BCT Module 05

Lecture Notes

BASIC CONTROL THEORY

Module 5 Control Applications in Marine and Offshore Systems

SEPTEMBER 2005

Prepared by Dr. Hung Nguyen

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TABLE OF CONTENTS Table of Contents..............................................................................................................................i List of Figures................................................................................................................................ iii List of Tables ..................................................................................................................................iv References .......................................................................................................................................v Objectives .......................................................................................................................................vi 1. Introduction .................................................................................................................................1 2. Pneumatic Control Systems.........................................................................................................1

2.1 Essential Requirements.........................................................................................................1 2.2 Basic Pneumatic Control Systems ........................................................................................2

3. Hydraulic Control Systems..........................................................................................................6 3.1 Hydraulic Servo Valve and Actuator.....................................................................................6 3.2 Applications of Hydraulic Servo Valve.................................................................................7

3.2.1 Speed Control System ...................................................................................................7 3.2.2 Hydraulic Steering Machine..........................................................................................8

4. Electrical and Electronic Control Systems ................................................................................10 4.1 Analogue Control Systems..................................................................................................10 4.2 Digital (Computer-based) Control Systems........................................................................12 4.3 PLCs (Sequence Control Systems) .....................................................................................13

4.3.1 The Processor Unit ......................................................................................................13 4.3.2 The Input/Output Section ............................................................................................14 4.3.3 The Programming Device ...........................................................................................14

5. Ship Autopilot Systems .............................................................................................................15 5.1 Mathematical Foundation for Autopilot Systems ...............................................................15

5.1.1 Autopilots of PID Type ...............................................................................................15 5.1.2 P Control .....................................................................................................................16 5.1.3 PD Control ..................................................................................................................17 5.1.4 PID Control .................................................................................................................18

5.2 Automatic Steering Principles.............................................................................................19 5.2.1 Proportional Control....................................................................................................19 5.2.2 Derivative Control.......................................................................................................21 5.2.3 Integral Control ...........................................................................................................22

5.3 Marine Autopilots in Market...............................................................................................23 5.3.1 Autopilot System PR-6000 (Tokimec) ........................................................................23 5.3.2 Autopilot System PR-2000 (Tokimec) ........................................................................23 5.3.3 Autopilot System PR-1500 (Tomimec) .......................................................................24

6. Dynamic Positioning Systems ...................................................................................................24 6.1 Basic Principles of Dynamic Positioning Systems .............................................................25 6.2 IMO DP Classfications .......................................................................................................27

7. Roll Stabilisation Systems .........................................................................................................28 7.1 Fin Stabilisation Systems....................................................................................................29

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7.2 Rudder Roll Stabilisation System .......................................................................................31 8. Trend of Control Systems ..........................................................................................................32 Summary of Module 5...................................................................................................................32 Exercises........................................................................................................................................33

iii

LIST OF FIGURES Figure 5.1.........................................................................................................................................3 Figure 5.2.........................................................................................................................................4 Figure 5.3.........................................................................................................................................5 Figure 5.4.........................................................................................................................................5 Figure 5.5.........................................................................................................................................6 Figure 5.6.........................................................................................................................................7 Figure 5.7.........................................................................................................................................7 Figure 5.8.........................................................................................................................................8 Figure 5.9.........................................................................................................................................9 Figure 5.10.......................................................................................................................................9 Figure 5.11.....................................................................................................................................11 Figure 5.12.....................................................................................................................................11 Figure 5.13.....................................................................................................................................12 Figure 5.14.....................................................................................................................................12 Figure 5.15.....................................................................................................................................13 Figure 5.16.....................................................................................................................................14 Figure 5.17.....................................................................................................................................15 Figure 5.18.....................................................................................................................................15 Figure 5.19.....................................................................................................................................16 Figure 5.20.....................................................................................................................................20 Figure 5.21.....................................................................................................................................21 Figure 5.22.....................................................................................................................................21 Figure 5.23.....................................................................................................................................22 Figure 5.24.....................................................................................................................................22 Figure 5.25.....................................................................................................................................23 Figure 5.26.....................................................................................................................................23 Figure 5.27.....................................................................................................................................24 Figure 5.28.....................................................................................................................................25 Figure 5.29.....................................................................................................................................25 Figure 5.30.....................................................................................................................................26 Figure 5.31.....................................................................................................................................26 Figure 5.32.....................................................................................................................................29 Figure 5.33.....................................................................................................................................30 Figure 5.34.....................................................................................................................................31 Figure 5.35.....................................................................................................................................31

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LIST OF TABLES Table 5.1 ........................................................................................................................................27 Table 5.2 ........................................................................................................................................29

v

REFERENCES AMC (unknown year), Lecture Notes on Automation, Australian Maritime College, Launceston Chesmond, C.J. (1990), Basic Control System Technology, Edward Arnold, UK. Fossen, T.I. (1994), Guidance and Control of Ocean Vehicles, John Wiley and Sons, UK. Fossen, T.I. (1994), Marine Control Systems – Guidance, Navigation and Control of Ships, Rigs

and Underwater Vehicles, Marine Cybernetics, Trondheim, Norway. Haslam, J.A., G.R. Summers and D. Williams (1981), Engineering Instrumentation and Control,

Edward Arnold, UK. Kou, Benjamin C. (1995), Automatic Control Systems, Prentice-Hall International Inc., Upper

Saddle River, New Jersey, USA. Nguyen, H.D. (2000), Self-tuning Pole Assignment and Optimal Control Systems for Ships,

Doctoral Thesis, Tokyo University of Mercantile Marine, Tokyo, Japan. Ogata, Katsuhiko (1997), Modern Control Engineering, 3rd Edition, Prentice-Hall International

Inc., Upper Saddle River, New Jersey, USA. Perez, T. (2005), Ship Motion Control – Course Keeping and Roll Stabilisation Using Rudder

and Fins, Springer-Verlag, London. Richards, R.J. (1993), Solving in Control Problems, Longman Group UK Ltd, Harlow, Essex,

UK. Seborg, Dale E., Thomas F. Edgar and Duncan A. Mellichamp (2004), Process Dynamics and

Control, 2nd Edition, John Wiley & Sons, Inc., Hoboken, New Jersey, USA. Taylor, D.A. (1987), Marine Control Practice, Butterworks, UK. Tetley, L. & C. Calcutt (2001), Electronic Navigation System, Butterworths Heinemann, Woburn,

MA.

vi

AIMS

1.0 Explain structures, operating principles of control systems in industries and maritime engineering.

LEARNING OBJECTIVES 1.1 Describe operating principles of pneumatic control systems 1.2 Describe operating principles of hydraulic control systems 1.3 Describe operating principles of electrical and electronic systems including analogue control

systems, digital control systems and programmable logic controllers 1.4 Describe operating principles of autopilot systems for marine vehicles. 1.5 Describe operating principles of dynamic positioning systems 1.6 Describe operating principles of roll stabilisation systems

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1. Introduction As mentioned in the earlier modules, computer science, high performance programming languages, I/O interface techniques and modern control theories allow very complicated control systems to be designed for different purposes. A modern control system is a combination of pneumatic, hydraulic and electronic elements. The trend of new control systems are computer-based control systems in which the control algorithms are designed in the form of software. Control applications in industries and marine and offshore systems may be as follows:

• Pneumatic control systems • Hydraulic control systems • Electrical and electronic control systems, including analogue, digital control systems

and PLCs (programmable logic controllers) • Surface vessels’ autopilot systems • Manoeuvring, control and ship positioning systems • Engine and machinery control systems • Control systems for underwater vehicles and robotics • Traffic guidance and control systems

In this Module, we deal with pneumatic, hydraulic, and electronic control systems and some control applications in industries and maritime engineering such as ship autopilots, dynamic positioning systems, roll stabilisation systems and so on. 2. Pneumatic Control Systems In previous modules, we dealt with principles of PID pneumatic control systems. This section gives more information about practical sides of pneumatic control systems. 2.1 Essential Requirements a) The air must be free of:

• Oil, • Moisture • Dust.

b) Sources of contamination are • Air intake – dust, oil vapour and water vapour • Compressor – oil, water, carbon wear particles and corrosion products

c) Reduction of contaminants • System design • Correct operation • Regular maintenance

System design: System to be used for control air supply only, preferably of a ring main type and sized to suit number of items of equipment in the circuit. Design features: (a) Compressor discharge pressure should be high enough to prevent condensation and minimise power requirements. Instruments and controllers require a supply of about 1.5 bar whilst some actuators may require 5 bar.

2

Operating at a high discharge pressure and reducing pressure at the instruments helps to dry the air and reduce size of components. (b) Quantity: System should be sized to match maximum expected demand. (i) match future expansion (ii) allow 10% leakage factors (iii) prevent excessive operation of compressors (c) Quality (dryness): Often this is over-emphasized resulting in increased costs. Most instruments will accept as a maximum. (i) 500ppm water vapour (ii) 1ppm solids >| micron (iii) 1gmHC/100m3 Dryness is achieved by (a) siting of air intake (b) sizing of air receiver (c) auto drains (d) sloping lines (e) tapping from top of distribution manifold to instruments (f) drains at low points (g) use of either: (i) Absorbent driers (ii) Refrigerant driers Compressor Types: Governed by the dryness and oil content of the air. Early instruments required totally oil free air, however modern instruments will tolerate some oil. Improvement in filtration systems has allowed use of oil lubricated compressors. Filtration: (a) Coalescing filters (b) Bronze filters (c) Air intake filters Operation/Maintenance:

• Operate compressors at rates discharge pressures. • Check moisture drains regularly. • Filters to be changes at prescribe intervals. • Ensure new instruments are correctly connected. • Site compressor suction in as clean and cry an area as possible. • Ensure automatic driers functioning. • Overhaul at prescribed intervals.

2.2 Basic Pneumatic Control Systems Pneumatic control systems are compressed air to supply energy for the operation of valves, motors, relays and other pneumatic control equipment. Consequently, the circuits consist of air lines. Pneumatic control systems are made up of the following:

1. A source of clean, dry compressed air which is stored in a receiving tank at a pressure capable of supplying all the pneumatic devices in the system with operating energy.

3

Pressure in the receiving tank is normally maintained between 2.5-10bar depending on the system.

2. A pressure reducing station which reduces recurving tank pressure to a normal operating pressure of 1-1.5bar again depending on system requirement.

3. Air lines which can either be copper or polyethylene tubing connect the air supply to the controlling devices (thermostats and other controllers). These air lines are called “mains”.

4. Controlling instruments such as thermostats, humidistats and pressure controllers are used to position the control valves.

5. Intermediate devices such as relays and switches. 6. Air lines leading from the controlling devices to the controlled devices. These air lines

are called “branch lines”. 7. Controlled devices such as valves or damper actuators. These can either be called

operators or actuators. A typical application of a pneumatic process controller is shown in Figure 5.1. The function of the controller is to open and close the control valve so as to manipulate the inflow rate, in the presence of fluctuations in outflow rate. It does this in order that the liquid level in the tank, as measured by the transducer, shall match as closely as possible the desired value, as determined by the manually adjusted set point.

Figure 5.1 Scheme and block diagrams for closed loop control of liquid level in a vessel, using a pneumatic process controller.

SCHEMATIC DIAGRAM

BLOCK DIAGRAM

CONTROLLER CONTROL LAW

VALVE & POSITIONER

PLANT PROCESS

REFERENCE TRANSDUCER SENSITIVITY

LEVEL TRANSDUCER measured level (process

variable) signal actual level

outflow rateinflow rate

set point = desired level

level referencesignal level error

signal

LEVEL CONTROLLER

controlleroutput

VALVE POSITIONER

CONTROL VALVE

SET POINT KNOB

LEVEL CONTROLLER

LEVELTRANSDUCER

outflowrate

measured level signal

manipulated inflow rate

4

The functions of the pneumatic controller are:

• To enable the set point signal to be generated • To receive the feedback signal representing the measured level • To generate an error signal by comparing the above two signals • To amplify the error signal and to incorporate dynamic terms, in generating the

controller output signal. The control law can incorporate one or more of the terms known as proportional action, integral action, and derivative action which have been described in Module 3. Figure 5.2 shows a symbolic representation of a controller containing only proportional action (P Controller). In practice, the PV and set point bellows may be coupled (differentially) to the flapper through fairly complex linkage arrangements. The flapper-nozzle amplifier and its out put pressure responds, nonlinearly, to minute changes in flapper displacement. The air relay behaves as a unity follower, so that its output pressure tracks the amplifier output pressure, but with significant increase in volumetric flow capacity. The feedback bellows completes a high gain negative feedback loop, and equilibrium is established by a force balance at the flapper. Thus, the controller output pressure is proportional to the difference between the set point and process variable pressures. The constant of proportionality may be adjusted by manually changing the moment arm ratios of linkages (not shown) which couple the feedback bellows to the flapper.

Figure 5.2 Symbolic representation of a pneumatic process controller incorporating only proportional action

AIR RELAY

FEEDBACK BELLOWS

SET POINT BELLOWS PV BELLOWS

flapper feedback displacement ∝ output pressure

supply air

supply air

FLAPPER-NOZZLEAMPLIFIER

process variable pressure

flapper input displacement ∝ (set point pressure – PV pressure)

set point pressure

controller output pressure

5

Integral action may be incorporated by adding a series connected combination of variable restriction and (integral action) bellows in the feedback path, as shown in Figure 5.3. The restriction is analogous to a variable resistor and the bellows is analogous to a capacitor, so that adjustment of the restriction will cause the integral action time constant to be ‘tuned’. If a second, variable (derivative) restriction is added at point X in Figure 5.3, in series with the proportional action bellows, adjustment of this restriction will cause the derivative action time constant to be tuned.

Figure 5.3 Symbolic representation of a pneumatic process controller incorporating proportional and integral action

Figure 5.4 shows the faceplate of a typical pneumatic indicating process controller, and the features shown are common to all general purpose analog process controllers.

Figure 5.4 Faceplate of a typical pneumatic process controller showing instrument displays and manual controls

AIR RELAY

PROPORTIONAL ACTION BELLOWS

SET POINT BELLOWS PV BELLOWS

supply air

supply air

FLAPPER-NOZZLE AMPLIFIER

process variable pressure

flapper input displacement

set point pressure

controller output pressure

INTEGRAL ACTION BELLOWS

VARIABLE RESTRICTION

1000 %

90

40

50

60

70

80

KNOB TO CONTROL THE CONTROLLER OUTPUT DIRECTLY, IN THE MANUAL MODE

SET POINT (SCALE) ADJUSTMENT KNOB

FIXED SET POINT MARKER

AUTO-MANUAL MODE CHANGEOVER SWITCH

CONTROLLER OUTPUT INDICATOR

MOVING DEVIATION INDICATOR

percentage deviation (deviation = process variable – set point)

6

3 Hydraulic Control Systems 3.1 Hydraulic Servo Valve and Actuator Purely hydraulic controllers are really a controller-actuator combination. Their input signal is a physical displacement that alters a servo valve.

Figure 5.5 Hydraulic servo valve and actuator When the spool of the servo valve is exactly central, the supply of hydraulic oil is prevented from reaching the actuator piston. The piston is held in place by the oil trapped between it and the servo valve spool. If the link then receives an input force, it moves and oil under pressure flows through the servo valve. This oil exerts a force on the actuator piston, making it move. Movement of the actuator rod causes the link to move at Y. The link pivots about X and moves at point P. The movement at P represents negative feedback. For example, an initial upward movement at X admits oil into the upper half of the actuator, forcing the piston down. This counters the initial movement at X. For any given input (X), a new position of equilibrium (Y) is rapidly reached. The lengths a and b determine the amount of negative feedback and the relationship of Y to X. Ideally, this controller has a first-order characteristic equation. Thus, theoretically, it cannot oscillate. In practice, however, the compressibility of the oil and mass of the piston-oil introduce a second-order (inertial) term.

LOAD

P

ba

Y X

Drain

Drain

Fluid supply

Input movements Output movements

Actuator

Servo valve

7

This gives the possibility of an oscillatory response to step changes in input. The inherent damping (friction and leakage) ensures that any oscillation dies away. But additional damping (usually of the dashpot or vane type) may be necessary to prevent excessive overshoot and long settling time. 3.2 Applications of Hydraulic Servo Valve 3.2.1 Speed Control System Let’s consider a speed control system as shown in Figure 5.6. If the engine speed increase, the sleeve of the fly-ball governor moves upward. This movement acts as the input to the hydraulic controller. A positive error signal (upward motion of the sleeve) causes the power piston to move downward, reduces the fuel-valve opening, and decrease the engine speed. A block diagram for the system is shown in Figure 5.7.

Figure 5.6 Speed control system

Figure 5.7 Block diagram for the speed control system in Figure 5.6

Oil under pressure

k

b

Engine

z

y

e

ω

a2 a1

sK

21

1

aaa+

E(s) Output Y(s)

21

2

aaa+

kbsbs+

Z(s)

8

If the flowing condition applies

1sK

kbsbs

aaa

21

1 >>++

(5.1)

the transfer function Y(s)/E(s) becomes

)s(E)s(Y =

bskbs

aaa

aaa

1

21

21

2 +++

=

+bsk1

aa

1

2 (5.2)

The speed controller is of the proportional and integral (PI) control. 3.2.2 Hydraulic Steering Machine Hydraulic servo valve is applied in the rudder handling system. Figure 5.8 shows a hydraulic steering machine. The ship actuator or the steering machine is usually controlled by an on-off rudder control system. The on-off signals from the rudder controller are used to open and close the port and starboard valves of the telemotor system.

Figure 5.8 Simplified diagram of a two-stage hydraulic steering machine Assume that both the telemotor and floating lever are initially at rest in position (a). The telemotor can be moved to position (b) by opening the port valve. Suppose that the rudder is still in its original position corresponding to position (b); this will cause the steering cylinder valve to open. Consequently, the floating lever will move to position (c) when the desired rudder angle has been reached. The maximum opening of the steering cylinder valve, together with the pump capacity, determines the maximum rudder speed. Figure 5.9 shows a block diagram of the steering machine with its dynamics. Amerogen (1982) suggested a simplified steering machine for rudder as shown in Figure 5.10. This representation is based on the telemotor being much faster than the main servo and that the time constant Td is of minor importance compared with the influence of the rudder speed.

port

poil

poil

starboard

Relay operated valves poil

(a)

(b)

(c)

rudder

telemotersteering cylinder floating lever

9

Figure 5.9 Simplified diagram of the hydraulic steering machine

Figure 5.10 Simplified diagram of the hydraulic steering machine Generally, the rudder angle and rudder rate limiters in Figure 5.10 will typically be in the ranges:

35max =δ degrees 7)s(deg/312 max <δ≤ (deg/s) (5.3)

for most of commercial ships. The requirement for minimum average rudder rate is specified by the classification societies such as American Bureau Shipping (ABS), Det norske Verits (DnV), Lloyds, etc. It is required that the rudder can be moved from 35 degrees port to 35 degrees starboard within 30 seconds. Fossen reported that according to Eda and Crane (1965) the minimum design rudder rate in dimensional terms should satisfy: 9.132min =δ (U/L) (deg/s) (5.4) where U is the ship speed in m/s and L is the ship length in m. Recently, much faster steering machine have been designed with rudder speeds up to 15-20 (deg/s). A rudder speed of 5-20 (deg/s) is usually required for a rudder-roll stabilisation (RRS) system to work properly. Another model of the rudder could be

( )( )( )( )( )( )

≥δ−δ∆δ−δ−δ−

≥δ−δ∆δ−δ−−δ=δ

0if/exp1

0if/exp1

ccmax

ccmax

(5.5)

The parameter ∆ will depend on the moment of inertia of the rudder. Typical values will be in the range 103 ≤∆≤ .

s1

δc δ δmax δ max

from autopilot

rudder limiter

rudder rate limiter

)sT1(sK

f+

δc δ δmax

main servo telemotor system

Rudder control algorithm

Angle transducer

rudder servo

)sT1(s

K

d+

Angle transducer

10

In Japan, the MMG (Mathematical Model Group) suggested the following steering machine:

aTrudc

c

+δ−δδ−δ

=δ (5.6)

where Trud is the time constant of rudder (seconds) and a is a constant used to avoid zero-dividing. 4 Electrical and Electronic Control Systems In earlier modules, we have dealt with very basic principles of PID electrical and electronic control systems. Generally electrical and electronic control systems can be categorised into three types: 1) analogue control systems; 2) digital (or discrete) control systems; and 3) programmable logic controllers (PLCs). This section will outline three types of electrical and electronic control systems. 4.1 Analogue Control Systems The control system is interconnected using current or voltage signals. There is no standard range. Typical common ranges are:

Current: 4-20mA, 10-50mA Voltage : 0-10V, 1-5V, -5V-+5V, -10V-+10V

The tendency is to use 4-20mA in the loop since the elevated zero (range) means fault findings is easier and the current loop is less prone to signal noise. Electronic controllers are most sensitive, have wider adjustment ranges on PI and D actions, but often require signal conversion to pneumatic at the final control element. Figure 5.11 illustrates a three-term controller with separate sections. The controller consists of comparator circuit, proportional controller (P-action), integrator (I-action), and defferentiator (D-action) and power amplifier. Figure 5.12 and Figure 5.13 illustrate an application of PID controller into a flow control system at the Australian Maritime College. In this system, the PID controller plays role as a comparison element and controller in which the controlling signal is computed. To operate the whole control system, it is necessary for user to set control gains (including proportional control gain, integral gain (or integral time) and derivative gain (or derivative).

Sensor

(Feedback signal)

Setpoint

Comparator circuit

Actuating error

Integrator Integrator Proportional gain

11

Figure 5.11 Three-term controller with separate sections

Figure 5.12 The flow control bench system arrangement (Control Engineering Lab, AMC)

Controller C/P Converter Actuator

Rot

amet

er

D/P Cell

Water tank

R

Controller

Globe valve

Valve (Closed)

Control valve

kPa

mA

Valve (Closed)

Orifice plate

D/P Cell 4-20mA

250 Ω

Square RootCircuit

DC 24V

Bailey Controller

PUMP

12

Figure 5.13 Connection diagram of the flow control bench system (Control Engineering Lab, AMC)

4.2 Digital (Computer-based) Control Systems Nowadays computers have been used in many control systems. The microprocessor based control systems allow user to configure set point variables and a range of subsidiary functions by means of a keyboard, and display control variable digitally by various indicators. Input signals can be digital or analogue and can be linearised as required. Some controllers will accept multiple inputs at the same time, allowing improved control as in gas flow.

• Output signals is by user specification, either • Solid state or mechanical relay digital, or 4-20mA analogue.

Computer interfacing by using optional boards (I/O (A/D-D/A) interface boards) allows computer supervisory control. Figure 5.14 shows a computer-based (digital) control system with I/G interfaces.

Figure 5.14 Digital control system using computer (software) and I/O interfaces Figure 5.15 shows the block diagram of a computer-based (digital) autopilot system using a recursive estimation algorithm in combination with the optimal control law (Nguyen, H.D., 2000).

Computer (Control

Software)

DAC

ADC

PROCESS

Final Control

Measurement

I/O Interfaces

13

4.3 PLCs (Sequence Control Systems) PLC stands for Programmable Logic Controller. The first PLC was developed in 1968-1969. The PLC has become an unqualified success. PLCs are now produced by over 50 manufacturers. Varying in size and sophistication, these electronic marvels are rapidly replacing the hard-wired circuits that have controlled the process machines and driven equipment of industry in the past. This section outlines operating principles of a PLC. A programmable logic controller is a solid state device designed to perform the logic functions previously accomplished by electro-mechanical relays, drum switches, mechanical timers/counters, etc. for the control and operation of manufacturing process equipment and machinery. A typical PLC consists of three components. These components are the processor unit, the input/output section (I/O interface) and the programming device. 4.3.1 The Processor Unit (CPU) The processor unit houses the processor which is the ‘brain’ of the system. This brain is a microprocessor-based system which replaces control relays, counters, timers, sequencers, and so forth and is designed so the user can enter the desired circuit in relay ladder logic. The processor then makes all the decisions necessary to carry out the user program for control of a machine or process. It can also perform arithmetic functions, data manipulation and communication between the PC, remotely located PC’s, and/or computer systems. A DC power supply is required to produce the low level DC voltage used by the processor. This power supply can be housed in the processor unit or may be a separately mounted unit depending on the model and/or the manufacturer. The processor can be referred to as a CPU (Central Processing Unit). 4.3.2 The Input/output Section

Autopilot u(t) = -Kx(t)

Steering machine

Ship (Shioji Maru)

Noises

RPE Estimator

Outputs

Feedback

Set

State space model (F,G)

Riccati equation

Optimal calculator

Figure 5.15 Block diagram of a computer-based autopilot system

State feedback control gain

δδδδ tδδδδ

Computing unit (computer)

Dynamic systemDesign settings

θθθθ

K

14

Input/output Section (see Figure 5.7b) CPU and

Programming device

The input/output section consists of input modules and output modules for communication with peripherals (real world devices). The real world input devices may be pushbuttons, limit switches, analogue sensors, selector switches and so on, while the real world output devices could be hard wired to motor starters, solenoid valves, indicator lights, position valves, and the like. 4.3.3 The Programming Device The programming device may be called an industrial terminal, program development terminal, programming panel or simply programmer. Regardless of their names, they all perform the same function and are used to enter the desired program in relay ladder logic that will determine the sequence of operation and ultimate control of the process equipment or driven machinery. The programming device may be a hand held unit with an LED (light emitting diode) display, an LCD (liquid crystal display), a desktop type with a CRT display or other compatible computer terminals.

Figure 5.16 (a) Conceptual structure of a PLC-based control system; (b) Mitsubishi PLC (input/output section)

There are several types of PLC. Each type has its own features. Figure 5.17 shows an example of a PLC-based control system (AMC Control Lab). The PLC is Mitsubishi MELSEC FXon-24MR-ES. The CPU is Pentium 4 with Windows XP.

Output devices

Input Gates

Output lines

Input lines

CPU Programming

device

Switches Sensors Etc.

Motors Relays Lamps Etc.

(a)

(b)

15

Peripherals

Figure 5.7 Mitsubishi PLC-based Control System (AMC Control Lab) 5. Ship Autopilot Systems 5.1 Mathematic Foundation for Autopilot Systems Autopilots for course-keeping are normally based on feedback from a gyrocompass measuring the heading. Heading rate measurements can be obtained by a rate sensor, gyro, numerical differentiation of the heading measurement or a state estimator. This is common practice in most control laws utilizing proportional, derivative and integral action. The control objective for a course-keeping autopilot can be expressed as dψ = constant. This control objective is illustrated in Figure 5.18. On the contrary, course-changing manoeuvres suggest that the dynamics of the desired heading should be considered in addition.

Figure 5.18 Autopilot for automatic heading 5.1.1 Autopilots of PID-Type Most autopilots for ship steering are based on simple PID-control laws with fixed parameters. To avoid that the performance of the autopilot deteriorating in bad weather and when the speed of the ship changes, HF rudder motions must be suppressed by proper wave filtering, while a gain scheduling technique can be applied to remove the influence of the ship speed on the hydrodynamic parameters. For simplicity, let the LF motion of a ship be described by Nomoto’s 1st-order model: δ=ψ+ψ KT (5.8)

Steering Machine SHIP

Waves, wind & current

PID-typed Autopilot

dψ cδ δ ψ

16

Based on this simple model the control laws of P, PD-, and PID-type using feedback from the LF state estimates will be discussed. The performance and robustness of the autopilot can be evaluated by using the simulation set-up showed in Figure 5.19. The proposed simulator models 1st-order wave disturbances as measurement noise while wave drift forces, wind and sea currents are treated as a constant disturbance.

Figure 5.19 Simplified simulation set-up for course-keeping autopilot 5.1.2 P-control Let us first consider a proportional control law: ( )ψ−ψ=δ dPK (5.9) where 0KP > is a regulator design parameter. Substitution of (5.9) into (5.8), yields the closed-loop dynamics: dPP KKKKT ψ=ψ+ψ+ψ (5.10) From this expression the eigenvalues are found to be:

T2

TKK411 P2,1

−±−=λ (5.11)

Since, 0TKK41 P <− for most ships, it is seen that the real part of the eigenvalues are given as:

KW

2nω

n2ζω

K Steering Machine

Autopilot cδ cδdψ

Ship (Nomoto’s 1st-order model)

Wave drift Wind & current

Whitenoise

w

1st-order wave disturbance

Hψ

ψLψ

17

T21Re 2,1 −=λ (5.12)

Consequently, the suggested P-controller will not stabilize an open-loop unstable ship (T < 0). For stable ships (T > 0) the imaginary part of the closed-loop eigenvalues and thus the oscillatory motion can be modified by adjusting the regulator gain KP. For instance, a critically damped system is obtained by choosing:

TK41K P = (5.13)

5.1.3 PD-control Since, the use of a P-controller is restricted to open-loop stable ships with a certain degree of stability, another approach has to be used for marginally stable and unstable ships. A stabilizing control law is obtained by simply including derivative action in the control law. Consider a control law of PD-type in the form: ( ) ψ−ψ−ψ=δ DdP KK (5.14) Here KP > 0 and KD > 0 are the controller design parameters. The closed-loop dynamics resulting from the ship dynamics and the PD-controller are: ( ) dPPD KKKKKK1T ψ=ψ+ψ++ψ (5.15) This expression simply corresponds to a 2nd-order system in the form: d

2n

2nn2 ψψ=ψω+ψζω+ψ (5.16)

with natural frequency nω (rad/s) and relative damping ratio ζ . Combining (5.15) and (5.16) yields:

T

KKPn =ω and

P

D

TKK2KK1+=ζ (5.17)

The relative damping ratio is typically chosen in the interval 0.8 ≤ ζ ≤ 1.0, whereas the choice of nω will be limited by the resulting bandwidth of the rudder δω (rad/s) and the ship dynamics 1/T (rad/s) according to:

T1 < 24421 24

2n +ζ−ζζ−ω < δω (5.18)

ship dynamics closed-loop bandwidth rudder servo

18

For a critically damped ship ( 1=ζ ) the closed-loop bandwidth bω is related to the natural frequency nω of the closed-loop system (5.17) by a factor of 0.64, that is nb 64.0 ω=ω . Alternatively, we can solve (5.10) for KP and KD which yield:

K

TK2n

Pω=

K1T2K n

D−ζω= (5.19)

Here nω and ζ can be treated as design parameters. 5.1.4 PID-Control During autopilot control of a ship it is observed that a rudder off-set is required to maintain the ship on constant course. The reason for this is a yaw moment caused by the rotating propeller and the slowly-varying environmental disturbances. These are wave drift forces (2nd-order wave disturbances) and LF components of wind and sea currents. However, steady-state errors due to wind, current and wave drift can all be compensated for by adding integral action to the control law. Consider the PID-control law:

( ) ( )( ) ττψ−ψ+ψ−ψ−ψ=δt

odIDdP dKKK (5.20)

where KP > 0, KD > 0 and KI > 0 are the regulator design parameters. Applying this control law to Nomoto’s 1st-order model: ( )0KT δ−δ=ψ+ψ (5.21) where 0δ is the steady-state rudder off-set, yields the following closed-loop characteristic equation ( ) 0KKKKKK1T IP

2D

3 =+σ+σ++σ (5.22) Hence the triple (KP, KD, KI) must be chosen such that all the roots of this 3rd-order polynomial become negative, that is 0Re i <σ for (i = 1, 2, 3) (5.23) This can be done by applying Routh’s stability criterion. Another simple intuitive way to do this is by noticing that δ can be written as:

( )ψ−ψ

++=δ d

IDP sT

1sT1K (5.24)

where the derivative and integral time constants are TD = KD/KP and TI = KP/KI, respectively. Hence, integral action can be obtained by first designing the PD-controller gains KD and KP according to the previous discussions. This ensures that sufficient stability is obtained. The

19

next step is to include integral action by adjusting the integral gain KI. A rule of thumb can be to choose:

10T

1 n

I

ω≈ (5.25)

which suggests that KI should be chosen as:

KT

10K

10K

3n

Pn

Iω=ω= (5.26)

Now let’s consider some practical aspects of designing an autopilot system. 5.2 Automatic Steering Principles Whatever type of system is fitted to a ship, the basic principles of operation remain the same. Before considering the electronic aspects of an automatic steering system it is worthwhile considering some of the problems faced by an automatic steering device. In its simplest form an autopilot system compares the course-to-steer data, as set by the helmsman, with the vessel’s actual course data derived from a gyro or magnetic repeating compass, and applies rudder correction to compensate for any error detected between the two input signals. Since the vessel’s steering characteristics will vary under a variety of conditions, additional facilities must be provided to alter the action of the autopilot parameters in a similar way that a helmsman would alter his actions under the same prevailing conditions. For a vessel to hold a course as accurately as possible, the helm must be provided with data regarding the vessel’s movement relative to the course to steer line. “Feedback” signals provide this data consisting of three sets of parameters.

• Position data: information providing positional error from the course line • Rate data: rate of change of course data • Accumulative error data: data regarding the cumulative build-up of error.

Three main control functions acting under the influence of one or more of the data inputs listed above are: proportional control, derivative control and integral control. 5.2.1 Proportional Control This electronic control signal causes the rudder to move by an amount proportional to the positional error deviated from the course line. The effect on steering, when only proportional control is applied, is to cause the vessel to oscillate either side of the required course, as shown in Figure 5.20. The vessel would eventually reach its destination although the erratic course steered would give rise to an increase in fuel expended on the voyage. Efficiency would be downgraded and rudder component wear would be unacceptable.

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Figure 5.20 An early electro-mechanical autopilot system using telemotors

(Tetley L. et al. 2001)

21

At the instant an error is detected, full rudder is applied, bringing the vessel to starboard and back towards its course (Figure 5.21). As the vessel returns, the error is reduced and autopilot control is gradually removed. Unfortunately the rudder will be amidships as the vessel approaches its course causing the vessel resulting in a southerly error. Corrective data is now applied causing a port turn to bring the vessel back onto course. This action again causes an overshoot, producing corrective data to initiate a starboard turn in an attempt to bring the vessel back to its original course. It is not practical to calculate the actual distance of the vessel from the course line at any instant. Therefore, the method of achieving proportional control is by using a signal proportional to the rudder angle as a feedback signal.

Figure 5.21 The effect of applying proportional control only. The vessel oscillates about the course to steer 5.2.2 Derivative Control With this form of control, the rudder is shifted by an amount proportional to the “rate-of-change” of the vessel’s deviation from its course. Derivative control is achieved by electronically differentiating the actual error signal. Its effect on the vessel’s course is shown in Figure 5.22.

Figure 5.22 The effect of applying derivative control only Any initial change of course error is sensed causing a corrective starboard rudder command to be applied. The rate-of-change decreases with the result that automatic rudder control decreases and, at point X, the rudder returns to the midships position. The vessel is now making good a course parallel to the required heading and will continue to do so until the autopilot is again caused to operate by external forces acting on the vessel.

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An ideal combination of both proportional and derivative control produces a more satisfactory return to course, as shown in Figure 5.23. Figure 5.23 Applying a combination of proportional and derivative control brings the vessel

back to on track. The initial change of course causes the rudder to be controlled by a combined signal from both proportional and derivative signals. As the vessel undergoes a starboard turn (caused by proportional control only) there is a change of sign of the rate of change data causing some counter rudder to be applied. When the vessel crosses its original course, the rudder is to port, at some angle, bringing the vessel back to port. The course followed by the vessel is therefore a damped oscillation. The extent of counter rudder control applied is made variable to allow for different vessel characteristics. Correct setting of the counter rudder control should cause the vessel to make good its original course. Counter rudder data must always be applied in conjunction with the output of the manual “rudder” potentiometer, which varies the amount of rudder control applied per degree of heading error. Figure 5.24 (a) If “counter rudder” and “rudder” controls are set too high, severe oscillations are produced before the equipment settles. (b) If “counter rudder” and “rudder” controls are set too low, there will be little overshoot and sluggish return to the course. Figure 5.24(a) and (b) show the effect on vessel steering when the counter rudder and rudder controls are set too high and too low, respectively. 5.2.3 Integral Control Data for integral control is derived by electronically integrating the heading error. The action of this data offsets the effect of a vessel being moved continuously off course. Data signals are produced by continuously sensing the heading error over a period of time and applying an appropriate degree of permanent helm.

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Figure 5.26 Autopilot system PR-2000 Courtesy of Tokimec Co. Ltd. (Japan)

In addition to proportional control, derivative control and integral control, autopilots normally have the yaw, trim, draft, rudder limit, and weather controls. 5.3 Marine Autopilots in Market The marine autopilot receives signals from directional sensors such as the gyrocompass and uses them to automatically control the helm for navigation. The history of the TOKIMEC marine autopilots dates back to 1925 with the development of the P1 single pilot and the P2 single pilot. Later TOKIMEC integrated the gyrocompass into the autopilot unit ("GYLOT") and also developed the "Navigation Console" with radar and other navigational instruments all built in. The performance and reliability of these products obtained the overwhelming support of the marine market. Today, TOKIMEC offers the following series of autopilots.

PR-6000 For medium to large vesselsPR-2000 For small to medium vesselsPR-1500 For small craft

5.3.1 Autopilot System PR-6000 This high-grade autopilot model was designed with three fundamental concepts in mind: expanding and strengthening helm functions, thorough safety considerations, and improved reliability and more intelligent maintenance functions.

• IBS (Integrated Bridge System) compatibility • Improved interface • Complete range of controls • Compatible with a variety of steering systems • Safety considerations designed in • Standard compatibility with digital output gyros

5.3.2 Autopilot system PR-2000 This best-selling model has been installed in over 15,000 small and medium vessels including fishing boats, coastal craft, and merchant ships, and is renowned for its stable performance and ease of use.

• Designed for operational simplicity • More affordable, with improved course holding ability • Variety of system configurations (stand-alone model,

GYLOT model, console model) • Compatible with a variety of steering systems


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5.3.3 Autopilot system PR-1500 Features of PR-1500 are as follows: High-grade Functions; Easy to Operate Wide range of automatic steering modes

• Work mode augments the conventional automatic steering function: Work mode is used under operational conditions which differ from normal operation - such as trawling and slow speeds, etc.

• Automatic navigation mode is standard feature: Standard NMEA interface simplifies connections with GPS navigators or plotters.

Easy steering and easy-to-view display • Remote Azimuth Holding is standard feature: Remote Azimuth Holding can be

initiated during remote steering. When the vessel is turned on a planned course by remote steering with the RAH switch activated and remote controller dial returned to the neutral position, the course setting can be stored in memory.

• Evasive steering (Override function) standard feature: NFU steering can be employed in any of the steering modes.

• Total information display: The large size LCD provides a comprehensive display of data such as ship's heading, set course, rudder angle, and control constants.

• Self-diagnostic function simplifies maintenance: Internal checks of main functions can be performed at the front panel.

6. Dynamic Positioning Systems In the 1960s systems for automatic control of the horizontal position, in addition to the course, were developed. Systems for the simultaneous control of the three horizontal motions (surge, sway and yaw) are today commonly known as dynamic positioning (DP) system. More recently anchored positioning systems or position mooring (PM) systems have been designed. For a free floating vessel in DP the thrusters are the prime actuators for station-keeping, while for the PM system the assistance of thrusters are only complementary since most of the position keeping is provided by a deployed anchor system.


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DP systems have traditionally been a low-passed application, where the basic DP functionality is either to keep a fixed position and heading or to move slowly from one to another location. In addition, specialized tracking functions for cables and pipe-layers, and operations of remotely operated vehicles (ROVs), have been included. The traditional autopilot and way-point tracking functionalities have also been included in modern DP systems. The trend today is that high-speed operation functionality merges with classical DP functionality, resulting in a unified system for all speed ranges and types of operations. Figure 5.28 DPS manufactured by Kawasaki Heavy Industries Co. Ltd.

The first DP systems were designed using conventional PID controllers in cascade with low pass and/or notch filters to suppress the wave-induced motion component. Figure 5.28 shows an illustration of a DP system (the control console unit) developed by Kawasaki Heavy Industries Co. Ltd., Japan. Figure 5.29 shows a conceptual diagram of a DPS.

Figure 5.29 Conceptual diagram of a DPS 6.1 Basic Principles of Dynamic Positioning System The basic forces and moments act on a vessel operated in seawater as shown in Figure 5.30. Ship steering dynamics is represented by an appropriate state space model as follows. BuAxx += (5.27) DuCxy += (5.28) where x and u are the vector of state variables and the vector of control variables, respectively, y is the vector of outputs and A, B, C and D are the matrices consisting of parameters (coefficients).

Steering Machine (rudder controller)

Slave ManeuveringUnit

Gyrocompass (Course)

Indicators (Monitors) Course Ship speed Position Rudder angle Pitch angle Revolution Wind direction Wind speed

DPS (Advanced

Technology)

GPS/GNSS D-GPS (Position)

Barometer (Wind D & S)

Log & Sounder (Speed, depth)

CPP Controller (Pitch)

Propeller Controller

Side Thruster Controller

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In order to obtain the values of state variables and parameters, many measuring techniques, filtering and identification procedures are applied. An example of the filtering procedure is Kalman filter. In order to compute the control signals for the DPS, a control law with a criterion function is applied. For examples, PID control or optimal control has been applied in the DPS. Figure 5.31 shows a block diagram of a DPS. Interested readers can find more information about the DPSs in Fossen (1994) and Fossen (2002).

Figure 5.30 Basic forces and moments (Kongsberg Maritime)

Figure 5.31 Dynamic positioning system Example: an optimal control algorithm (H. Nguyen, 2000) In order to design an optimal control system (e.g. autopilot system or DPS), in general, it is assumed that the ship to be controlled is described by a discrete-time state space (matrix) model as follows.

)t()()t(

)t()()t()()1t(xCy

uGxFxθθθθ

θθθθθθθθ=

+=+ (5.29)

where x(t) is the vector of state variables, u(t) is the vector of control variables, and F( θθθθ ), G( θθθθ ) and C( θθθθ ) are matrices formed by estimated parameters. The linear optimal control law is to minimize the quadratic cost function (JO)

D/RTK-GPSCompass

Control system(DPS)

1st-order wave disturbance

Environmental loads due to wind, wave and currents

Positioning heading

Low-frequency estimates of position, heading, velocities and biases Observer +

wave filter

Reference computation

27

[ ]−

=

+=1M

0t

TTO )t()t()t()t(J RuuQεεεεεεεε 5.30)

where Q and R are weighting matrices (symmetric and positive definite matrices) weighting the cost of heading errors against the control effort, )t(εεεε is the ship heading error and u(t) is the rudder angle. It should be noted that the system (5.29) could be an MIMO ARX (Auto-Regressive eXogenous) model, which could be transformed into a state space model as in (5.29). The solution to this problem can be found by applying the R. Bellman’s Principle of Optimality: “An optimal policy, or optimal control strategy, has the property that, whatever the initial state decision, the remaining decision must form an optimal control strategy with respect to the state resulting from the first decision.” Minimizing the cost function leads to finding solution of the following discrete-time matrix Riccati equation, and then the control signals can be calculated by the following expression. )t()t( Kxu −= (5.31) where K is the state feedback control gain resulting from the solution of the Riccati equation. Interested readers can find more information about optimal control in H. Nguyen (2000), Forsen (1994) and Fossen (2002) and therein references. 6.2 IMO DP-Classifications Dynamic positioning systems are classified by IMO as shown in Table 5.1.

Table 5.1 Classifications of DPS according to IMO

IMO Corresponding Class Notations (Manufacturers) Description

DP Class ABS LRS DNV

Manual position control and automatic heading control under specified maximum environmental conditions

- DPS-0 DP (CM) DNV-T

Automatic and manual position and heading control under specified maximum environmental conditions

Class 1 DPS-1 DP (AM) DNV-AUT DNV-AUTS

Automatic and manual position and heading control under specified maximum environmental conditions, during and following any single fault excluding loss of a compartment. (Two independent computer systems).

Cass 2 DPS-2 DP (AA) DNV-AUTR

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Automatic and manual position and heading control under specified maximum environmental conditions, during and following any single fault including loss of a compartment due to fire or flood. (At least two independent computer systems with a separate back-up system separated by A60 class division).

Class 3 DPS-3 DP (AAA) DNV-AUTRO

7. Roll Stabilization Systems According to Fossen (1994), the main reasons for using roll stabilizing systems on merchant ships are to prevent cargo damage and to increase the effectiveness of the crew. From a safety point of view it is well known that large roll motions cause people to make more mistakes during operation due to sea sickness and tiredness. For naval ships certain operations such as landing a helicopter or the effectiveness of the crew during combat are of major importance. Therefore, roll reduction is an important area of research. Several solutions have been proposed to accomplish roll reduction. The most widely used systems are (Van der Klugt 1987): Bilge keels: Bilge keels are fins in planes approximately perpendicular to the hull or near the

turn of the bilge. The longitudinal extent varies from about 25 to 50 percent of the length of the ship. Bilge keels are widely used, are inexpensive but increase the hull resistance. In addition to this they are effective mainly around the natural roll frequency of the ship. This effect significantly decreases with the speed of the ship. Bilge keels were first demonstrated in about 1870.

Anti-Rolling Tanks: The most common anti-rolling tanks in use are free-surface tanks, U-

tube tanks and diversified tanks. These systems provide damping of the roll motion even at small speeds. The disadvantages of course are the reduction in metacentre height due to free water surface effects and that a large amount of space is required. The earliest versions were installed about 1874.

Fin Stabilizers: Fin stabilizers are a highly attractive device for roll damping. They provide

considerable damping if the speed of the ship is not too low. The disadvantages with additional fins are increased hull resistance (except for some systems that are retractable) and high costs associated with the installation. They are also required that at least two new hydraulic systems are installed. It should be noted that fins are not effective at low speed and that they cause drag and underwater noise. They were first granted a patent by John I. Thornycroft in 1889.

Rudder-Roll Stabilisation (RRS): Roll stabilization by means of the rudder is relatively

inexpensive compared to fin stabilizers, has approximately the same effectiveness, and causes no drag or underwater noise if the system is turned off. However, RRS requires a relatively fast rudder to be effective, typically 205max −=δ (deg/s). Another disadvantage is that the RRS will not be effective if the ship’s speed is low.

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Table 5.2 Overall comparison of ship roll stabilizer systems (Sellars & Martine 1992)

Stabilizer Type General Application

% Roll Reduction

Price ($×1000) Installation Remarks

FINS (small fixed)

Mega yatchs, naval auxiliaries

90 100-200 Hull attachment, supply and install power and control cables

Speed loss, largest size about 2m2.

FINS (retractable)

Passenger, cruise, ferries, large Ro-Ro, naval combatants


Sizes range from 2m2 to about 15m2.

FINS (large fixed)

Naval combatants


Speed loss

TANKS (free surface)

Work vessels, ferries, small passenger and cargo ships

75 30-50 Install steelwork supply and install power and control cables

Includes liquid level monitor

TANKS (U-tube)

Work vessels, Ro-Ro vessels

75 200-300 Install instrument cables

Includes heel control system cables

RRS Small, high speed vessels

50-75 50-250 Install power and control cables

New development, more robust steering gear may be required

Bilge keels Universal 25-50 … Hull attachment Speed loss 7.1 Fin Stabilization System The motions of the ship in a seaway can result in various undesirable effects, examples of which are human discomfort and cargo damage. Only the rolling of a ship can be effectively reduced by stabilization. Active or fin stabilization will now be considered. Figure 5.32 shows a typical fin stabilizer arrangement.

Figure 5.32 Typical fin stabiliser arrangement

Art view

CG

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The actions of waves on ship in a seaway result in rolling. If the rolling couple applied by the sea can be opposed then the vessel will be stabilized. The rolling acceleration, velocity, angle and the natural list of the vessel must all be determined in order to provide a suitable control signal to activate the fins. The stabilizing power results from the lift on aerofoil fins located on opposite sides of the ship. The angle of the fins is controlled in order to produce an upward force on one side of the vessel and a downward force on the other. The resulting couple will oppose the couple-inducing roll. One type of control unit uses an angular accelerometer which continuously senses the rolling accelerations of the ship, see Figures 5.22. The sensor is supported on air bearings to eliminate friction and provided by a small oil-free compressor via filters and driers and the system is sealed in operation. The accelerometer output signal is proportional to the rolling acceleration of the ship. This signal is first electronically integrated to give a rolling velocity signal and then integrated again to give a roll angle signal. Each signal can be adjusted for sensitivity and then all three are summed. The summed signal is fed to a moving coil servo valve which is located in the hydraulic machinery which drives the fins. The stroke of the hydraulic pumps and the overall gain of the system can each be adjusted. A fin angle transmitter is provided for each fin to provide a feedback to the servo valve. This type of stabilization will provide roll reduction in excess 90% at resonance and where low residual roll occurs over a wide range of frequencies. However, at low speed the stabilizing power falls off and when the vessel is stopped no stabilization is possible. Figure 5.34 shows the block diagram of the Denny-Brown-AEG Fin Stabilizer.

Figure 5.33 Stabilizer control system

Torque

Coil

Sensor Sense Amp

Torque Amp

CR Filter

Drift Corrector

Port fin Angle

Indicators

AR bearing assembly

Handroll input +12V DC

Gain

STBD Servo-Amp

SummingAmp

Integrator

Velocity integrator

Drift Corrector

Pump Control

Pot

STBD MC unit on Main pump

STBD FFB potSTBD fin

Angle Amp

Roll Ouput

Inverter

Roll Angle

Integrator

Accelera-tion Filter

Range Switches

Port Servo Pot

Port MC unit on

main pump

Port FFB pot port fin

Angle Amp

Summing Amp

Atten-uator

Inter-locks

Pump Control

Pot

STBD finAngle

indicators

Timer (1.5 min)

Stabilizer Off for

35 sec RLG

Running Relay RLH

Velocity integrator relay input

31

7.2 Rudder Roll Stabilisation System According to Perez (2005), rudder roll stabilisation is a technique based on the fact that the rudder is located aft and also below the centre of gravity of the vessel, and thus the rudder impacts not only yaw but also roll moment as shown in Figure 5.35. RRS is an extra feature of the course autopilot.

Figure 5.35 Rudder induced rolling moment

Figure 5.34 Denny-Brown-AEG ship stabilisation system using fin angle control

SIGNAL CONVERTER LOG

ACCELEROMETER

SHIP PORT FIN

SIGNAL CONVERTER

STARBOARD FIN

FIN ANGLE TRANSMITTER

MAIN PUMP

SERVO VALVE

SERVO PUMP

FIN ANGLE TRANSMITTER

VELOCITY INTEGRATOR

ROLL INTEGRATOR

SUMMING AMP

M FIN M FINM SEA

MAIN PUMP

SERVO VALVE

SERVO PUMP

Rudder force Rudder force

CG CG

Art view

32

Most of the drawbacks of conventional active fin stabilisers and anti-roll tanks are overcome by RRS. Provided that the speed of ship and the rudder rate are sufficiently high, this technique can be applied to different ship types: small and large naval vessels, patrol vessels, ferries and some Ro-Ro vessels. The main advantages of RRS are as follows:

• Medium to high performance. This can be in the range of 50-57% of roll reduction • Relatively inexpensive • No resistance in calm water conditions • No large spaces required • Can be combined with other stabilisers to achieve higher performance

Some disadvantages of RRS are indicated as follows:

• Ineffective at low speeds. Nevertheless, this can be higher than that of fins because the rudders are located in the race of the propellers; and thus operate in higher speed flows than fins.

• Drag is produced when in use. Nevertheless, this can be less than the drag of fin stabilisers, provided that the ship turning is prevented.

• Rudder machinery upgrade may be needed to achieve high performance faster than rudder motion.

• Need sophisticated control systems to extend the good performance to different sailing conditions.

8. Trend of Control Systems New technologies have been advanced. IT (computers with high speed CPUs, high performance software, network and Internet), wireless communication technology and satellite technology allow very complicated control systems to be designed. In future, control systems will be integrated computer-based systems with high performance and multi-functions. Figure 5.36 shows an example of a newly-developed dynamic positioning system.

Figure 5.36 Example of newly-developed dynamic positioning system (Courtesy of NUST)

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SUMMARY OF MODULE 5 Module 5 is summarised as follows.

• Pneumatic control systems • Hydraulic control systems • Electrical and electronic control systems including analogue control systems,

programmable logic controllers (PLCs) and digital (computer-based) control systems. • Autopilot systems for marine vehicles • Dynamic positioning systems • Fin stabilisation systems • Rudder stabilisation system.

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Exercises 1. A damper-spring-mass system is shown in the following figure. Write a differential equation for the relationship between the output displacement y(t) and the input force u(t). Use the following numerical values: P = 20N, m = 200kg, λ =100Ns/m, k = 600N/m, and initial conditions: y(0) = 0 and )0(y = 0. Assuming that the output displacement is measured by a displacement transducer that has sensitivity of Km = 5 and the displacement is controlled by a PID controller with control gains KP, KI and KD, draw a block diagram and write the total feedback transfer of the system. Using MATLAB/Simulink make a simulation program for the system and find control gains such that the system is stable. 2. Consider the position control system shown in the following figure. Write a MATLAB program or Simulink model to obtain a unit-step response and a unit-ramp response of the system. Plot curves x1(t) versus t, x2(t) versus t, x3(t) versus t, and e(t) versus t [where e(t) = r(t) – x1(t)] for both the unit-step response and the unit-ramp response.

m

u(t)

y(t)b

k

s1

s1

r x1 4

1s1.02

+

e 5

x2 x3

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3*. Consider the hydraulic servo system shown in the following figure. Assuming that the load reaction forces are not negligible, derive a mathematical model of the system. Assume also that the mass of the power piston is included in the load mass m. 4. Consider the liquid control system shown in the following figure. The controller is of the proportional type with proportional control gain KP. The set point of the controller is fixed. Draw a block diagram of the system, assuming that changes in the variables are small. Obtain the transfer function between the level of the second tank and the disturbance input qd. Obtain the steady state error when the disturbance qd is a unit step function.

h1

qi

V1 R1

Cross-sectional area A1

qd

h2qo

V2 R2

Cross-sectional area A2

Proportional controller

k

b

m

q

y

q

ps p0p0

p1 p2

1 2 3 4 x

y

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5*. Consider the liquid level control system shown in the following figure. The inlet valve is controlled by a hydraulic integral controller. Assume that the steady state pilot valve displacement is 0X = , and steady state valve position is Y . We assume that the set point R corresponds to the steady state head H . The set point is fixed. Assume also that the disturbance inflow rate qd, which is small quantity, is applied to the water tank at t = 0. This disturbance causes the head to change from H to hH + . This change results in a change in the outflow rate by qo. Through the hydraulic controller, the changes in head causes a change in the inflow rate from Q to iqQ + . (The integral controller tends to keep the head constant as much as possible in the presence of disturbances.) We assume that all changes are of small quantities. Assume the following numerical values for the system: C = 2 m2, R = 0.5 sec/m2, Kv = 1 m2/sec, a = 0.25 m, b = 0.75 m, K1 = 4 sec-1, obtain the response h(t) when the disturbance input qd is a unit-step function. Also obtain this response h(t) with MATLAB or Simulink. 6. A surface ship is represented by the following Nomoto’s manoeuvring model: δ=ψ+ψ KT where ψ is yaw angle (rad) and δ is rudder angle (rad), T = 7.5 seconds (time constant of ship), K = 0.11. Ship speed is constant, v = 15 knots (1NM = 1,852.00 m). The position of the ship is represented by the following model: ψ−ψ= sinvcosux ψ+ψ= cosvsinuy

H +h

Q +qi

VR

Cross-sectional area A

h

Q +qo

Y +yqd

ba x

37

where u is surge velocity and v is sway velocity (assuming that v = 0). The ship’s heading is control by a PID autopilot system with control gains of KP, KI and KD. It is assumed that the rudder angle for the PID autopilot is in range of -10o (port) to +10o (starboard), rudder rate in range of -5 deg/s to +5 deg/s, error (between the actual yaw angle and set course) in range of -180o to +180o, and yaw angle in range of 0-360o. Using one of the steering machine models (for rudder) in previous section (Section 2.2.2), draw a block diagram and make a MATLAB program or Simulink for the PID autopilot.

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