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Propulsion Control Part 2 of 2

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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: [email protected]

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

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

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:

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

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

Plant control

Low level control

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

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:

Effect on Actual Power for Different Low Level Controllers

Alternative 1:

Propeller speed controlled or pitch controlled

Alternative 2:

Propeller torque or power control

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

- 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

- 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

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

- Mapping from thrust to power
- Motor torque setpoint found by shaft speed feedback

Power algorithm:

Weakness with power control:

- Singular for zero shaft speed

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

Propeller data:

Shaft Speed: 0-10 rps

Thrust characteristics

- Wave height: 8cm
- Wave period: 1s

Actual Thrust

Actual Thruster

Torque

Shaft Speed

Motor Torque

Motor Power

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:

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

Actual Thrust

Actual Thruster

Torque

Shaft Speed

Motor Torque

Motor Power

Experiments: Sensitivity to Changes in Advance Ratio

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

- Combined power/torque control
- Load torque observer for performance monitoring
- Anti-spin thruster control for extreme conditions

- 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

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

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

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

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

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.

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)

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:

Ventilation

Normal conditions

Fast response during rapid load changes: Estimation delay 0.15-0.2 seconds

Robust towards modelling errors

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:

Normal conditions

Ventilation

May be used for monitoring, ventilation detection, thrust re-allocation

and as feedback to an anti-spin thruster controller.

- Monitor the estimated torque loss factor:
- Define limits for beginning and termination of ventilation:
- Set the ventilation flag high or low:

Other detection schemes:

- Monitoring of motor torque
- Monitoring of shaft speed
- Combined detection (several criteria)

- 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:

- Reduce the thrust command in order to lower the shaft speed to some optimal value .
- Modified thrust command during ventilation:

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

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

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

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

Thrust

Torque

Shaft speed

Motor torque

Power