PID-type controller for marine cycloidal propeller: a simulation study

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.

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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

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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.

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Correspondence to Vishwanath Nagarajan.

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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

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Keywords

  • PID control
  • Marine cycloidal propeller
  • manoeuvring
  • Hydrodynamics
  • Pitch angle