0] Interconnection with Integrator 6 [] CLPS by LPV OF 6 [] LMI Based Design of LPV OF 6 [] LMIs for OF Design 6 [] Scheduled PID Controller 6 [5] LPV Control of MONOTO Model 6 Case Case Case 0

21 Outline [6] HYWIND [7] 7 LQI Control Linear-Quadratic- Integral Design of Linear-Time- Invariant Control LPV Control Linear-Matrix- Inequality Based Design of Linear- Parameter-Varying Control Applications Underwater Vehicle Flexible Riser 5 Azimuth thrusters 6 Nomoto s Model 7 Wind Turbine [9] 風力発電機の運転モード 7 風力発電機の数学モデル [0] 7 5 バッテリー V(m/s) ω(rad/s) 風力発電機モデル 風レンズ風車の空力トルク特性 風レンズ風車の数学モデル : カットイン風速 : 定格風速 : カットアウト風速 : 定格出力 可変負荷により任意電流値が実現可能 [] 風力発電機のLPVモデル 7 [] モードの制御目的 7 風力エネルギーを最大限 獲得すること 風レンズの周速比が常に最適周速比となるように回転数制御 制御目的 : 出力係数 トルク係数 周速比

22 モードのLPVモデル [] 7 モードの制御目的 [] 7 風エネルギーから獲得したパワーを定格出力に抑える モード における風速の変動幅は 出力係数 トルク係数 次のポリトピック型 LPV モデルを導出することができる 制御目的 : ただし 周速比 [5] モードのLPVモデル 7 [6] モードのLPVモデル 7 図 6. 風速と係数 A の関係 LPV モデリング問題を解決する つのアプローチ トルク係数曲線を 次関数近似 カットアウト風速時 定格風速時 実際のモード のシステム変動 カットアウト風速と定格風速間が線形システム変動の場合 風速と回転数の つのパラメータに線形依存した風力発電機の状態方程式が導出される ポリトピック型 LPV モデルを導出することができない [7] モードのLPVモデル 7 カットアウト風速 数値シミュレーションによる検討 モード の計算結果 モード の計算結果 [8] 7 風速 [m/sec] 使用したフィールド計測風速データの時系列 定格風速 従来制御方式によるアプローチ 回転速度 [rad/sec] 線形パラメータ変動制御方式