Propulsion Control Part 2 of 2

1. Propulsion ControlPart 2 of 2 Øyvind Smogeli and Asgeir J. Sørensen, Department of Marine Technology, Norwegian University of Science and Technology, Otto Nielsens Vei 10, NO-7491 Trondheim, Norway E-mail: Oyvind.Smogeli@ntnu.no Asgeir.Sorensen@ntnu.no

2. Outline Part 1: Modelling • Motivation and problem formulation • Mathematical modelling • Propeller characteristics • Propeller losses and dynamics • Experimental results Part 2: Local control • Conventional local thruster control • Combined power and torque control • Sensitivity to thrust losses • Propeller load torque observer • Torque loss calculation • Anti-spin control • Simulation results • Experimental results

3. Propulsion and Thruster Control • Thrust and power allocation (over/under actuated systems) • Pitch/rpm/torque/ power control • Combined torque and power control • Anti-spin thruster control • Combined rudder and propeller control PITCH or RPM CONTROL POWER TORQUE CONTROL POWER VARIABLE TORQUE CONSTANT TORQUE

4. Thruster Modelling for Control: A summary Thruster dynamics: first order motor model rotational dynamics with friction propeller load torque propeller thrust propeller power Desired thrust and torque: Thrust and torque loss factors:

5. Propeller Block Diagram q x Thruster p p unit . . ( ) f q x Q p p Q a T T Q Q n Shaft Motor ref . m a c ( ) f Control Dynamics Dynamics T n

6. Controller Structure Office Systems Business enterprise/ Fleet management Office Network Ship 3: Ship 2: Ship 1: Operational management Real-Time Control Local optimization (min-hour) Control layers Fault-Tolerant Control High level (0.1-5 s) Plant control Real-Time Network Low level (0.001-1 s) Actuator control

7. DP Controller Structure Plant control Low level control

8. Disturbances T n T a ref ref g ( ) T ref Relation Between Plant Control and Actuator Control Typical thrust and moment characteristics for a speed controlled fixed pitch propeller: Tref = ρwD4KT0|nref|nref Qref = ρwD5KQ0|nref|nref is the actual developed thrust subject to disturbance and losses T a

9. Thrust Allocation Relation between 3 DOF control vector - surge, sway and yaw and r number of thruster/propellers is: is the thruster configuration matrix Ý Þ T J 3 r × u is the commanded control input vector - often (pitch)2 or (speed)2 ref is the commanded control input vector - in Newton T ref is the thruster force coefficients (NB! will be different for CPP or FPP) á â K diag k = i Commanded control input provided by r thrusters is: The thrust produced by thruster unit i is:

10. Effect on Actual Power for Different Low Level Controllers Alternative 1: Propeller speed controlled or pitch controlled Alternative 2: Propeller torque or power control

11. Low Level Controller Designs Control in moderate seas • Shaft speed control • Torque control • Power control • Combined power/torque control Anti-spin control in extreme seas Combined power/torque control with spin detection and setpoint optimization due to severe thrust losses: • Ventilation • Water exits

12. Shaft Speed Controller Design • Conventional control scheme • Mapping from thrust to shaft speed • Setpoint controlled by e.g. PID controller Weakness with speed control: • Severe power fluctuations in waves • Wear and tear of propulsion equipment

13. Torque Control • Mapping from thrust to torque • Motor torque setpoint given by desired torque Qref = (DKQ0/KT0 )Tref Weakness with torque control: • Power fluctuations for high thrust • Speed transients during ventilation and in-and-out of water effects

14. Inner Torque Algorithm If the shaft inertia Isis high, feedforward terms from the reference torque/power may be needed to speed up the response of the propeller The torque is limited by the maximum available torque and the power α = 1.1 - 1.2 is the rated (nominal) torque and power

15. Power Control • Mapping from thrust to power • Motor torque setpoint found by shaft speed feedback Power algorithm: Weakness with power control: • Singular for zero shaft speed

16. Numerical Simulations Applying RPM, Torque and Power Control • Propeller: • Wageningen B-470 • D = 4m • Z = 4 • EAR = 0.7 • nmax = 3.5rps • Is = 5000kgm2 • Tref = 400kN • Sea state: • JONSWAP spectrum • Wave height: 4m • Wave period: 10s • Simulations for a supply vessel with main particulars [L,B,T]=[80,18,5.6]m

17. Open Water Experiments Set-up: MCLab Propeller data: Shaft Speed: 0-10 rps Thrust characteristics

18. Experimental Results: Local Thruster Control • Wave height: 8cm • Wave period: 1s Actual Thrust Actual Thruster Torque Shaft Speed Motor Torque Motor Power

19. Sensitivity Functions to Thrust Losses Sensitivity function - ratio of actual to reference thrust: T a Ý 6 Þ ª s T ref Shaft speed feedback control: Torque feedback control: Power feedback control:

20. Sensitivity to Changes in Advance Ratio KT and KQ as functions of Ja or Va, ignoring all other loss effects: Sensitivity function Open water propeller diagram

21. Experiments Results: Sensitivity tests Actual Thrust Actual Thruster Torque Shaft Speed Motor Torque Motor Power

22. Experiments: Sensitivity to Changes in Advance Ratio

23. Sensitivity as Function of Ventilation 1 Reduced propeller disc area 0.8 Propeller torque loss function h 0.6 Q 0.4 Propeller thrust loss function h T 0.2 Submergence/propeller radius h/R -0.5 0 0.5 1 1.5 2 h/R Torque s Q 1 Power s 0.8 P 0.6 RPM s n 0.4 Notice that maintaining thrust may lead to unacceptable high values of propeller speed (rps) during ventilation 0.2 -0.5 0 0.5 1 1.5 2 h/R

24. New Methods in Propulsion Control • Combined power/torque control • Load torque observer for performance monitoring • Anti-spin thruster control for extreme conditions

25. Combined Power/Torque Control • Torque control: Qcq = Qref = ρwD5KQ0|nref|nref • Power control: Qcp = Qref = Pref / (2π |n|) Qc = α(n)Qcq + (1- α(n)) Qcp • Combined control: • Weight function: α(x) = e-k|pxIr • k,p,r tuning factors • Avoids singularities for n=0

26. Combined Power/Torque Control Result Result: - Utilize the best properties of both power and torque control. - Valid for all setpoints and operating conditions • Propeller: • Wageningen B-470 • D=4m • Z=4 • EAR=0.7 • nmax=3.5rps • Is=5000kgm2 • Sea state: • JONSWAP spectrum • Wave height: 4m • Wave period: 10s • High thrust reference => high shaft speed => power control • Low thrust reference => low shaft speed => torque control • Shaft speed zero-crossing => singularity for power control

27. Ventilation and Water Exits A sudden loss of thrust and load torque may occur when operating with high propeller loading close to the surface. • Low propeller loading: Loss of effective disc area • High propeller loading: Ventilation • High submergence: Conventional thrust curve • Wagner effect gives rise to hysteresis in thrust production

28. Anti-spin Thruster Control A vessel operating in extreme environmental conditions may experience sudden losses of thrust capability due to ventilation and in-and-out-of water effects. Idea: Formulate anti-spin control as used in car wheel anti-spin • Detect ventilation • Reduce shaft speed • Detect ventilation termination • Increase shaft speed to old operating point Effect: • Reduced wear and tear • Less power transients • Better thrust production

29. Simulation Results: - Ventilation incident

30. Anti-spin Control Concept The general ideas of anti-spin control are to: • Reduce the wear and tear of the propulsion unit by preventing uncontrolled propeller racing • Limit the load transients on the power system • Optimize the thrust production and efficiency in transient operation regimes

31. Anti-spin Thruster Control

32. Propeller Load Torque Estimation For a propeller operating in rapidly changing environmental conditions, can we estimate the propeller loading? Current velocities Vc Wave velocities Vw Propeller velocities Vp Submergence h Varying loading Qa With some system knowledge, the answer is yes.

33. Propeller Load Torque Observer Equations The control plant model of the shaft control dynamics is: Propeller load torque Rotational inertia Friction coefficient Markov time constant Shaft speed White noise Motor torque Measurement The propeller load torque has been modeled as a 1st order Markov process. The observer equations are: Observer gains Input The linear observer is easily proven to be stable (GES)

34. Propeller Load Torque Observer Analysis Write on matrix form: The error dynamics become: where The error dynamics are UGES if F is Hurwitz, which is implied by positive definiteness of (-F). By Sylvester’s theorem (-F) is positive definite if:

35. Propeller Load Torque Observer Simulations Ventilation Normal conditions Fast response during rapid load changes: Estimation delay 0.15-0.2 seconds Robust towards modelling errors

36. Torque Loss Calculation The torque loss factor is defined as the ratio of actual to nominal propeller load torque: The nominal torque may be calculated from the measured shaft speed: An estimate of the torque loss factor is then calculated from the estimated propeller load torque: Avoid the singularity for n = 0 by a weighting function:

37. Torque Loss Calculation Simulations Normal conditions Ventilation May be used for monitoring, ventilation detection, thrust re-allocation and as feedback to an anti-spin thruster controller.

38. Ventilation Detection • Monitor the estimated torque loss factor: • Define limits for beginning and termination of ventilation: • Set the ventilation flag high or low:

39. Ventilation Detection and Anti-Spin

40. Ventilation Detection Simulations Other detection schemes: • Monitoring of motor torque • Monitoring of shaft speed • Combined detection (several criteria)

41. Primary Anti-spin Control Action • Reduce the commanded torque from the combined controller with modification factor : • Use the estimated torque loss as modification factor during ventilation: • Result: a different shaft speed controller:

42. Secondary Anti-spin Control Action • Reduce the thrust command in order to lower the shaft speed to some optimal value . • Modified thrust command during ventilation:

43. Experimental Set-up: MCLab Propeller: • D = 250 mm • Z = 4 • P/D = 1 • EAR = 0.55 Duct: • L/D = 0.5 • L = 118.8 mm • Di = 252.1 mm

44. Experiments: Controller comparison Slow-motion sinusoidal submergence with period T= 10s and thrust reference 140N Thrust Green: RPM control Blue: Combined control Red: Primary Antispin Black: Primary+Secondary Antispin Torque RPS Motor torque Power

45. Experiments: Controller comparison #2 Slow-motion sinusoidal submergence with period T= 5s and thrust reference 180N Thrust Green: RPM control Blue: Combined control Red: Primary Antispin Black: Primary+Secondary Antispin Torque RPS Motor torque Power

46. Experimental Results: Anti-spin details Blue: Measured propeller torque Red: Estimatied propeller torque Blue: Estimated torque loss factor Red: Ventilation detection flag Submergence Primary antispin action: Gamma Secondary antispin action: nras

47. Experimental Results: Anti-spin main data Thrust Torque Shaft speed Motor torque Power