rudder roll stabilisation

ControlEng. Practice,Vol. 3, No. 5, pp. 703-708, 1995 Printed in Great Britain 0967-0661/95 $9.50 + 0.00

Pergamon 0967-0661(95)00047-X

SEA-TRIAL EXPERIMENTAL RESULTS OF FIN/RUDDER ROLL STABILISATION M.T. Sharff*, G.N. Roberts** and R. Sutton*** *Royal Naval Engineering College, Plymouth, PL5 3AQ~ UK **Gwolt Collegeof Higher Education, Newport, NP9 5XR, UK ***University of Plymouth, Plymouth, PL4 8AA, UK

(Received October 1994; in final form January 1995)

Abstract: This paper reports on full-scale roll stabllisation trials on board a frigate-size Royal Naval warship. The trials entailed comparing the e~ficacy of the ring functioning alone, with the combined effects of the fi-~ and rudders operating in congress to reduce roll motions. The rudders were employed in a supplementary role and no mechanical modifications were made. To afford a comparison of the results the clam acquired is presented in the RMS form. Keywords: Fins, Rudders, Roll Stabillsation, Classical Control

expedient and most attractive to the Royal Navy. This paper reports on the first phase of sea trials conducted on board a frigate-size warship during 7-8* March 1994. The second section describes the linear mathematical models of the ship system on which depends the control theory to generate adequate controllers. Also, the physical constraints are described. The third section deals with the comml theory adopted. Prior to going on board considerable technical preparations were made which are elaborated in section 4. Penultimately, trials conducted are detailed and results presented. Finally, some conclusions are drawn, with suggested recommendations.

1. INTRODUCTION

The roll stabilisafion of ships when subject to the indemen~es of its operating environmem has been an active area of research since the advent of large-scale shipping. A plethora of devices have been constructed and implemented with varying degrees of success. Perhaps the most propitious dcvico has been the Brown Broth~ fin stabil/sers.

Recosnising their advantages in ship opm~'ty, the Royal Navy as a matter of policy fits such equipment to all its warships of appropriate size. Recent advances which have demonstrated the feasibility of ufiliJing the rudder in roll stabilisation (ItRS) (Cowley 1972; Amemngen 1987) has imparted an impetus to the Royal Navy to initiate research effort into this area, specifically, to examine the effectivenms of the rudders in a secondary stabilisation role to the fins.

2. SYSTEM MODELLING

Royal Naval frigates are, as mentioned, equipped with fin stabilisers. These are geometrically located inthe plane ofthe centre of gravity (cog) ofthe ship when loaded ,nder normal conditions. Thus, since moments act through the cog of any body, the fin~ can impart the maximum roll moment possible. The relative location of these is shown in Figure 1.

Using the rudders exclusively in the stabilisation role would have detrimental repermmmons on the rudder bearings and servomechanism due to the added motion. However, it is possible to ~cumvent the necessarily expensive costs of upgrading the

rndder bearings and inmulllng more powerfel motors

The synthesis of controllers for any system requires a linear mathematical representation of their associated dy-amics. The initialeffort is then to

in the hydraulics ff they are u"tdised as described. Hence, this route of enhanced stabilisation is 703

704

M.T. Sharifet al.

acquire such models which accurately embody the physical bebaviour of the plant.

Centreoffrevtty---] [7

derived empirically. The parameters were subsequently refined by Whalley (1981) and Roberts (1989).

.

2.2 Rudder dynamics

~

LFin~a~

TwinProlpella'ands ]t:addm Fig 1. Location of fins and rudders Figure 2 is a multivariable model of the ship system in terms of fin/rudder induced motions. The transfer functions which relate fin/rudder to ship motions are of interest only (gll(s) and gl2(s)). These were derived from sea trials and successively refined over time. To ensure their reliability, comparisons were performed with the seakeeping prediction software at Haslar, U.K. This software has been developed utilising strip themy, and verified with extensive sea trials data. The results afforded a degree of confidence in the models which will be employed in subsequent controller design

Poll

FinA n Z l ~ ~.~ Rudder

08~ O.e OA

~°~

s

Sway

10

IS

29

Yaw P

35

4o

45

5o

Fig. 3 Rudder-induced ship motion

gl2(s) -

2. I Stabilising fins The fins act as actuators in the control loop; imparting a regulated moment about the ship's axis of roll in opposition to the sea-induced roll. Marshfield (1981) derives a simple second-order transfer function to model this roll (1). t,0.25 s2+2~0.58+0.25

30

The transfer function is derived in a similar manner as previously (2)

Fig. 2 Multivariable ship motion model

-

25

In terms of roll stabilisation, several studies, for example (Amerongen, 1982) and (Katebi, 1978), have been conducted to establish the applicability of utilising the rudders exclusively in the stabilisation of ships. However, it is realised that this characteristic may rather be harnessed in congress with the fin stabilisers to accrue greater roll stabilisation.

Angle

gl l(s)

In ships of appropriate size a peculiar phenomenon is observed, namely that when the ship's rudder is 'pro-over' the ship exhibits a proclivity to initially heel inwards. During this heel in the 'wrong' sense, no significant yaw motion occurs. Eventually the ship rolls outwards and the ship enters a steady-state turn. Such behaviour is illustrated by Figure 3 which shows the roll and yaw motions with the typical time scales involved. This ephemeral roll motion may he explained by hydrodynamic considerations detailed in (Rawson and Tapper, 1984).

(1)

Here k , represents the non-linear relationship between the moment generating effectiveness of the fins and ship speed. The damping ratio, ~,, is

tn°250-sT5~) 0,s.2aX,2+o.25s+o.25 )

(2)

A non-minimum phase zero is incorporated to impart an initial inward heel to the model when simulated in the time.domain. As before, kl2 is a parameter to represent the non-linear behaviour of the rudder with ship speed.

Both models are now accurately represented by the mathematical models, partiodarly at a ship cruising speed of 18 knots. This is then the nominal model exploited for controller design.

Fin/RudderRoll Stabilisation 2.3 Fin and rudder hydraulics

The effectiveness of roll stabilisation is completely dependent upon the servomechani.qn which activates the control surfaces. *o' [

I

,o"I ,o.i I@

to*

F~mJt}

m*

I¢

Fig. 4 Typical roll and servomecimniswofrequency response This is illustrated in Figure 4, which shows a typical f~equency response of ship roll and servomechanism. If the servomechani.cm frequency response enco~ the entire ship roll response then it will actively stabilise at all frequencies of motion. At the very minimum it should extend beyond the ship roll resonance peak, where sea-induced roll is amplified. For both the fin and rudder hydraulics there are associated with their mechanics two non-linearities, which are modelled as shown in Figure 5.

705

servomeclmnism reduces, further exacerbating the deficiency in slew. There are other detrimental repercussions to be considered: wear of the components increases, greatly reducing Mean Time Between Failure (MIBF), introduction of intolerable phase lags, precipitating system instability, generation of spurious frequency components, and most significantly, invalidation of linear control laws. Therefore, it is imperative that some contingency algorithm be available to avoid saturation. It is possible to relate the RMS value to the bandwidth of the servomechanism. Therefore, a scheme is used which monitors this RMS level and alters the g~in of the control s i t ~ l such that the bandwidth remains above a predetermined value (Sharif, 1993).

2.4 Sea disturbance

Uustabilised roll motions on a ship are induced by the hydrodynamicinteraction between the sea and the ship's hull. An adequate model representation of this 'noise' is required in order to ascertain the frequency and amplitude envelope of the pertufoations the ship is likely to encounter in the environment. This information is used to design a controller which has appropriate sensitivity properties enabling it to reject the interference. A representation of the sea spectrum may be well encapsulated by the Bretschneider model (3), where H is the significant wave height and T the modal period.

solo) -

69~ [ H i ] 2

]

~1

(3)

Fig. 5 Non-linear servomechanism model The first saturation dement models the maximum angles of excursion. For adequate stabilisation, the slew of the servomechanism is of paramount importance. This is non-linear to the extent that their maximum rate is restricted. This slew limitation is manifested by bandwidth consideration of the frequency response in Figure 4. The slew non-linearity is modelled by the second saturation element in the feedback loop. For the fins the nmximum angle of excursion is ~-30o; for the rudders ~.28°. Slews of ,.30°s -I and :L-6°S-I for fins and rudders are representative of the Royal Navy vessels considered. The servomechanisms are driven into saturation if either amplitude or frequency, or both components, of the control signal is excessively large. The consequence of this is that the bandwidth of the

This gives the ~ of the sea and may be implemented in software for time simulation by passing white noise through a Laplace domain trangfer function which approximates (3), the Bretschneider spectrum.

3. CONTROL STRATEGY Having established reliable models for the pertinent constituents of the ship system, it is possible to proceed with the control design. As this paper reports the first phase of sea trials, the controllers tested were derived from well-promulgated control themy, namely classical control. The configuration of the overall fins and rudder stabilisation loops are shown in Figure 6. Since there is no interference between rudder and fin loops, they

706

M.T. Sharifet al.

may be treated independently in the controller dcsiSn. Furthen~re, there is suffident frequen~ separation between redder-induced roll and yaw motions such that the effect of the rudder in its roll stabilisation role has a negligible detriment on yaw motions.

/ \ Imaginary

2-

~

w) Locus

:

le,.~. I -ft

11+K(JcO)G(J~o)I/

~

./

> [K(J~) G(I~)I

Fig. 7 Nyquist locus of ship stabilisation system Fig. 6 Fin/rudder control configuration The controller can exactly oppose the disturbance moment with the fin/redder generated moment only at one f~luency. This frequency location is chosen at the roll resonance of the ship. Therefore, the strategy is to ascertain the phase lag introduced by the fin/ship, or redder/ship, interaction and the servomechanism and inject the phase advance of the same magnitude. Hence, the net phase will be zero between the control action and the ship motion and complete roll reduction will result at roll resonance. However, at other frequency locations the roll redu~on will be less than complete. Figure 7 illustrates the method of roll reduction. It is a Nyquist locus of the system. Considering the fin loop only, the same analysis follows for the rudder loop. The disturbance rejection tr~_n~er function is given by o i -6 = l~,dslgn(s)

(4)

It can be seen from (4), where D is the disturbance and 0 the roll angle, and from Figure 7, that the system will accrue roll reduction provided that [(1 +Oa~/co)gll(/m)l < l, effectively at those fi~luencies where the locus lies outside the unit circle, centred at (-1,0). Amplification of roll will occur over the locus when it is inside unit circle. For both the fin and rudder loops the following transfer function, (5) and (6) respectively, for the controllers will achieve the phase objectives as susgested by (Lloyd, 1974).

Gc~(s) =

(k~,~t~,t~)thk~

(5)

The parameters, k n etc and k.~ etc, may be selected by the designer to meet particular objectives in motion stabilisation. The remaining parameters, k~ and k,,, are the ship's speed-dependent gains to account for non-linear hydrodynamic variations in fin and rudder performance. The parameters kfs and 1% dictate the amount of roll reduction achieved, given the constraints in terms of servomechanism saturation.

4. P R E P A R A T I O N F O R T H E S E A T R I A L S

In order to record data and control the actuators, a considerable amount of preparation was required, in terms of not only the software and controller design, but also of the hardware implications necessary to interface with the fin and rudders, given the nature of the environment on board a warship.

4.1 Software development

To implement the controllers, they must be convened into a digital representation. Using a bilinear transformation technique difference equations for the controllers were derived and subsequently encoded into software routines in C++. A prerequisite for this method is the consideration of the sampling time adherence to the Nyquist sampling criteria. The natural roll period of the ship is approximately 10.5 seconds. It was decided that a 0.5 second sampling period should not only provide an accurate reconstruction o f the signals but also sufficient period for data storage, graphical display, and calculation for the next control output.

0.003~s +0.43a2 +0.43a+ I

4.2 Interface to ship

G ~ (s ) = (k'1*2"t'2**t's)t'*k"

oo*.,%0~.,+,

(6)

It was imperative to interface with the ship's fin/rudders with the minimal of disruption to ship operations and machinery. A schematic of the wiring configuration is given in Figure 8.

Fin/Rudder Roll Stabilisation . . . . . . . . . . . . . . . . . . . . . LC.C.

t ..J ' W~ktd~p Cemlmtar

Y

i.~i . . . . . . - ~ -

707

weather is not expedient for roll stabilisation trials. Typical roll motions which were experienced are shown in Figure 9.

- -"..... ost

. . . . . . . . . . . . . . . . . . . . . .

oe~

- "

~;,-~t . . . . ~ -

I°:

.......

.04

I "-'" I . . . . . . . . . . . . . . . . . . . . . . .

4).Q

Fig. 8 !nterconncction schematic The computer was installed in the workshop. NormAlly the fins are controlled by the ship's Central Control Unit (CC'U) located in the Ship Control Centre (SCC). The CCU provides demand signals to the Nfvom~lmnimnR situated in the Gas Turbine Room (GTR) and test outputs for the user. It was pom~ole to dim:onuect this route and replace it with computer~ signals, namely FRS mode. The configuration incotlmmtes a safety feature, in that it is physically possible to revert to CCU control of the fins should a malfimcfion occur in the computer.

Fig. 9 Typical roll motions experienced However, significant fin motion was (dnerved indicative of stabilisation occurring, therefore, it was decided to proceed with the trials. A summary of the fin/rudder configurations of operation are given in Table 1.

Table I Summary of modes of oueration for trials. The signals reqnired to be associated with the rudder loop are heading error and autopilot demand. The Auto Steering Unit (ASU), which is located at the bridge, furnishes both these signals. The connections betwoen the bridge and the rudder servomechanism, in the tiller flat, were broken and re-routed via the workshop and computer. This necessitated the signals travelling approximately 50 metres one way without the aid of boosters. Fortunately, this did not prove to he a serious impediment to effective signal re~on.

The autopilot sitma! is superimposed on the RRS signal lest interferencc occur with the direction of the ship. T l ~ r e , when the RRS is not engaged, the autopilot is the default signal to the rudders. In this way both the fins and the rudder systems are completely controlled by the computer software. 5. RESULTS

A large number of individual trials were conducted with varions controllers and the fin/rudder modes of operation. The fins and rudders were engaged with three different sequences, and repeated several times with an assortment of controllers. Each sequence had a duration of 400 seconds. The data was subsequently analysed and presented in terms of RMS values. For the entire duration of the trials the sea remained at around state two. Unfortunately, such calm

II

I

Time

0:100 socs

100-400 secs

Mode CCU

FRS

RRS

CCU

FRS

RRS

Sqnl

ON

OFF

OFF

OFF

OFF

ON

Sqn2

ON

OFF

OFF

ON

OFF

ON

Sqn3

ON

OFF

OFF

OFF

ON

ON

Results for sequence 1. This involved having the ship stabilised by the fins for the first 100 seconds using the CCU generated signal. After I00 seconds the RRS was engaged and the fins switched off and set to their neutral position. This would afford direct comparison of fin stabilisation with RRS. Table 2 Typical results of sequence 1 RMS

Roll

FinActivity P ~

~

Time <100 >100 <100 >100 <100 >100 <100 >100 P,un] 0.19 0.19 0.94

0

0

2.39 8.21 10.4

Pare2 0.42 0.49 1.46

0

0

5.83 9.81 10.9

Two sets of runs are shown with sequence I in Table 2 for two different controllers. RMS statistics are collated for various relevant sitm~ls, before and after 100 seconds. It is seen that when the fins are switched off the roll value does not change significantly for either controller during RRS

M.T. Sharif et al.

708

operation. Also, the fins and rudder activity remain within acceptable bounds.

Results for sequence 2. This sequence will establish that employing the rudders in a supplementary role will result in enhanced levels of roll reduction. The trials entailed employing the CCU fin stabilisers during the entire 400 seconds test period. After 100s the RRS was engaged. The results are displayed in Table 3, for two typical runs. For both controllers, when the rudders are engaged higher stabilisation levels are achieved, of approximately 25%. Note also that fin activity correspondingly diminishes as the rudders assist in generating the roll-correcting moments.

Table 3 Tvvical results of seouence 2 RMS

Roll

Fin A~ivity R . a ~

~

Time <100 >100 <100 >100 <100 >100 <100 >100 Run l 0.63 0.46 4.48 1.08

0

3.46 10.1 11.3

Run2 0.61 0.45 4.17 1.01

0

3.13 10.3 10.8

Results for sequence 3. The final sequence entailed controlling both the rudders and fins from the computer. Therefore, the CCU signal was replaced by the computer signals after 100s. At the same time the rudders were engaged in the stabilisation mode. The resulting RMS values are shown in Table 4.

Roll

Fin Activity a a a , , ~

In conclusion, the sea trials gave encouraging results in utilising the rudders in a supplementary role to the fins, without any modifications to the machinery. It is envisaged that at higher sea states the saturation-prevention mechanism will realise its potential. The next phase of trials will examine other controllers which will be arrived at via different control theory, and the results will be presented.

REFERENCES

Amemngen, J. van. (1987) RRS: Controller Design and Experimental Results, 8th Ship Control Systems Symposium ppl. 128-1.142 Amemngen, J. van. (1982) Stabilisation, 4th

Symposium on Ship Automation, pp 43-50

Table 4 Typical results of sequence 3 RMS

Despite these unsuitable environmental conditions, valuable conclusions can be derived from the data gathered. Sequence 1 manifests the similar effectiveness of the rudders with fins in roll stabilisation at low sea states. The trials vindicated the most important objective, that employing the rudders in a supplementary role with the fins enhances roll stabilisation, as can be demonstrated by the results from Sequence 2. Furthermore, the results compare favourably with the time simulation data generated at the design stage, affording considerable confidence in the mathematical models for future control design. Finally, the experience tested the reliability and versatility of all aspects of the software and hardware which was developed.

~va~

Time <100 >100 <100 >100 <100 >100 <100 >100 Runl 0.57 0.57 1.28 0.85

0

3.41 9.94

11

Run2 0.58 0.54 1.3 0.77

0

2.99 10.8 11.1

When the computer controls both the fins and rudders the roll RMS exhibits a marginal improvement. As expected from previous results. The fin activity decreases due to RRS being operational.

6. CONCLUSIONS AND DISCUSSION

As mentioned earlier the sea state remained very low. Such comparatively small amplitudes of roll motion will not greatly exert the controllers. Therefore, their full effectiveness can not be appreciated. Furthermore, due to ship operations the speed remained at 12 knots, limiting the moment-generating capabilities of the actuators.

Rudder

Roll

International Operation and

Cowley, W.E. (1972) The Use ofRudderasRoll Stabilisor, 3th Ship Control Systems Symposium Vol. C Katebi, M.R. (1978) LQG Autopilot and RRS Control Systems, Design 8th Ship Control Systems Symposium pp3.69-3.84 Lloyd, A.ILJ.M. (1974) Roll Stabiliser Fins : A Design Procedure, RINA Architects Vol. 85 pp233-254 Marshfield, B. (1981) HMS **** Roll Stabilisation Trials, Admiralty Marine Technology Establishment R81012 (Restricted) Rawson, K.J., E.C. Tupper (1984) Basic Ship Theory, Longnmn, Bath Roberts, G.N. (1989 Ship Motion Control Using a Multivariable Approach, PhD Thesis, University of Wales Sharif, M.T. (1993) Investigation of Bandwidth Dependency on RMS Values in Servomechanisms, ILN.E.C., Internal Report 93025 (Restricted) Whalley, 1L, J.H. Westcott (1981) Ship Motion Control, 6th Ship Control Systems Symposium ppHl. 1-Hl.16