Vol.49, No.3, 336/ Consideration Regarding Automation of Controllable Pitch Propeller for Mooring Pier in Stormy Weather Masayoshi Doi, Kazuhi

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1 Vol.49, No.3, 336/ Consideration Regarding Automation of Controllable Pitch Propeller for Mooring Pier in Stormy Weather Masayoshi Doi, Kazuhisa Nagamoto, Kenichi Idenawa and Yasuchika Mori The purpose of this study is a design of an automatic peering system with a Controllable Pitch Propeller (CPP) in the case of the stormy weather. A velocity response of CPP has a delay time. Especially, this study verifies the ship s propelling force against the CPP angle and detects the delay time by analyzing the data of the propelling force. The CPP angle is controlled by Generalized Minimum Variance Control (GMVC). This study arranges the GMVC for the automatic mooring system. The proposed GMVC has wind and a tidal effect s terms. The wind effect s term is considered by the ship s drift with the wind. The predicted wind velocity is calculated by the AR model of wind change. The AR model of wind is used for the GMVC of the peering system. Key Words: predictive control, generalized minimum variance control, controllable pitch propeller, time delay, ARMA model 1. 1) 3) Faculty of Engineering, Hiroshima Institute of Technology, Miyake, Saeki-ku, Hiroshima Yuge National Maritime College, 1000 Yuge Shimoyuge, Kamishima-cho, Ochi-gun, Ehime Graduate School of System Design, Tokyo Metropolitan University, 6 6 Asahigaoka, Hino Received December 27, 2011 Revised April 24, 2012 () (Controllable Pitch Propeller) 4) CPP CPP CPP CPP CPP CPP CPP 10 5) (Generalized Minimum TR 0003/13/ c 2011 SICE

2 Variance Control) 6) 9) CPP ARMA (Auto Regressive Moving Average) ARMA [m] 1 2 mv2 = μf s(0 <μ<1) s μ GMVC PID GMVC GMVC pt Fig. 3 Fig. 1 Controllable pitch propellers Fig. 2 Mooring load with CPP angle A setup to moor the ship to pier in the strong wind (1) 0 (2) CPP ARMA (3) ARMA (4) GMVC AR (5) GMVC Δ 2. 10) CPP Fig. 1 CPP CPP CPP Fig. 2 1 CPP Fig. 2 0 CPP 1 4 CPP 0 Fig kn CPP 4 24 kn CPP m/sec 2.67 m/sec CPP CPP CPP Fig. 3 CPP 10 5) CPP CPP CPP CPP ARMA CPP

3 338 T. SICE Vol.49 No.3 March 2013 Fig. 4 Closed control system of CPP propelling with GMVC ARMA 12) A(q 1 )y(k) = q j B cpp(q 1 )u cpp(k) + W cd wind (k)+d tidal (k)+ξ(k), 2 A(q 1 )=1+a 1q a nq n, B cpp(q 1 )=b 0 + b 1q b mq m. Fig. 5 Components of wind pressure GMVC GMVC Fig. 4 GMVC CPP GMVC CPP CPP CPP ) 1) R = 1 2 ρc(a cos2 φ + B sin 2 φ)v 2. 1 R [N/m 2 ] ρ [0.125 kg/m 3 ] C φ v [m/sec] Fig CPP CPP u cpp(k) CPP [ ] y(k) [m/sec] [m/sec] d wind (k) d tidal (k) ARMA k W c W c 6. 2 q 1 1 q j CPP ξ(k) 0 σ 2 0 CPP ARMA (ARMA) q 1 ARMA GMVC ARMA 5. CPP (1) (2) (3) (4) (5) (6) (7) () (8) CPP (1) (2) (3) + (4) (5) (6) (7) ( ) (8) Half Ahead Dead Slow Ahead

49 3 2013 3 339 ARMA (2) 13) ARMA A(q 1 ) B(q 1 ) θ =[a 1,,a n,b 0, b m] T. 3 θ ϕ(k) ϕ(k) =[ y(k 1),, y(k n), u(k 1), u(k m)] T, 4 y(k) y(k) =θ T ϕ(k)+ξ(k).

4 ARMA (2) 13) ARMA A(q 1 ) B(q 1 ) θ =[a 1,,a n,b 0, b m] T. 3 θ ϕ(k) ϕ(k) =[ y(k 1),, y(k n), u(k 1), u(k m)] T, 4 y(k) y(k) =θ T ϕ(k)+ξ(k). 5 1 ŷ(k +1) = [1 A(q 1 )]y(k +1)+B(q 1 )u(k) = θ T ϕ(k). 6 J N (θ) J N (θ) =1/N l(k, θ, ε(k, θ)). 7 l(k, θ, ε(k, θ)) ε(k, θ) =y(k) ŷ(k θ). 8 ˆθ(N) = argmin J N (θ). 9 (12) J N 0 R(N)ˆθ(N) =f(n), 14 ˆθ(N) =R 1 (N)f(N) CPP CPP CPP 1 Fig CPP CPP (1) (2) 0 5 CPP 0.5 (3) (4) Fig. 7 Fig. 8 CPP 3 Fig. 7 CPP l(k, θ, ε(k, θ)) = ɛ 2 (k, θ), 10 J N (θ) J N (θ) =1/N ε 2 (k, θ) =1/N {y(k) θ T ϕ(k)} 2, 11 J N (θ) J N (θ) =c(n) 2θ T f(n)+θ T R(N)θ, 12 Fig. 6 Training ship Yugemaru (12) R(N) f(n) c(n) R(N) =1/N ϕ(k)ϕ T (k), f(n) =1/N y(k)ϕ T (k), c(n) =1/N y 2 (k), 13 Fig. 7 Angle change of CPP (ahead 3 degrees)

5 340 T. SICE Vol.49 No.3 March 2013 Fig. 8 Velocity responses (ahead 3 degrees) Table 1 Coefficients of ARMA model regarding CPP propelling Fig. 9 A locus of ship s drifting Fig. 8 Fig. 7 Fig. 8 CPP 10 CPP ARMA (2) A(q 1 ) B(q 1 ) u(k) y(k) CPP 2.5 ARMA (2) A(q 1 )= q q 2, B cpp(q 1 )= Table 1 CPP ARMA GMVC ARMA CPP CPP ARMA 8 16 m/sec 12 m/sec 12 m/sec CPP Table 1 CPP1.5 ARMA (2) d tidal (k) d tidal (k) ARMA (2) 6. 2 (1) CPP 0 (2) GPS (3) Fig m/sec 25 [ ] [ ] [ ] mile mile = m 6m/sec 0.6 m/sec 0.6 m/sec 150 ARMA W c W c = 1 645, 17 W c (17) W c =1/645 Fig. 9 6m/sec m/sec (17) (17) W c =1/645 W c (17)

6 CPP GMVC CPP GMVC GMVC GMVC CPP GMVC J = E{h(k + j) 2 }. 18 h(k + j) h(k + j) = P (q 1 )y(k + j) R(q 1 )w(k + j) + S(q 1 )Δu cpp(k) 19 P (q 1 )=1+p 1q p np q np, R(q 1 )=r 0 + r 1q r nr q nr, S(q 1 )=s 0 + s 1q s ns q ns. w(k) CPP P (q 1 ) R(q 1 ) S(q 1 ) Δ Δ=1 q 1 GMVC J = E{h(k + j) 2 } (19) y(k + j) k Diophantine P (q 1 )=E(q 1 )A(q 1 )Δ + q j F (q 1 ), 20 E(q 1 )=1+e 1q e j 1q (j 1), F (q 1 )=f 0 + f 1q f h q h, E(q 1 ) F (q 1 ) (19) (20) Δ Δ GMVC 14) (19) P (q 1 )y(k + j) Diophantine (20) P (q 1 )y(k + j) = E(q 1 )B cpp(q 1 )Δu cpp(k)+f (q 1 )y(k) +ΔE(q 1 )W cd wind (k + j)+δe(q 1 )d tidal (k + j) +ΔE(q 1 )ξ(k + j). 21 (19) (21) Fig. 10 Block diagram of closed loop system with proposed GMVC J = E[{E(q 1 )B cpp(q 1 )Δu cpp(k)+f (q 1 )y(k) +ΔE(q 1 )W cd wind (k + j)+δe(q 1 )d tidal (k + j) R(q 1 )w(k + j)+s(q 1 )Δu cpp(k) +ΔE(q 1 )ξ(k + j)} 2 ]. 22 (22) ĥ(k + j k) J = E[{ĥ(k + j k)+δe(q 1 )ξ(k + j)} 2 ], ĥ(k + j k) ĥ(k + j k) = E(q 1 )B cpp(q 1 )Δu cpp(k)+f (q 1 )y(k) 23 +ΔE(q 1 )W cd wind (k + j)+δe(q 1 )d tidal (k + j) R(q 1 )w(k + j)+s(q 1 )Δu cpp(k), 24 ĥ(k + j k) =0 CPP GMVC (25) {E(q 1 )B cpp(q 1 )+S(q 1 )}Δu cpp(k) = R(q 1 )w(k + j) F (q 1 )y(k) ΔE(q 1 ){W cd wind (k + j)+d tidal (k + j)}, 25 GMVC Fig GMVC(25) GMVC(25) d wind (k + j) d tidal (k+j) CPP d tidal (k+j) d tidal (k) Fig : m/sec

7 342 T. SICE Vol.49 No.3 March 2013 Fig. 11 Change of strong wind (typhoon No.6, 11:30 40, July 19, 2011) CPP d wind (k+j) AR 15) AR Fig. 12 Ship s velocity with wind (17 m/sec) G(q 1 )d wind (k) =e(k), 26 e(k) G(q 1 ) q 1 j d wind (k + j) =N(q 1 )d wind (k)+m(q 1 )e(k + j), 27 M(q 1 ) N(q 1 ) Diophantine 1=G(q 1 )M(q 1 )+q j N(q 1 ), 28 M(q 1 )=1+m 1q m j 1q (j 1), N(q 1 )=n 0 + n 1q n ngq ng, G(q 1 ) {g 1, g 2,,g ng} J = E{e(k) 2 } j ˆd wind (k + j) =N(q 1 )d(k), 29 GMVC(25) ˆd wind (k + j) {E(q 1 )B cpp(q 1 )+S(q 1 )}Δu cpp(k) = R(q 1 )w(k + j) F (q 1 )y(k) E(q 1 ){W c ˆdwind (k + j)+d tidal (k)}, 30 (30) d tidal (k +j) d tidal (k) 9. CPP GMVC 8 Fig m/sec m/sec 17 m/sec Fig. 13 CPP control with GMVC 1.7 m/sec CPP Table 1 CPP2.5 CPP ARMA Table 1 CPP2.5 1 CPP GMVC ˆd wind (k + 10) = n 0d(k)+n 1d(k 1), GMVC Fig. 12 (12 22 m/sec 100 ) (m/sec) CPP ( ) Fig. 12 CPP m/sec 1.8 m/sec 6kN 20 kn CPP Fig. 13 Fig. 14 CPP GMVC Fig. 13 CPP Fig. 14 Fig. 13 Fig. 14 Q =0 Q =0.5 Q =30

8 Fig. 14 Velocity with GMVC Fig. 15 Velocity with PID and GMVC GMVC Q = m/sec Q =0 0.1 m/sec CPP 20.7 Q = m/sec Q = m/sec Fig. 13 Fig. 14 GMVC(25) {E(q 1 )B cpp(q 1 )+S(q 1 )}Δu cpp(k) = R(q 1 )w(k + j) F (q 1 )y(k) E(q 1 ){W cd wind (k + j)+d tidal (k + j)}, 32 Fig PID GMVC PID PID (1) (0 m/sec) (2) (3) PID PID Kd = Kp = Ki= PID sec GMVC Q = m/sec Fig. 15 CPP GMVC PID GMVC PID Fig. 15 GMVC 0.2 m/sec PID 0.8 m/sec GMVC PID 10. CPP ARMA CPP CPP ARMA CPP GMVC GMVC AR GMVC CPP PID GMVC CPP GMVC REDAS 1 (2005) 2 (1977) 3 (1966) 4 KAMOME PROPELLER Co Ltd. (1961) 5 M. Doi, T. Takehira, K. Nagamoto and Y. Mori: Delay Time of Propelling Force with Ship s Controllable Pitch Propeller (CPP), ICCAS-SICE2009, 551/554 (2009) 6 C 119-C11, 1420/1426 (1999) 7 P.E. Wellstead and M.B. Zarrop: Self-Tuning Systems,

344 T. SICE Vol.49 No.3 March 2013 John Wiley & Sons Ltd. (1991) 8 D.W. Clarke and P.

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Mori: Visual Tracking for References Generated by a Stochastic Model, Asian

9 344 T. SICE Vol.49 No.3 March 2013 John Wiley & Sons Ltd. (1991) 8 D.W. Clarke and P.J. Gawthrop: Self-Tuning Control, IEE Proc., 120D-6, 633/640 (1979) 9 D.W. Clarke, C. Mohdadi and P.S. Tuffs: Generalized Predictive Control, Automatica, 23-2, 137/160 (1987) , 111/116 (2007) /211 (1981) /280 (1981) 13 Matlab (1996) 14 C 119-C4, 496/501 (1999) 15 T. Kamiya, M. Doi, H. Mochiyama and Y. Mori: Visual Tracking for References Generated by a Stochastic Model, Asian Journal of Control, 5-3, 437/444 (2003) ( ( )) ( ) ()

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