361

1 CONTROL SYSTEMS APPLIED TO STEERING OF

THE SHIP MOTION

The regulation of the motion of a merchant ship

seems to be one of the most difficult control problems.

In fact, the ship is the multidimensional, strongly

non-linear and non-stationary object (Fossen 2011).

External disturbances like waves and wind play an

important role in the whole regulation process

therewithal. They can change reaction of the vessel to

steering signals.

There are a few methods to classify control

systems used for steering of the vessel movement.

One of them is the classification in view of the ship's

speed. From this point of view the control systems can

be divided into three types:

1 for speed close to zero:

− dynamic stabilization of position DSP (Fossen

2002),

− stabilization of ship placement in relation to the

hydrodynamic structure, position mooring (e.g.

Weather Vaning) (Hals 2004).

2 for small speed i.e. 'Slow or Very Slow ahead' and

'Slow or Very Slow Astern' used mainly in

harbours, navigation channels etc.:

− controlled motion with any drift angle (crab-

wise motion) (Gierusz at al. 2007, Rybczak

2018),

− controlled movement following ROV unit

(Fossen 2002).

3 for large speed i.e 'Full ahead' or a similar one

used on open sea:

− stabilization of heading (Tomera 2016),

− the trajectory keeping (Tomera 2018, Łebkowski

2018),

− steering during turning operations (Zhogui &

Xiuyan 2011),

− roll minimization (Perez 2005),

− UNREP operations (Bowman 2009),

Another classification can be built taking into

account the propulsion units and their mutual

cooperation. The following cases can be recognized:

1 conventional propeller and blade rudder used for

very small speed (Shouji 1990),

Prediction Control Systems in Marine Applications

W. Gierusz & A. Miller

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: The paper presents one of the modern control methods used for steering of the ship motion. The

different automatic systems used to navigate the vessels are described at the beginning. Next, prediction control

methodology is presented and multidimensional MPC regulator applied to steering of the training ship is

shown as a technical product. Tests results from the real-time experiments with the mentioned controller are

presented at the end of the article.

http://www.transnav.eu

the

International Journal

on Marine Navigation

and Safe

ty of Sea Transportation

Volume 14

Number 2

June 2020

DOI:

10.12716/1001.14.02.12

362

2 two or more pods installed close to each other

when any pod (pods) are under accelerated water

stream from another pod (pods) (Gierusz 2016),

3 two or more fins used for roll stabilization with

two blade rudders (iSSMC 2014)

4 active trim tabs or active interceptors used with

any propulsion devices (e.g. screws or waterjets)

(Ride Control Systems 2015)

From control theory point of view the one-

dimensional regulators (SISO ones) and the multi-

dimensional types of regulators (the MIMO ones) can

be recognized.

One-dimensional regulators (SISO ones) can be

applied only for a few control systems (e.g. heading

or trajectory stabilizations). They seem to be rather

simple regulators but due to non-linear and non-

stationary properties of the ship they often lead to

modern and very sophisticated solutions e.g. adaptive

or robust controllers.

The majority of cases presented above belong to

the multi-dimensional types of regulators (the MIMO

ones) due to the necessity to steer a few of ship's

velocities simultaneously. The review of such

solutions can be found in (Fossen 2011).

2 USED PREDICTIVE CONTROL METHODOLOGY

2.1 Main features of the Model Predictive Control

Historically MPC (Model Predictive Control)

regulator comes from LQR (Linear Quadratic

Regulator) designed by Kalman in 1960, which is an

optimal control with the objective function

minimization (Kalman et al. 1960). This mathematical

operation gives a proportional controller in which

constraints cannot be incorporated. First MPC

regulators, in form in which they are known

nowadays, were designed in the 1970s. They are

based on MPHC (Model Predictive Heuristic Control)

presented by Richalet in (Testud et al. 1978).

MPC is an algorithm which determines optimal

control values taking into account constraints. When

it is applied to the real plant these constraints

(saturation of the actuators, technological and safety

constraints and control signals rate of change) are

very useful. First MPC controllers were applied to the

slow-changing processes such as ratification of fuel,

polymer production (Zavala & Biegler 2009) wood

cellulose and paper production. Computers evolution

and increase of their computing power caused an

increase in interest in the predictive regulators in

other areas as well. Nowadays they are used to

control linear, nonlinear, one-dimensional and

multidimensional plants.

MPC regulators are discrete-time systems in which

control signals are computed on-line. Therefore

computations effort and time is proportional to the

degree of systems complication. This is the reason

why in marine applications MPC controller works

with linearized internal model. Because of use of the

internal model predictive controller can deal with

plants in which number of inputs is not equal to the

number of controlled variables. It also considers

internal interactions and cross-coupling which occur

in the ship dynamics (Miller 2016a).

2.2 Idea of the ship motion predictive control

Ship is a highly nonlinear plant characterized by large

inertia. Moreover it moves in an environment with

wind and waves disturbances. MPC algorithms are

dedicated for such plants, because they incorporate

process model, deal with physical constraints and use

past and predicted future outputs to compute control

signals. Ship's trajectory tracking controller works

based on Equations 1 and 2.

( ) ( ) ( )

|, 1|,,( 1|)

uk ukk uk k uk N k



= + … +−



(1)

( ) ( ) ( )

| 1| 1, 2, ,

uk pk uk N k p N p N+ = + − ⇔ ≥ ∧= …

(2)

where:

u – control horizon,

N – prediction horizon

u(k+1|k) – control signal predicted in k-time for (k+1)-

time

k k+1 k+2

k+N

reference trajectory s(k)

predicted output signal y(k|k)

measured output signal y(k)

predicted control signal u(k|k)

measured control signal u(k)

past

future

prediction horizon N

control horizon N

Figure 1. Predictive trajectory tracking idea.

Figure 1 illustrates predictive trajectory tracking

problem. Optimization is done on-line to allow for the

fastest possible convergence of the reference trajectory

and predicted output signal. Algorithm computes

output signals in control horizon and beyond it

control is constant and equal to the last one estimated

in the control horizon. Figure 2 illustrates a block

diagram of the MPC controller used in ships for the

trajectory tracking. It is connected in series to the

plant.

Figure 2. Predictive trajectory tracking controller block

diagram.

363

Ship is a MIMO (Multiple Input Multiple Output)

plant, when taking into account trajectory tracking

problem. So optimization problem is a

multidimensional one. Its cost function J has the

following form described by Equation 3.

( ) ( )

( )

pN p

J xkpk ykp ukp

−

= =

= + − + +∆+

∑∑

(3)

where:

x(k) – state space vector,

M – output matrix,

y(k+p) – output signals vector in (k+p)-time,

∆u(k+p) – control signal increments vector in (k+p)-

time,

Q(p) – output signal weights matrix,

R(p) – control signal increment weights matrix.

Control signals optimization process is based on

the information about ship included in its dynamics

model, knowledge about constraints and predicted

disturbances, past and future predicted outputs. In

case of a ship steering process we define constraints

as physical ones for the actuators and their real rates

of turn. Weight matrix of control signals penalizes for

fast and big changes of input signals, that lead to

increased ships operating costs and actuators

exhaustion. In turn, output signal weights matrix

enforces accuracy of the trajectory tracking. Trajectory

should be known and provided to the algorithm in

whole prediction horizon for a better performance.

Otherwise, it is treated as constant which can degrade

control quality.

Plant dynamics model is very important, when

control quality is taken into account. Incremental

state-space model was used in presented MPC system

for Underway Replenishment operations (Miller

2016a). In the mentioned above system output and

control signals defined as deviations.

2.3 Model predictive algorithms in marine applications

MPC is a group of model-based control algorithms

that have been developed since early 1970s. They

come from Dynamic Matrix Control (DMC), which is

known as first generation of the MPC, developed for

Shell Oil (Holkar & Waghmare 2010). This control

strategy may be applied to the stable linear objects

and does not work with nonlinear plants having

cross-couplings between several channels in their

dynamics. It is useless to control ship motion, but can

be applied to the ships diesel engine and regulate

emission (Kozlik 2016).

Model Predictive Heuristic Control (MPHC) uses

FIR linear model to estimate future control signal.

Richalet in 1978 proposed extended version of

predictive algorithm that includes reference trajectory

(Testud et al. 1978). It defines plants closed-loop

behavior and is treated as an output signal. Algorithm

estimates control signals iteratively and chooses these

that ensure minimization of the error between

reference and set point trajectory. MPHC is a base for

ships predictive regulators, despite the fact that it

incorporates FIR model which is better for chemical

processes control.

Generalized Predictive Control (GPC) is the most

popular and widely used MPC algorithm. Its first

version was proposed by Clarke in 1987 (Clarke,

Mohtadi & Tuffs 1987). GPC algorithm predicts future

output signals based on polynomial or state-space

models. It can be used for MIMO plants that are non-

minimal phase, unstable and having variable dead-

times. It is also possible to add predictive feedforward

controller object deals with measurable disturbances.

This is common situation in ships motion control,

where wind and waves are present. In GPC

optimization is done on-line. The values of future

controls are determined based on predefined quality

indicator by solving quadrating programing task.

According to the Equation 3 (see section 2.3)

summands are squares of the differences between set-

points and output signals estimated in prediction

horizon and control signals deviations in the last

sample time. During MPC controller synthesis length

of the horizons, cost function form and constraints are

modified. Moreover, in GPC changing predictor may

be used (Camacho & Alba 2013), which extends

algorithm application capabilities.

Rapid evolution of the GPC algorithm is proved by

its usage in developing Intelligent Transport Systems

to follow a line and guide unmanned vehicle along it

(Horiuchi, Tamatsukuri & Nohtomi 2000). GPC

algorithm is also a part of Scientific Environments like

MATLAB, LabVIEW and SciLab, which shows its

usage in industrial applications and research.

3 PREDICTION CONTROL IN UNREP

OPERATIONS

3.1 Underway Replenishment (UNREP)

Underway Replenishment (UNREP) derives from

navy. It is a form of Ship to Ship transfer that is

undertaken when 2 ships are moving close to each

other. Nowadays it has also found application in

merchant navy. Two ships – Ship To Be Lightered

(STBL) and Service Ship (SS) are moving close to each

other in order to allow for fast cargo shipment

between them. STBL is a guiding ship which means it

moves with constant speed and course. SS is an

approaching ship that changes course and speed to

bring them to the STBL’s motion parameters. UNREP

procedure allows STBL to change course and speed

not more than 10

and 1kn.

During commercial UNREP maneuver navigator

controls ship manually and estimates distance

between vessels using markers placed on boards and

line connecting them. Furthermore, radar, GPS and

AIS are used for distance and ships’ relative position

assessment. But their accuracy is too small to use

them in automatic control systems.

Increasing number of VLCCs and big gas carriers

that cannot enter smaller harbors. They have to be

reloaded in open waters due to their big draught and

restricted maneuverability. In Arctic areas feeders

having an ice class are used to transport petroleum

and LNG products. In this case also Ship to Ship

operations are carried out. It leads to UNREP

companies (e.g. STP Inc., STS Limited UK, Teakey)

arising.

364

Regardless of the type of ships participating in

UNREP, manoeuver is carried out in the same way. It

is divided into three phases: approach, parallel

motion, departure. Figure 3 illustrates them

schematically.

Figure 3. UNREP phases schematic.

In approach phase SS ship adjusts speed and

course to the STBL, approaching it from the aft with

an absolute course difference smaller than 20

Navigator monitors and controls their relative

position in order to decrease relative speed and

course difference to zero while maintaining a constant

transverse difference between their sides. During

parallel motion SS sails near STBL with zero course

difference and longitudinal shift, maintaining

constant transversal shift. During departure phase

both ships should return to their previous or any

other particular course. STBL should maintain its

course and speed while SS maneuvers the course and

speed.

3.2 MPC based UNREP control system

Ship in automatic control system is an autonomous

surface vessel (ASV). UNREP MPC algorithm creation

involved the same methods as in autonomous ships’

formation or mobile robot control. Main difference

requiring special attention are: constraints due to

merchant ships inertia; relatively small powers and

performance of the propellers; restricted

maneuverability compared with tugs or off-shore

vessels. Developed MPC algorithm uses leader-

follower (Wang 1991) approach, where SS follows up

STBL ship.

In order to implement predictive control,

approaching ship has to be positioned relatively to

guide ship. Figure 4 illustrates how SS is placed in

coordinate system associated with the STBLs center of

gravity. In this system are three output variables:

transversal deviation (∆x), longitudinal deviation (∆y)

and course difference (∆ψ).

Figure 4. Relative ships placement during UNREP.

Figure 5. LNG carrier “Dorchester Lady” silhouette (Gierusz

2015).

MPC regulator is used to control SS training LNG

carrier “Dorchester Lady” presented in Figure 5 and

virtual ship whose dynamics is adequate to training

VLCC “Blue Lady”. Both ships (owned by Foundation

for Safety of Navigation and Environment Protection)

are built in scale 1:24. LNG carrier is equipped with

azipods and manipulated variables in the control

system are their set-points (∆n) and angles of rotation

(∆δ) changes.

Ship dynamics forced prediction horizons, control

horizons and constraints values (presented in Table 1)

to guarantee the possibility of finding a solution by

solving the square programming task.

Table 1. MPC weights and horizons.

_______________________________________________

Parameter Value

_______________________________________________

Prediction horizon 55 [samples]

Prediction horizon 4 [samples]

∆n rate of change weight 1 [-]

∆δ rate of change weight 53 [-]

∆x weight 20 [-]

∆y weight 220 [-]

∆ψ weight 10 [-]

_______________________________________________

This research gave a technical product – MPC

controller applied to the training LNG carrier. It

proved that there is a possibility to build a predictive

controller used to steer SS ship during UNREP

maneuver. The difficulty in its application is

requirement of the identification of ship dynamics

linear incremental model (Miller 2016a). Also

interaction forces and moments acting on both vessels

should be taken into account. They have to be

measured or estimated before the model identification

(Miller 2016b).

4 RESULTS

All time responses are results of the MPC control of

LNG carrier “Dorchester Lady” (SS) sailing in the

vicinity of the virtual VLCC “Blue Lady” on the Silm

Lake. All trials are real-time experiments recorded

with the use of Simulink Real Time Toolbox. We

present two trials: first phase UNREP maneuver –

approach and its second phase – parallel motion. Both

of them are illustrated by two figures, namely time

trials and ships’ trajectories marked by their

silhouettes. First position of each vessel is indicated

by a red ship. Measured values are indicated by the

solid and set points by the dotted lines in all time

trials.

365

60 80 100

120 140

160

x [m]

60 80 100

120 140

160

y [m]

60 80 100

120 140

160

-10

[deg]

60 80 100

120 140

160

time [s]

wind speed in ships scale [B]

Figure 6. Transversal, longitudinal and course

deviation trials for the approach phase of UNREP.

100 150

y[m]

-120

-100

-80

-60

-40

-20

x[m]

UNREP trajectory

virtual BL

Figure 7. Approach UNREP phase trajectory.

60 80 100

120 140

-0.5

0.5

x [m]

60 80 100

120 140

0.5

1.5

y [m]

60 80 100

120 140

-5

[deg]

60 80 100

120 140

time[s]

wind speed in ships scale [B]

Figure 8. Transversal, longitudinal and course deviation

trials for the parallel motion of UNREP.

-20

60 80 100

y[m]

-100

-80

-60

-40

-20

x[m]

UNREP trajectory

virtual BL

Figure 9. Parallel motion UNREP phase trajectory.

In the first phase STBL moves at constant course

and speed of 1.05[m/s]. SS ship decreases the

longitudinal and transversal distance and enters

second phase of maneuver, parallel motion, in 50

second of the trial presented in Figure 6. There are

oscillations in transversal shift (∆y) due to the

increased speed of wind that is an unmeasured

disturbance in this system. Increased course

deviations (∆δ) are the result of constant transversal

distance between ship boards maintenance. Figure 7

illustrates vessels’ trajectories during approach phase

of UNREP. SS significantly approached STBL in 1/3th

of the trial, which responds to ∆y decrease almost to

zero in 60

second presented in Figure 6.

During parallel motion both ships are moving at

constant course and speed of 1.05[m/s]. MPC

controlled SSs position to guarantee longitudinal

deviation

[ ]

0xm∆=

and transversal deviation

[ ]

1 ym∆=

(see Figure 8). Wind speed change caused

oscillations in lateral distance. They are indicated by

the change of ∆y and DL (SS) position in trajectory

(see Figure 9).

Presented results show that MPC for UNREP

operations fulfills its role in different weather

conditions. It was applied to the real sailing training

ship whose dynamics is heavy nonlinear and pods

have limitations in power and angle setting accuracy.

5 CONCLUSIONS

The main purpose of presented work was to show the

application of the modern control method to steering

of the ship motion.

A few conclusions can be formulated in relation

to the MPC approach in marine industry. MPC

control strategy was invented for petrochemical

industry, but it can be successfully used to control

ship. Its main advantages are: ability to generate sub-

optimal control sequence in the presence of wind and

wave disturbances, possibility to incorporate

actuators’ constraints directly in the algorithm and

probability of getting better performance and

smoother control signal than in conventional control

methods. his is connected with control signals

determination based on the internal ship dynamics

model.

Real-time trial results show that it is possible to

maintain the Service Ship's motion parallel to the

STBL one during UNREP operation by means of the

multidimensional MPC regulator. Presented MPC

automatic control system works also in the presence

of wind disturbances. Even if the wind speed in

squalls exceeds 8B in ship’s scale which appropriate

to gale or strong gale. These are conditions where in

normal exploitation underway replenishment cannot

be done due to regulation restrictions. The usage of

the MPC approach enables also addition of the

predictive feedforward controller for measurable

disturbances. It will decrease large influence of the

wind on steering accuracy what will be the aim of the

future work.

Predictive control system applied to UNREP

control needs three coordinates reference frames to

properly describe steering process and incremental

366

discrete state-space liner mathematical model of the

ship for synthesis. This approach fastens and

simplifies MPC algorithm operation compared with

nonlinear ship's model incorporation into MPC

structure. But quality of the identified model

determines the quality of control. Linearized model is

a key element of the whole UNREP automatic control

system. It should be adequate, minimize bias and it

parameters should be reliable in whole input signal

range and used in algorithm prediction horizon.

Identification of the reliable linearized model is a clue

of the whole regulator synthesis.

The use of modern control methods is the future of

ship automation. It leads to the better performance,

lower costs and less environmental pollution

associated with reduced energy consumption in the

control process.

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