Abstract
The paper presents a methodology to design an electric controller for marine cycloidal propeller. The controller is designed considering the torque and the rotational speed limit of the motor. The influence of manoeuvring dynamics of the ship, rotational speed of the disc, eccentricity ratios and torque, pitching speed and pitch angle of the blades on the controller design are investigated. Feedback signals are used for the controller and combined with multiple PID control logic for controlling the motion of disc and blades. The proposed PID controller helps to stabilize the rotational speed of propeller blades and disc when requirement of torque exceeds the maximum limit of motor torque. The proposed control algorithm enhances the chances of optimizing propulsion efficiency of the blade. This is achieved due to decoupling of the motion of individual blades. Simulation results of different manoeuvring and straight run cruising conditions demonstrate the application of proposed control scheme. Finally, the simulated results are validated with the experimental results of mechanically controlled cycloidal propeller.
Similar content being viewed by others
Abbreviations
- \(\left\{ \begin{gathered} S \hfill \\ P \hfill \\ \end{gathered} \right\}\) :
-
Starboard or port propeller
- a (m):
-
Chord length of blade
- C D :
-
Coefficient of drag
- CF (N):
-
Centrifugal force
- CG:
-
Centre of gravity of blade aerofoil section
- C L :
-
Coefficient of lift
- C M :
-
Coefficient of moment
- CCW:
-
Counterclockwise direction
- CW:
-
Clockwise direction
- dt (s):
-
Time step
- D (m):
-
Diameter of disc
- \({e_{\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) :
-
Eccentricity ratio
- \({e_{1\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (m):
-
The distance of eccentricity point along y-axis from disc centre in disc co-ordinate system
- \({e_{2\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (m):
-
The distance of eccentricity point along x-axis from disc centre in disc co-ordinate system
- FD (N):
-
Drag force on propeller blade
- \({F_{X\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (N):
-
Component of thrust on the port/starboard disc along the x-axis in disc co-ordinate system
- \({F_{Y\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (N):
-
Component of thrust on the port/starboard disc along the y-axis in disc co-ordinate system
- Ib (kg-m2):
-
Mass moment of inertia of the blade about z-axis
- Id (kg-m2):
-
Mass moment of inertia of the disc about the z-axis
- K db :
-
Derivative gain of the blade controller
- k dd :
-
Derivative gain of the disc controller
- K Ib :
-
Integral gain due to blade pitching of the blade controller
- K Id :
-
Integral gain due to disc rotation
- K Pb :
-
Proportional gain of the blade controller
- k Pd :
-
Proportional gain of the disc controller
- L (N):
-
Lift force on blade
- LS (m):
-
Length of ship
- MB (kg):
-
Mass of the propeller blade
- MD (kg):
-
Mass of the propeller disc with all accessories including blade and machinery
- NB (rpm):
-
Rotational speed of propeller blade
- \({N_{D\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (rpm):
-
Rotational speed of propeller disc
- O :
-
Centre of propeller disc
- P :
-
Steering centre
- Pb (KW):
-
Powers consumed by blade actuator
- Pd (KW):
-
Powers consumed by disc actuator
- \({Q_{BF\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (N-m):
-
Torque due to bearing friction on propeller disc
- \({Q_{BL\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Torque due to fluid friction on the propeller disc
- \({Q_{TH\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Torque on propeller disc due to resultant thrust on vertical bearing
- \({Q_{D\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Hydrodynamic torque on propeller disc
- r (m):
-
Radius of the propeller blade shaft
- rb (m):
-
Average radius of propeller blade bearing
- R (m):
-
Radius of propeller disc
- Rd (m):
-
Average radius of propeller disc bearing
- RTS (N):
-
Resistance force on ship
- Rn:
-
Reynolds number of propeller disc
- t (s):
-
Time
- \({T_{x\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (N):
-
Thrust acting on the blade stock due to hydrodynamic action along the x-axis of disc co-ordinate system
- \({T_{y\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N):
-
Thrust acting on the blade stock due to hydrodynamic action along the y-axis of disc co-ordinate system
- u (m/s):
-
Velocity of ship
- VR (m/s):
-
Resultant inflow velocity on blade
- VT (m/s):
-
Tangential velocity on propeller disc
- vx (m/s):
-
x component of velocity of ship
- vy (m/s):
-
y component of velocity of ship
- Z :
-
Total number of blades in a propeller unit
- \({\alpha _{\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (deg):
-
Angle of attack
- \({\theta _{\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (deg):
-
Blade orbit angle
- \({\dot {\theta }_{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\)(rad/s):
-
Angular velocity of propeller disc
- \({\ddot {\theta }_{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (rad/s2):
-
Angular acceleration of propeller disc
- \({\delta _{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (deg):
-
Pitch angle of propeller blade
- \({\dot {\delta }_{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (rad/s):
-
Angular velocity of propeller blade
- \({\ddot {\delta }_{\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (rad/s2):
-
Angular acceleration of propeller blade
- \(\lambda\) :
-
Advance coefficient of propeller disc
- \({\tau _{\left\{ {\begin{array}{*{20}{c}} S \\ P \end{array}} \right\}}}\) (N-m):
-
Torque on the stock of a single blade
- \({\tau _{{\text{BF}}\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Torque due to bearing friction on propeller blade
- \({\tau _{TH\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Torque on single blade due to friction force in vertical bearing
- \({\tau _{HY\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (N-m):
-
Torque on single blade due to hydrodynamic lift and drag force
- \({\phi _{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) (deg):
-
Angle of the connected line of eccentricity point and blade stock with the positive \({x_2}\)-axis of disc co-ordinate system
- \({\eta _{O\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\) :
-
Open-water efficiency
- \({\eta _{\text{D}}}\) :
-
Propulsive efficiency
- \({\mu _{\left. h \right|b}}\) :
-
The rolling friction coefficient of the horizontal support bearing of propeller blade
- \({\mu _{\left. h \right|d}}\) :
-
The rolling friction coefficient of the horizontal support bearing of the disc
- \({\mu _{\left. v \right|b}}\) :
-
The vertical bearing friction coefficient of propeller blade
- \({\mu _{\left. v \right|d}}\) :
-
The vertical bearing friction coefficient of propeller disc
- \(\nu\) :
-
Kinematic viscosity
- \({\xi _{\left\{ \begin{subarray}{l} S \\ P \end{subarray} \right\}}}\)(deg):
-
Angle between resultant flow and thrust direction
- CP:
-
Centre of pressure
- ECMCP:
-
Electronically controlled marine cycloidal propeller
- MCP:
-
Marine cycloidal propeller
- PPS:
-
Pulses per second
- SP:
-
Stock position of the blade
- VSP:
-
Voith Schneider Propeller
References
Lee DK, Jeong Y, Shin JG, Oh D (2014) Optimized design of electric propulsion system for small crafts using the differential evolution algorithm. Int J Precis Eng Manuf Green Technol 1(3):229–240. https://doi.org/10.1007/s40684-014-0029-9
Balchen JG, Jenssen NA, Mathisen E, Saelid S (1980) A dynamic positioning system based on Kalman filtering and optimal control. Model Identif Control 1(3):135–163. https://doi.org/10.4173/mic.1980.3.1. No.
Sorensen AJ, Sagatun SI, Fossen TI (1996) Design of a dynamic positioning system using model-based control. Control Eng Pract 4(3):359–368
White AS (2013) Limits to control of ship capsize using cycloidal propellers compared to active fins. World J Model Simul 9(2):130–138
Altosole M, Donnarumma S, Spagnolo V, Vignolo S (2018) Simulation of a marine dynamic positioning system equipped with cycloidal propellers. In: Guedes Soares, Santos (eds) Progress in maritime engineering and technology. Taylor & Francis Group, London. ISBN 978-1-138-58539-3
Altosole M, Donnarumma S, Spagnolo V, Vignolo S (2017) Marine cycloidal propulsion modelling for dp applications. VII International Conference on Computational Methods in Marine Engineering, MARINE
Bradley S, Urzon AJ (2015) United States patent application publication—cycloidal marine-propulsion system. Filed: May 12, 2015, Appl. No: 14/709,551, Pub. No: US 2015/0321740 A1, Pub. Date: Nov. 12
Halder A, Walther C, Benedict M (2017) Unsteady hydrodynamic modeling of a cycloidal propeller. Fifth International Symposium on Marine Propulsion Smp’17, Espoo, Finland, June
Dash AK, Nagarajan V, Sha OP (2016) Bifurcation analysis of a high-speed twin-propeller twin-rudder ship manoeuvring model in roll-coupling motion. Nonlinear Dyn 83:2035–2053. https://doi.org/10.1007/s11071-015-2463-9
http://voith.com/en/products/services/power-transmission/vsp-voith-schneider-propeller-10002.html. Accessed on 16 May 2018
Turbo V. Voith turbo voith schneider® propellers for mine countermeasure vessels shock resistance of voith schneider® Propeller n.d. http://www.voith.com/en/976_e_vtmh_brochure_vspformcmv_g_1912e.pdf. Accessed on 21 Sept 2017
Nandy S, Nagarajan V, Sha OP (2018) On the heuristic based electronic control of marine cycloidal propeller. Appl Ocean Res 78:134–155. https://doi.org/10.1016/j.apor.2018.05.013
https://w3app.siemens.com/mcms/infocenter/dokumentencenter/ld/InfocenterLanguagePacks/catalog-d83-2/loher-vario-high-voltage-motors-catalog-d83-2-2015-en.pdf. Accessed on 16 May 2018
https://w3app.siemens.com/mcms/infocenter/dokumentencenter/ld/Documentsu20Catalogs/dc-motor/da12-2008-en.pdf. Accessed on 16 May 2018
http://www.shipspotting.com/gallery/photo.php?lid=2189054. Accessed on 16 May 2018
ABS (2006) Guide for vessel manoeuvrability. American Bureau of Shipping, Houston
Jurgens D, Palm M (2009) Voith Schneider propeller—an efficient propulsion system for DP controlled vessels. Dynamic Positioning Conference, October 13–14, 2009
Ficken NL, Dickerson MC (1969) Experimental performance and steering characteristics of cycloidal propellers. Department of Navy, Naval ship research and development center, Report 2983
Voith Schneider propeller designer manual (2018) http://160.75.46.2/staff/takinaci/dersler/advpropsys/week_10/vtmh_am_brochure_g1861_designer-manual_e.pdf. Accessed on 26 June 2018
Voith Schneider propeller current application and development (2018) https://pdfs.semanticscholar.org/b2d7/8bedbdff5893120de12a7a1d128045e8712d.pdf. Accessed on 26 June 2018
Nandy S, Nagarajan V, Sha OP (2015) An alternative control option of marine cycloidal propeller. ISBN 978-81-8487-509-6, INCAM 13–15 June 2015, IIT Delhi, India, pp 621
Nandy S, Nagarajan V, Sha OP (2015) Improving efficiency of marine cycloidal propeller for coastal shipping. ISBN 978-1-909024-49-6, ICSOT 10–11 December 2015, Organized by RINA, U.K. & IIT Kharagpur, India, pp 107–118
Nandy S, Nagarajan V, Sha OP (2016) Optimization of blade pitch angle of an electronically controlled marine cycloidal propeller. International Conference on computational and experimental marine hydrodynamics, 24–25 November, 2016, Organized by RINA, U.K. & IIT Madras, India
Acknowledgements
The first author is awarded by “High value PhD Scholarship” under “Prof R P Gokarn Innovation Grant” by Tiara Charitable Foundation for experimentation. First author would like to express deepest gratitude and hearted acknowledgment of thankfulness to co-authors for their full support, engagement, expert guidance, encouragement and valuable comments and suggestions during the research work.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Nandy, S., Prabhu J, J., Nagarajan, V. et al. PID-type controller for marine cycloidal propeller: a simulation study. J Mar Sci Technol 25, 111–137 (2020). https://doi.org/10.1007/s00773-019-00635-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00773-019-00635-2