Adaptive pitch control for ships with diesel mechanical and hybrid propulsion

Shipping urgently needs to reduce its impact on the environment, both due to CO2, NOx and particulate matter (PM) emissions and due to underwater noise. On the other hand, multifunction ships such as offshore support vessels, anchor handling and towing vessels, naval vessels and wind farm construction and support vessels require fast and accurate manoeuvring and need highly reliable systems to support reduced or no crew. Diesel mechanical propulsion with controllable pitch propellers provides high efficiency and low CO2 emissions, but has traditionally been poor in manoeuvrability, can suffer from thermal overloading due to manoeuvring and requires significant measures to meet NOx and PM emission regulations. The control strategy of diesel mechanical propulsion with fixed combinator curves is one of the causes of the poor manoeuvrability, thermal overloading and cavitation noise during manoeuvring, such as slam start and intermediate acceleration manoeuvres. This paper proposes an adaptive pitch control strategy with slow integrating speed control that reduces fuel consumption, CO2, NOx and PM emissions and underwater noise, improves acceleration performance, limits engine loading and prevents engine underand overspeed. A simulation study with a validated model of a case study Holland class Patrol Vessel demonstrates 5–15% reduction in fuel consumption and CO2 emissions, compared to the baseline transit control mode in the ship speed range from 6 to 15 kts, during constant speed sailing. Moreover, the adaptive pitch control strategy reduces acceleration time from 0 to 15 kts with the slam start procedure by 32% compared to the baseline manoeuvre control mode and by 84% for an intermediate acceleration from 10 to 15 kts, while preventing thermal overloading of the engine, during straight line manoeuvres. Combining this control strategy with hybrid propulsion, running an electric drive in parallel with the propulsion diesel engine, can potentially further reduce fuel consumption at low speeds while also improving acceleration performance even more. Therefore, hybrid propulsion plants with controllable pitch propellers and adaptive pitch control can provide a significant contribution to the urgent reduction of environmental impact of shipping and to the need for more autonomous and reliable ship systems.


Introduction
The United Nations emissions gap report [1] identifies an urgent need to increase the reduction in CO 2 emissions across the globe to meet the goals of the Paris Agreement. Thus, the 72nd Marine Environmental Protection Committee meeting of the International Maritime Organisation (IMO) agreed to 'reduce total annual global shipping emissions by 50% over 2008 by 2050', in its initial strategy on greenhouse https://doi.org/10.1016/j.apenergy.2018.07.080 gas emissions reduction for ships [2]. While improved planning of vessel operations [3,4], either with manned or autonomous vessels [5,6], and improved route planning [7], taking into account weather and loading conditions [8][9][10] can all help reduce emissions, single ships also need to reduce their emissions for a given operating profile with advances in power and propulsion systems [11]. Economic studies suggest that, in shipping, the transition to alternative fuels, such as LNG, bio-methanol or synthetic fuels, will be gradual and that diesel engines will continue to provide most propulsion and electric power over the next decades [12]. Therefore, increasing efficiency of diesel mechanical and hybrid propulsion is even more important.
According to estimates in the UN emission gap report, shipping can contribute 0.7 GtCO 2 emission reduction by increasing its efficiency [1]. Brynolf et al. [13] provide estimates of the energy efficiency improvement potential of various design and operation aspects. While the savings potential of most design aspects, such as waste heat recovery [14][15][16][17][18], hull coatings and lubrications, hybrid power supply [19][20][21] and hull design have been quantified in [13,22], the savings potential of engine-propeller interaction is qualified as significant, but not yet quantified [23]. Geertsma et al. [24] quantify a savings potential for pitch control of up to 30% at certain speeds and operating modes for vessels with diesel mechanical propulsion and high manoeuvrability requirements, at the expense of slow acceleration and increased engine thermal loading. How these fuel savings can be achieved while also accelerating fast and limiting engine thermal loading has so far not been addressed.

Literature review
The most applied control strategy for pitch control is the use of a fixed relationship between the setpoint: lever position or virtual shaft speed; and the control actions: propeller pitch ratio and engine speed [25][26][27]21]. The optimum propeller pitch ratio and gearbox ratio is then determined for the design point of the propulsion plant, according to the matching procedure proposed in [28] or, alternatively, in [29].Vrijdag et al. [30] conclude that one combinator curve cannot achieve optimal cavitation performance while maintaining engine loading limitations across all operating conditions, due to variations in

Nomenclature
Greek Symbols α eff effective angle of attack in deg α i shock free entry angle onto the leading edge of the propeller profile in deg α wk angle of the vertical wave movement at the propeller centre in rad β hydrodynamic pitch angle in rad λ air excess ratio ω wv wave radial frequency in rad/s ρ sw density of seawater in kg/m 3 σ f stoichiometric air fuel ratio of the fuel σ n cavitation number θ pitch angle in rad θ red pitch angle reduction in rad ζ significant wave amplitude in m Roman Symbols c 1 Vrijdag coefficient to calibrate the effective angle of attack D p propeller diameter in m f w wake fraction g standard gravity in m/s 2 i gb gearbox reduction ratio K I reset rate K Q propeller torque coefficient k w wave number in 1/m m 1 trapped mass at the start of compression in kg M e engine torque in Nm m f fuel injection per cylinder per cycle in kg M p propeller torque in Nm n e engine speed in Hz n p shaft speed in Hz n virt virtual shaft speed in Hz p 1 charge air pressure in Pa p 6 average pressure in the cylinder during exhaust opening in Pa ∞ p ambient water pressure at the center-line of the propeller in Pa p v vapour pressure of water at ambient temperature in Pa p d pressure in the exhaust receiver in Pa P os overspeed limitation gain P pd,0 pitch ratio at which zero thrust is achieved P pd propeller pitch ratio P us under-speed limitation gain Q p open water propeller torque in kNm q 23 specific heat release at constant volume in kJ/kg q 34 specific heat release at constant pressure in kJ/kg q 45 specific heat release at constant temperature in kJ/kg R a gas constant of air in J/ kgK R v ship resistance in N R X,cav fuel increase rate limitation to prevent cavitation R X,therm fuel increase rate limitation to prevent thermal overloading T 1 temperature at the start of compression in K T 6 average temperature in the cylinder during exhaust opening in K T p propeller thrust in N V 1 cylinder volume at the start of compression in m 3 v a advance speed of water into the propeller in m/s v s ship speed in m/s v w wakefield disturbance due to waves in m/s w i specific indicated work during the Seiliger cycle in kNm/ kg X I fuel injection setpoint from integrating speed control in % X PI fuel injection setpoint from fast PI speed control in % X λ lim, fuel injection limitation to limit air excess ratio λ in % of nominal X set fuel injection setpoint in % of nominal fuel injection z water depth in m at propeller center weather, ship loading and hull fouling. Therefore, Vrijdag et al. [31] propose a control strategy that maintains an optimum inflow angle of the water onto the propeller blade, angle of attack, in the pitch control region of the combinator, and demonstrates the feasibility of this approach in sea trials. The sea trials, in combination with simulation studies, also demonstrate that the engines are not thermally overloaded and acceleration performance improves significantly [32][33][34]. The impact on fuel consumption of the ship and the influence of the primary engine speed control strategy on system dynamics were not addressed. While engine speed control is used as a standard for propulsion engines due to its robust control and under-and overspeed protection [21], speed control does lead to significant and potentially damaging load disturbances in waves [35][36][37][38][39]. Alternative speed control strategies, such as ∞ H state feedback control [40], optimal speed feedback using speed signal amplification [39], multivariable adaptive extremum engine control [41] and Multiple Input and Multiple Output (MIMO) optimal speed and pitch ∞ H control [38], can all reduce the load fluctuation, but still aim to reject disturbance of engine speed due to waves with fuel injection control action. While a multivariable control scheme utilising a variable geometry turbocharger can improve manoeuvrability while maintaining smoke emission constraints, as proposed in [42], this requires a diesel engine with variable geometry turbocharger. Similarly, adaptive feedforward control of exhaust gas recirculation can reduce emissions in large diesel engines, but only if equipped with exhaust gas recirculation [43].
Alternatively, Sorensen and Smogelli [44] found that, for electric propulsion, primary control based on torque, power or combined torque-and-power control all gave less thrust, torque and power variance in waves than speed control, while accurately following thrust commands. While a slight increase in shaft speed fluctuation was observed, the stable nature of the propulsion system ensured shaft speed oscillations remained acceptable. For extreme situations, such as propeller emergence, thrust loss estimation and anti-spin thruster control can be added to prevent overspeed and thrust loss [45][46][47]. Similarly, Coraddu et al. [23] demonstrated with both simulation model experiments and free running model tests that torque and power control leads to lower load fluctuation in turns. Moreover, Blanke et al. [48] demonstrated in a tow-tank test environment that the propeller efficiency in moderate waves increases with up to 2% for torque control compared to speed control, due to the variation in advance speed from waves. Similarly, torque or power control for propulsion diesel engines has been reported by [35,49,50]. Both Faber [35] and Blanke and Nielsen [49] discuss how power control can lead to reduced loading and thermal fluctuations on propulsion diesel engines, but neither quantify the variance reduction or demonstrate the feasibility. Geertsma et al. [50] propose torque control and demonstrate torque control can eliminate thermal loading fluctuation due to waves and significantly reduce cylinder peak temperatures. However, practical feasibility and implementation with pitch control were not addressed.

Aim and contribution
While shipping urgently has to reduce its environmental impact due to emissions and underwater noise, many ship types, such as offshore vessels, interterminal transport vessels, windturbine construction and support vessels, ferries, and naval vessels also require fast and accurate manoeuvring and reduced maintenance to support reduced maintenance and autonomous shipping [5,51]. This study investigates how much fuel consumption and emissions can be reduced with the novel adaptive pitch control strategy, while also improving straight line manoeuvring performance and limiting engine thermal loading. Moreover, settings for this control strategy are proposed that minimise risk of propeller cavitation.
The novelty of this work is threefold: First, we propose a novel adaptive pitch control strategy for diesel mechanical and hybrid propulsion with controllable pitch propellers, which combines the angle of attack approach for propeller pitch control [31] with slow integrating speed control for diesel engine fuel injection. Secondly, we demonstrate how this approach can be used in a control strategy that works across the speed range of the ship to reduce fuel consumption and CO 2 emissions and increase acceleration performance, while consistently limiting engine thermal loading. Finally, we quantify performance improvement with the proposed control strategy for a case study patrol vessel compared to the current baseline control strategy.

Outline
The paper is organised as follows: in Section 2, we describe the diesel mechanical propulsion system with controllable pitch propeller of the case study Patrol Vessel, its modelling and model validation; in Section 3, we introduce the proposed control strategy and establish its settings; in Section 4, we evaluate the control strategy and compare its performance with the baseline control strategy of the case study Patrol Vessel; and finally, in Section 5, we present the main conclusions and discuss recommendations for further work.

System description
Diesel mechanical or hybrid propulsion with controllable pitch propellers typically consists of two shafts with controllable pitch propellers, a gearbox, and one or multiple diesel engines per shaft, as illustrated in Fig. 1. The two shafts with controllable pitch propellers provide redundancy and manoeuvrability. The gearbox is required to reduce engine speed to the lower propeller speed, as we do not consider large transport ships with slow speed two stroke engines. This configuration is typical for the multifunction ships that require silent, manoeuvrable, highly reliable and low emission propulsion.

Propulsion system model
Propulsion system performance is investigated using the modular, hierarchical and causal propulsion system model proposed and validated in [24]. The diesel mechanical propulsion system model is illustrated schematically in Fig. 3. In the modular, hierarchical and causal modelling paradigm proposed in [52], the direction of the arrows illustrates the causality of the coupled effort and flow variables. The torque M e from the diesel engine model drives gearbox and shaftline dynamics, resulting in engine speed n e in Hz. Subsequently, shaft speed n p determines propeller torque M p of the propeller model, and propeller thrust T p drives ship speed v s in m/s through the hull dynamics. Waves act as a disturbance on the propeller with wave orbital speed v w and added resistance in the resistance function R v ( ) v s . The fuel injection setpoint X set in % and pitch ratio setpoint P p,set act as control actions on the system, while the operator provides the control reference virtual shaft speed n virt in rps. This virtual shaft speed is the fictive shaft speed that results from the product of propeller pitch ratio P p and shaft speed n p , as follows: Legend: (1) Diesel engine (2) Gearbox (3) Sha (4) Controllable pitch propeller (5) Hull (6) Waves and wind (1) (2) where P pd 0 is the pitch ratio at which zero thrust is achieved and P pd,nom is the nominal pitch ratio. For the complete description of the model we refer to [24]. The wave model was improved to include the state wakefield disturbance due to waves v w in m/s and better represent the dynamic behaviour of waves as a function of ship speed v s in m/s and wave radial frequency ω wv in rad/s. In this section, we will summarise the model and its submodels and discuss the wave model improvement to this model.

Diesel engine
The diesel engine model is a mean value first principle model with state variables fuel injection per cylinder per cycle m f in kg, charge air pressure p 1 in Pa and pressure in the exhaust receiver p d in Pa. The model assumes an ideal gas, perfect scavenging, the six point Seiliger cycle, Büchi power and flow balance between compressor and turbine, Zinner blowdown for the temperature in the exhaust receiver and isentropic expansion with heat loss in the turbocharger. The model thus consists of a system of differential and algebraic equations with three state variables, control action fuel injection setpoint X set in %, input engine speed n e in Hz and output engine torque M e in kNm, and is described in detail in [24].
This mean value first principle model accurately represents mean values of engine efficiencies, temperatures, cylinder and scavenging flows and turbocharger pressures, based on calibration with FAT results. The model does not accurately capture all physical mechanisms, such as the turbocharger equation of motion and the gas exchange mechanism [53], as the models using compressor and turbine maps in [54][55][56]. This results in a significant reduction in simulation time to generate the performance map, shown in Fig. 9, from hours with the model in [56] to 23 s with this model. This reduced simulation time allows investigating hull-propeller-engine interaction shown in Fig. 4, and the benchmark manoeuvres proposed in [24]. Moreover, the model does not capture crank angle dynamics as in [57,58], combustion dynamics as in [59,60], or fluid dynamics as in [61]. For a short review of diesel engine models, we refer to [24].
The schematic presentation in Fig. 4 provides the interaction between the engine model subsystems and the governing equations as described in [24]. The summarising equations are as follows: where m 1 is the trapped mass at the start of compression in kg, λ is the air excess ratio, q 23 is the specific heat release at constant volume in kJ/ kg, from state 2 to state 3 of the Seiliger cycle, q 34 is the specific heat release at constant pressure in kJ/kg, from state 3 to state 4 of the Seiliger cycle, q 45 is the specific heat release at constant temperature in kJ/kg, from state 4 to state 5 of the Seiliger cycle, T 6 and p 6 are the average temperature and pressure in the cylinder during exhaust opening in K and Pa, at state 6 of the Seiliger cycle, and w i is the specific indicated work during the complete Seiliger cycle in kNm/kg.

Gearbox and shaft-line
The gearbox and shaft-line model consists of the equation of motion for shaft-line dynamics, assuming rigid coupling between the engine, gearbox, shaft-line and propeller, a linear torque loss model based on [62] and constant relative shaft-line losses. This model thus consists of a system of differential and algebraic equations with as inputs engine and propeller torque M e and M p in kNm, as state variable shaft speed n p in  Hz and as outputs shaft propeller speed and engine speed n p and n e in Hz [24]. The summarising equation is as follows:

Propeller
The propeller model uses the well-established open water test results and in particular the Wageningen C-series for Controllable Pitch Propellers [63,64]. For the pitch actuation system the model assumes a linear first order transfer function with a fixed time constant τ P to represent the time delay between changing the pitch setpoint and the actual movement of the pitch [24,[65][66][67]27]. Thus, the propeller model consists of a system of differential and algebraic equations with state variable propeller pitch ratio P pd , control action propeller pitch ratio setpoint P pd,set , input variables propeller speed n p in Hz, ship speed v s in m/s and wave orbital speed v w in m/s, and output variables propeller torque M p in kNm and propeller thrust T p in kN, represented by the following summarising equations:

Hull
The hull model represents ship motion in surge direction, as surge is most relevant for engine loading and loading effects due to turning can be represented as a disturbance after establishing its magnitude with 6 degrees of freedom models [68,27] or by applying a wake fraction variation δw, as proposed in [23]. The size of these wake variations can then be estimated based on the general trends reported in [23], although in this work we only consider straight line acceleration. The model represents the equation of motion with a system of differential and algebraic equations, including state variable ship speed v s , input variables ship resistance R v ( ) s in kN and propeller thrust T p in kN, and output variable ship speed v s in m/s. The summarising equation is as follows [24]:

Waves
The wave model takes two disturbances into account: the added resistance due to sea state, wind speed, fouling and displacement and the disturbance on the average speed of the water entering the propeller [24]. Additional effects, such as variances in the mean wake speed as a result of the pitching motion of the ship [69] or oblique inflow into the propeller [70] are neglected. The main cause of the disturbance on engine loading is the fluctuating wake speed of the water flowing into the propeller, as previously discussed in [50]. The orbital movement of water causes a disturbance on the average speed of the water entering the propeller, an exponential distribution of water speed along the depth of the propeller and an oblique inflow. In this study, we are interested in the significant disturbance of the wave orbital movement on the propeller loading, due to the significant wave height. We therefore consider the wake speed relative to the propeller center v w in m/s, as follows [71,72]: where ζ is the significant wave amplitude in m, ω wv is the wave radial frequency in rad/s, k w is the wave number in 1/m, z is the water depth in m at the propeller center, α wk is the angle of the vertical wave movement at the propeller centre in rad, and g is the standard gravity in m/s 2 .
The resulting model consists of a system of differential and algebraic equations with state variable angle of the vertical wave movement α wk , input ship speed v s in m/s, and output wake speed disturbance due to waves v wk in m/s. The summarising equations are as follows:

Baseline conventional control
The baseline conventional control strategy using two fixed combinator curves, rate limitations for acceleration and deceleration, and a pitch reduction strategy to prevent thermal overloading of the engine is described in [24]. The schematic representation of this control strategy is illustrated in Fig. 5 and the combinator curves for the case study patrol vessel are illustrated in Fig. 6. The transit mode aims to provide 'high propulsion efficiency within engine overloading limitations in design conditions' and the manoeuvring mode aims to provide 'high manoeuvrability within engine overloading limitations in design conditions' [24].
The control objectives and the tuning of the baseline conventional control strategy have been described in [73] and the resulting parameters are described and listed in [24]. In summary, the tuning procedure has led to conservative settings, in order to prevent overloading in the worst possible operating conditions. While the risk of thermal overloading has been eliminated, this might lead to reduced performance on Measures of Effectiveness [74] manoeuvrability, cavitation noise and fuel consumption. Ref. [24] concluded that the two operating modes led to very significant differences in performance: the transit mode reduces fuel consumption by up to 30% at 7 kts ship speed, reduces engine thermal loading by 90    while the manoeuvring mode reduces acceleration time from 0 to 15 kts by 41% compared to the transit mode.

Model validation
This model was validated with a case study Patrol Vessel, shown in Fig. 2, as described extensively in [24]. The diesel engine model (2)- (13) has been validated with Factory Acceptance Test measurements of the main diesel engines and the integrated propulsion system model consisting of (2)-(13), (14), (15)-(17), ()(18)- (21), with Sea Acceptance Trial measurements of the case study Holland-class Patrol Vessel, shown in Fig. 2. The model validation used the baseline conventional control strategy of the actual vessel described in Section 2.2. The parameters used for the model and the baseline control strategy are also described in detail in [24]. The validation demonstrates that 'the propulsion system model credibly predicts propulsion system behaviour within 5% accuracy' [24]. Moreover, the comparison of the model performance in waves with measurements on a Doorman class frigate as reported in [24], demonstrates the size and orientation of the ellipses in waves of sea state 6, which can also be observed for sea state 4 in Fig. 22, is representative for the effect in real waves, although quantification is not possible, as the exact wave height was not measured during the measurements at sea.

Adaptive pitch control strategy
The adaptive pitch control strategy aims to achieve many control objectives with essentially the same control actions as the baseline pitch control strategy. These control actions are propeller pitch ratio setpoint and fuel pump injection setpoint: p,set set . While the baseline control strategy uses measured system outputs propeller pitch ratio P p and engine speed n e , the adaptive pitch control strategy additionally uses the estimated hydrodynamic pitch angle: . The comparison of the simplified representation of both feedback control strategies is presented in Fig. 7. The following section extensively discusses the control objectives and how the proposed adaptive pitch control strategy achieves highly improved and near optimal performance for these objectives, within the physical limitations of the propulsion system components.

Control objectives
The control objective for the adaptive pitch control strategy is to optimise for the Measures of Effectiveness (MOEs) fuel consumption, manoeuvrability, engine thermal loading and, in some cases, cavitation noise, while providing the requested virtual shaft speed. In order to quantify the performance against these MOEs, we use the Measures of Performance (MOPs) [74] proposed in [24]. The control objectives derived from these MOPs are: 1. Provide requested virtual shaft speed n virt as defined in (1) [31]. 2. Maintain operation within the cavitation bucket for the widest possible operating conditions. 3. Minimise fuel consumption across the ship speed profile and for all operating conditions. 4. Maintain engine air excess ratio λ within predefined limits. We will investigate system performance against a number of minimum values of the air excess ratio λ. 5. Prevent engine overspeed and under-speed.
The proposed control strategy is presented schematically in Fig. 8. Next, we will discuss the proposed control laws and constraints, and how they achieve the control objectives.

Virtual shaft speed
The first control objective is to provide the requested virtual shaft speed as defined in (1). In the conventional control strategy, this is achieved with fixed combinator curves, as shown in Fig. 6. While the proposed adaptive pitch control strategy changes pitch based on operating conditions, the speed setpoint needs to be adjusted to compensate pitch changes. Therefore, the speed setpoint is determined from the actual pitch, as previously proposed in [31], as follows:

Maintain operation within the cavitation bucket
After experimentally determining the propeller cavitation bucket, Vrijdag [33] has developed a control strategy that is aimed at maintaining the optimum inflow angle of the water onto the propeller blade, the angle of attack, near its optimum value. Experiments demonstrate the effectiveness of this strategy in the − α σ eff n phase plane, which will be referred to as a cavitation plot in the remainder of this paper. This effective angle of attack α eff , is defined as follows: where α i is the shock free entry angle onto the leading edge of the propeller profile in deg, and c 1 is the coefficient to calibrate the effective angle of attack with the centre point of the cavitation bucket such that

Combinator curves
shaft speed for manoeuvring mode combinator relative pitch setpoint for manoeivring mode combinator shaft speed for transit mode combinator relative pitch setpoint for transit mode combinator Legend: ne,set speed setpoint P pd,set pitch ra o setpoint n e engine speed P pd propeller pitch ra o e ,set angle of a ack setpoint hydrodyamic pitch angle u(t) control ac ons Propulsion system baseline control strategy adap ve pitch control strategy where ∞ p is the ambient water pressure at the center-line of the propeller in Pa, p v is the vapour pressure of water at the ambient temperature in Pa, ρ sw is seawater density in kg/m 3 , and D p is the propeller diameter in m.
The proposed control strategy forms the basis for the control strategy proposed in this paper. While the implementation of the angle off attack strategy in [33] was aimed at minimising cavitation, the work already concluded that this control strategy improves acceleration behaviour and prevents the loss of ship speed due to pitch reduction when preventing engine loading. This study aims to quantify the benefits of the adaptive pitch control strategy and proposes an integrated control strategy aimed at achieving all control objectives mentioned above. The angle of attack setpoint α eff,set can be defined as a function of the virtual shaft speed, but in this case is taken constant and determines the normalised pitch control setpoint * P pd,set , as follows: where θ set is the pitch angle setpoint in rad, θ red is the pitch angle setpoint reduction in rad, β is the hydrodynamic pitch angle in rad, v a is the advance speed of the water relative to the propeller in m/s, and f w is the wake fraction, which is considered constant. While the actual hydrodynamic pitch angle cannot be directly measured, we assume this value is available. In [33] a method is proposed to derive the hydrodynamic pitch angle by measuring thrust and using the inverse of the four quadrant open water diagram. Moreover, a pitch angle reduction term θ red is added, which is proportional to the margin of the unlimited fuel injection setpoint to the fuel injection limitations, as follows: where P θ is the proportional pitch angle reduction gain, X mar is the fuel injection margin as defined in (39) and θ red,max indicates the maximum value of the pitch angle reduction. When the control objective to minimise acceleration time is also strived for, the air excess ratio limitation of the engine causes pitch reduction. Subsequently, the angle of attack is not maintained at its optimum value. In a separate low cavitation mode the air excess ratio limitation is prevented by limiting the fuel injection increase rate limitation, R X,cav .

Minimise fuel consumption
The operating points of four components determine the fuel consumption of a direct mechanical propulsion plant with controllable pitch propeller: the diesel engine, the gearbox, the shaft-line and the propeller. The speed and fuel injection of the diesel engine, in combination with the charge pressure, determine the specific fuel consumption of the engine. The speed and torque of the shaft-line and gearbox determine their losses, which are relatively small and will not be considered for the control strategy. Finally, the propeller open water efficiency is determined by the operating point of the propeller, governed by ship speed, wake-field disturbance from waves and propeller speed and pitch. Moreover, automotive and maritime research has shown that quasi static behaviour to a large extent determines the fuel consumption of cars and ships [75][76][77], although Blanke et al. [48] have demonstrated the engine control strategy can utilise the varying inflow velocity to increase the propeller efficiency in moderate seas, as will be addressed in Section 3.1.4.
The operating point at which the diesel engine consumes the minimum amount of fuel for a given power can be established from the specific fuel consumption contour plot, shown for the case study diesel engine in Fig. 9. At the lowest fuel consumption for a given power, the gradient of the specific fuel consumption is zero. The theoretical cube law propeller curve with a design point at full speed at 90% of rated power is also shown in Fig. 9. On this propeller curve, the fuel consumption is very close to its lowest value for a give power, as the gradient of the specific fuel consumption is close to zero. Moreover, the diesel engine project guide recommends operating the diesel engine on  this propeller curve, as the margin to the engines power limit is sufficient [78].
Similarly, the control objective to operate the engine at or close to the operating point defined by the theoretical propeller curve also leads to the highest possible open water efficiency of the propeller, as the open water efficiency typically is highest at the highest possible pitch and the operating envelope of the engine does not allow increasing pitch, and thus the load, above the theoretical propeller curve. For engines with wide operating envelopes, alternative control strategies might lead to lower fuel consumption. One such strategy can reduce fuel consumption in part load by up to 7%, by using hybrid propulsion with power take-off for a sequentially turbocharged diesel engine, as discussed in [79]. In conclusion, the second resulting control objective is to operate the engine at or close to the operating point defined by the theoretical propeller curve with a design point at 90% rated power.
This control objective can be achieved by governing control action propeller pitch ratio setpoint P p,set and can be translated in maintaining a constant propeller torque coefficient K Q , which is defined as [25]: where Q p is the open water propeller torque in kNm, and D p is the propeller diameter in m. However, control objectives 3, 4 and 6 benefit from maintaining a constant effective angle of attack α eff , instead of a constant pitch or propeller torque coefficient K Q . Moreover, for the case study Patrol Vessel, with a nearly cubed resistance curve due to its low Froude number, maintaining a constant angle of attack also leads to operating the propeller at an almost constant propeller torque coefficient K Q and at or close to the theoretical propeller curve. Therefore, the propeller pitch ratio setpoint P p,set is controlled to maintain the angle of attack at its setpoint value α eff,set , as defined in (27) and (28).

Maintain engine air excess ratio
The engine air excess ratio, the relative amount of air that is left after complete combustion of all fuel, is an important indicator for engine thermal loading, as demonstrated in [80,81,56,24], and Figs. 9 and 10. While the air excess ratio contour plot in Fig. 9 illustrates the air excess ratio in stationary conditions, the air excess ratio during dynamic conditions, such as acceleration and wave induced disturbances, can be significantly lower or higher due to the turbocharger lag. In this section, we will first address wave induced disturbances and propose integrating speed control to resolve these and then propose a fuel injection constraint that maintains the air excess ratio at a minimum value during acceleration.
Geertsma et al. [50] have demonstrated that engine torque control as opposed to engine speed control can completely eliminate thermal loading fluctuation due to disturbance from waves. Moreover, Blanke et al. [48] have demonstrated with model experiments that torque control can lead to 2% fuel consumption reduction in moderate seas by utilising the varying inflow velocity onto the propeller blade, thus increasing the propeller efficiency. However, the first control objective is to provide the requested virtual shaft speed and torque control would require an additional torque sensor, that might be less reliable than speed sensing. Therefore, we propose to use integrating speed control, without a proportional gain on the speed error, similar to the slow integrating speed control strategy that Rubis and Harper [82] proposed for gas turbine mechanical propulsion, due to its good performance in heavy waves. Slow integrating speed control exhibits a similar dynamic behaviour in waves as torque control and, in combination with (24), also provides the requested virtual shaft speed. Thus, the following control algorithm is proposed to achieve slow integrating speed control: where X I is the fuel injection setpoint from integrating speed control, K I,ic is the reset rate for slow integrating speed control, i gb is the gearbox reduction ratio, and n e,nom is the nominal engine speed in Hz.
During an acceleration, the charge pressure will lag at a lower value due to the turbocharger inertia, which causes a higher thermal loading than in stationary conditions. In order to prevent thermal overloading, the objective thus is to maintain the air excess ratio at a minimum value. This can be achieved by first limiting the fuel pump position based on the charge pressure and secondly reducing the angle of attack setpoint when the fuel pump position is limited. The fuel pump position limitation is defined as follows, as derived from [24,Eqs. (4) and (5)]: where X λ lim, is the fuel injection limitation to limit the air excess ratio λ in % of nominal fuel injection m f,nom , V 1 is the cylinder volume at the start of compression in m 3 , R a is the gas constant of air in J/kg K, T 1 is the temperature at the start of compression in K and σ f is the stoichiometric air fuel ratio of the fuel.
Another important parameter to limit engine thermal loading is the rate of increase of exhaust valve temperature dT dt / ev during an acceleration, which is mainly determined by the rate of increase of torque and therefore fuel injection X. In order to limit this rate of increase, the proposed adaptive pitch control strategy incorporates a fuel injection increase rate limitation R X,therm to prevent thermal overloading due to a high dT/dt. Moreover, in order to prevent cavitation due to running into the air excess ratio limitation, a second setting for this rate is determined for the low cavitation mode: the torque increase rate limitation for reduced cavitation R X,cav .

Minimise acceleration time
The objective to minimise acceleration time is restricted by the objective to prevent engine thermal overloading [38] and thus by the objective to maintain engine air excess ratio. In traditional control strategies this is achieved by limiting the rate of the increase in engine speed during an acceleration manoeuvre, as demonstrated in [50,21].Vrijdag [31] has demonstrated, through a combination of simulation and validation, that the acceleration behaviour improves due to the proposed angle of attack control strategy with an acceptable engine thermal loading. In essence, the acceleration manoeuvre is faster, because the pitch is increased more slowly during the acceleration manoeuvre, leading to higher engine speed. Geertsma et al. [24] have demonstrated that indeed a reduced pitch during an acceleration manoeuvre increases engine speed and reduces engine thermal loading,  because the turbo charger pressure and thus the air excess ratio increases faster at higher engine speeds. In the proposed slow integrating speed control strategy, according to (34), speed increase rate limiters are not required, as will be demonstrated in the results of this paper. Therefore, the setting of the reset rate K I determines the speed of acceleration and needs to be determined in a trade-off between acceleration behaviour and engine thermal loading during an acceleration.
3.1.6. Prevent engine overspeed and under-speed Slow integrating speed control as defined in (34) introduces the risk of engine overspeed or under-speed due to disturbances, as integrating speed control follows the speed setpoint significantly slower than an aggressive PI controller. To prevent engine overspeed, the following fuel limitation is introduced: where X lim,os is the fuel injection limitation to prevent overspeed, n e,max is maximum engine speed, and P os is the overspeed limitation gain. Similarly, the following minimum fuel injection X min prevents engine under-speed: where n e,min is minimum engine speed, and P us is the under-speed limitation gain. Moreover, the fuel injection limitation and the fuel injection margin X mar are defined as: where X lim is the fuel injection limitation in %. Finally, the fuel injection is limited between the minimum fuel injection X min and the fuel injection limitation X lim , as follows: With a traditional combinator curve, reducing pitch at low speed settings while maintaining minimum engine speed prevents engine under-speed. When applying the adaptive pitch control strategy the pitch should also be constrained to the value associated with minimum engine speed, as follows: where n e,mins is the minimum engine speed setpoint. Finally, when pitch is limited to prevent engine under-speed, engine speed should be kept constant at minimum engine speed n e,min . In this region, slow integrating speed control can lead to excessive speed fluctuation, which will be limited by the under-speed fuel injection limitation described in (37). Nevertheless, in this region engine speed is better kept constant by applying traditional fast PI speed control, as described in [24], as follows: where X PI is the unlimited fuel injection setpoint for speed control, K P is the proportional gain and K I is the reset rate. PI speed control replaces slow integrating speed control when the engine speed setpoint is less or equal to minimum engine speed n e,min with a hysteresis of 2.5%. Effectively, PI gain scheduling [83] is applied in this case with a clear switching value, when the engine speed setpoint is at its minimum value with a hysteresis of 2.5% to prevent repetitious switching between the gain values. While repetitious switching is prevented by using the speed setpoint as switching variable, alternatively, a continuous function for the proportional gain P could be derived, as used in pitch control with gain scheduling for wind turbines [84].

Controller settings
With the traditional control strategy, many of the control parameters require extensive tuning [24,85,73,Section 3.3]. The resulting parameters of the traditional control strategy are listed in [24, Table 2 -6]. Alternatively, the proposed control strategy primarily requires limitations for physical parameters and a number of gains. The only parameters that require tuning are the gain and reset rate for speed control at minimum engine speed K P,sc and K I,sc , and the reset rate for slow integrating speed control K I,ic .
Various tuning strategies for PI control are discussed in literature [83,[86][87][88]. While Aström and Häggelund [83] provide an overview of tuning strategies, Xiros [86] proposes an improved PID tuning method for marine engine speed regulation to meet sensitivity ∞ H requirements. However, the stability of the system does not require stringent engine speed disturbance rejection criteria, as demonstrated in [50] and we aim to minimise torque fluctuations. Moreover, the reset rate for slow integrating speed control K I,ic physically primarily influences the rate of temperature increase dT dt / ev during an acceleration and therefore is tuned to achieve gradual dT dt / ev . Moreover, the influence of the gain and reset rate for speed control K K & p i on the behaviour in waves can be investigated with linearised propulsion system models as proposed in [87,88]. The parameters in this paper were based on this approach and the results in this paper demonstrate the stability of the used settings. The resulting control parameters for the proposed adaptive pitch control strategy are listed in Table 1.

Simulation experiments
The simulation experiments for the case study Holland class Patrol Vessel in this paper aim to compare the proposed control strategy with the baseline control strategy of the actual vessel, which has been used for the validation of the simulation model in [24]. We use two types of straight line manoeuvres to establish the Measures of Performance (MOP): sailing at constant speed and two acceleration manoeuvres. First, the slam start manoeuvre proposed in [89] is used to establish the shortest possible acceleration time from 0 kts to 15 kts ship speed, by setting the virtual shaft speed to the maximum value at the start of the manoeuvre. Second, intermediate sprints are used to establish MOPs during regular acceleration. For intermediate sprints, the virtual shaft speed setting is increased from the setting that provides the starting ship speed to the setting that achieves the speed at the end of the manoeuvre. These benchmark manoeuvres can be used to demonstrate that the proposed control strategy meets the objectives described in Section 3.1. Moreover, we have performed the proposed benchmark manoeuvres to establish the Measures of Performance (MOPs) proposed in [24]. As reported in [24], 'the ship resistance and the wave model parameters very strongly depend on the conditions in which the ship operates'. In this study, we consider the following two typical conditions: • Trial condition, defined as Sea State 0, wind speed of 3 m/s and no fouling.
• Design condition, defined as Sea State 4, wind speed of 11 m/s, head seas and wind and 6 months out of dock fouling.
The parameters that represent these conditions are shown in Table 2 and Fig. 11, from [24].
The simulation results have been obtained with MATLAB Simulink R2016b software on a PC with Intel Core i7 processor and 16 GB memory. The simulation to establish the slam start and intermediate   Fig. 11. Ship resistance from model tests corrected for environmental conditions and fouling in trial, design and off-design condition, from [24].

Evaluated control strategies
In the simulation experiments, the baseline transit and manoeuvre mode control strategies, as described in [24], are compared with the adaptive pitch control strategy as described in Section 3, with various settings as reported in Table 1. An overview of the 5 control strategies, their modes and settings used for the evaluation in Section 4 is listed in Table 3.

Virtual shaft speed
The first control objective is to provide the requested virtual shaft speed. This objective is one of the key reasons to employ traditional speed control, as feedback control on speed can robustly handle the uncertainty associated with weather conditions, ships course relative to the wind and waves, hull fouling and ships displacement. Figs. 12 and 13 present the results of the intermediate acceleration from 0 kts to 5 kts, 5 kts to 10 kts, 10 kts to 15 kts and 15 kts to maximum speed for trial conditions and for design conditions, reflecting two very different conditions and thus the described uncertainty.
The baseline control strategy provides the requested shaft speed unless pitch is reduced to prevent overloading, as described in [24, Section 3.2, pp. 1618-1619]. While engine speed control robustly maintains engine speed at the requested speed from the combinator curve, the pitch reduction strategy reduces pitch and therefore virtual shaft speed. Therefore, in conditions with a high ship resistance, such as design conditions, the traditional control strategy does not actually provide the requested virtual shaft speed, as shown in Fig. 12. Actually, even in trial conditions, at certain engine speed the requested virtual shaft speed is not achieved. The operator can achieve the required ship speed by requesting a higher virtual shaft speed than the virtual shaft speed required for that ship speed, which is clearly demonstrated by the high virtual speed setpoint of 200 rpm required to achieve 15 kts ship speed with baseline transit control in design conditions in Fig. 12b.
The proposed adaptive pitch control strategy, in this case with limited air excess ratio, follows the virtual shaft speed setpoint      accurately, because higher or lower pitch than nominal pitch is compensated with a proportional decrease or increase in speed setpoint due to (24). Only if the air excess ratio limitation λ min is higher than the air excess ratio on the theoretical propeller curve, for this engine higher than 1.50, the virtual shaft speed will not reach its setting as the air excess ratio limitation is not compensated by increased engine speed. Slow integrating speed control responds more slowly to changes in engine speed and therefore ship speed, leading to a slight overshoot in virtual shaft speed during acceleration, as shown in Fig. 12. However, this overshoot only leads to an overshoot in ship speed of 0.3 kts, and only in light trial conditions. During design conditions, when the engine margin is smaller, constant ship speed is only reached when the virtual shaft speed overshoot has already stabilised. Therefore, this overshoot is acceptable, also because it leads to significantly faster acceleration. The robust virtual shaft speed following capability under large uncertainties is a significant advantage of the proposed adaptive pitch control compared to the baseline strategy, that does not accurately follow the virtual shaft speed setpoint, and this behaviour is achieved with simple feedback control as opposed to complex algorithms as proposed in [90].

Maintain operation within the cavitation bucket
While the propeller of the patrol vessel has not been designed for low noise operation, the angle of attack at the design point of the propeller is too high for low cavitation behaviour. However, for the evaluation of the control objective to maintain operation within the cavitation bucket, we assume the cavitation bucket is centred around the angle of attack at the design point, which could be achieved at a lower angle of attack with a similar propeller with a larger diameter. Therefore, the objective of the control strategy is to maintain the angle of attack centred around the design angle of attack: 10.5 deg.
The cavitation plots at constant speed for trial and design conditions in Figs. 14 and 15 demonstrate that the adaptive pitch control strategy maintains the effective angle of attack at the desired angle of 10.5 degrees, irrespective of the uncertainties in weather conditions, while the effective angle of attack of the baseline transit and manoeuvre mode      Fig. 20. The fluctuation in angle of attack, caused by waves, does not increase with the adaptive pitch control strategy compared to the fluctuation in angle of attack with a constant pitch angle in the baseline control strategies, confirming the adaptive pitch control strategy does not lead to instability. However, the adaptive pitch control strategy with limited air excess ratio during acceleration does reduce pitch during the acceleration, as shown in Fig. 18 and then the angle of attack reduces during the manoeuvre, as shown in Fig. 16. This can be resolved by reducing the fuel injection increase rate to a lower value, R X,cav . Then the pitch reduces only to maintain the angle of attack centred around 10.5 deg as shown in Figs. 18 and 17, leading to a lower rate of increase of engine speed and slower acceleration as shown in Fig. 19.

Minimise fuel consumption
The control objective to minimise fuel consumption during constant speed sailing is achieved when the engine runs on the theoretical propeller curve as argued in Section 3.1.3. The fast adaptive pitch control strategy achieves operating points and ellipses on the theoretical propeller curve at various ship speeds for transit and design conditions, as shown in Fig. 21. Alternatively, in Fig. 22 the baseline transit control strategy operates well below the theoretical propeller curve, mainly due to its conservative settings to prevent engine overloading under any circumstances [24, Section 3.3, p. 1619]. Moreover, the baseline transit control strategy operates further away from the theoretical propeller curve during design conditions than during trial conditions. The orientation of the ellipses due to speed and torque fluctuation from waves changes due to slow integrating speed control: the torque fluctuations reduce to minimal values at the cost of a slight increase in speed fluctuations, as shown in Fig. 21, compared to the more vertical ellipses in Fig. 22, almost eliminating fluctuating air excess ratio and temperatures as shown in Fig. 28. Thus, we can conclude the adaptive pitch control strategy at constant ship speed compensates the uncertainty in weather conditions robustly and runs the engine at its most efficient operating    point with sufficient margin to the engine operating envelope. While the efficiency during acceleration does not heavily impact the fuel consumption over the operating profile of the ship, the efficiency during acceleration is also an indicator for acceleration performance. Therefore, Figs. 23 and 25 present the propeller open water efficiency and the effective engine efficiency during intermediate sprints and the slam start acceleration. During these accelerations, the engine efficiency and propeller efficiency are consistently higher for the fast adaptive pitch control strategy than for the baseline manoeuvre strategy. This has two reasons: first, the pitch in adaptive pitch control is higher and therefore the propeller operates at a higher open water efficiency; secondly, engine speed and engine load increase faster during acceleration, thus operating the engine at higher efficiency, because the adaptive pitch control strategy retracts pitch during the acceleration procedure to maintain the effective angle of attack as shown in Figs. 24 and 26.
The approach to minimise fuel consumption works very well with the proposed angle of attack approach, because fuel consumption is close to its minimum for a constant angle of attack for this particular engine. Nevertheless, if an engine has a different specific fuel consumption plot or if the trade-off between quasi-static NO x emissions and fuel consumption should be taken into account, still an optimum quasistatic relationship between engine speed and torque could be established, which can be either translated into a relationship between shaft speed n p and effective angle of attack α eff or shaft speed n p and propeller torque coefficient K Q . The input for the development of the setting for this approach are static specific fuel consumption or NO x emission maps, such as Fig. 9, Fig. 4 in [21], or Fig. 1 to 3 in [91]. Nuesch et al. [91] practically demonstrate NO x emissions can be addressed with a quasi-static approach, as opposed to particulate matter (PM) emissions, which are sensitive to turbo charger lag and primarily benefit from a smooth torque trajectory, one of the benefits of the proposed slow integrating speed control strategy. Moreover, the static PM emission map in Fig. 2, in [91], shows that PM emissions for that specific automotive diesel engine appears near its minimum around the theoretical propeller curve. Therefore, future work could be aimed at confirming the expectation that the proposed adaptive pitch control strategy with slow integrating torque control also has a positive influence on PM emissions, and at investigating the trade-off between fuel consumption and NO x emissions.

Maintain engine air excess ratio
Figs. 27 and 28 demonstrate that the proposed control strategy maintains the air excess ratio within the predefined limits, either above the minimum value of 1.45 or above the value of 1.6. When the air excess ratio λ min is kept at a higher value, the temperatures during the slam start and intermediate acceleration are significantly lower. The baseline manoeuvre mode maintains even higher air excess ratios during all manoeuvres and therefore maintains lower temperatures, but that is caused by the very conservative settings to prevent overloading in heavy off-design conditions. In the nominal operating point on the theoretical propeller curve at 700 rpm and 1650 kW, the air excess ratio also is 1.35 and the exhaust valve temperature 1350 K. Therefore, an air excess ratio of 1.45 and an exhaust valve temperature of 1350 K does not lead to engine thermal overloading. In almost all manoeuvres the maximum exhaust valve temperature remains below 1350 K, suggesting that the proposed control strategy with a minimum air excess ratio does not lead to thermal overloading. However, during the intermediate sprint from 10 to 15 kts the maximum cylinder temperature peaks to 1400 K, while the air excess ratio λ is maintained at a minimum value of 1.45. During this acceleration, engine speed ranges from 600 to 800 rpm, the range in which the air excess ratio is lowest and exhaust valve temperature highest during static conditions. Nevertheless, the higher temperature during this manoeuvre compared to other manoeuvres with the same minimum air excess ratio proves that the exhaust valve temperature is not directly dependant on the in-cylinder air excess ratio λ.
Close inspection of the simulation results shows that during this acceleration, the charge pressure lags, causing a reduced scavenge flow and therefore reduced exhaust valve cooling. This dependency of scavenge flow on charge pressure is clear from Eq. (29) and (30) in [24] and the relationship between scavenge flow and exhaust temperature is expressed in Eq. (51) in [24]. While further research would be required to establish whether this would indeed lead to thermal overloading of the engine, an alternative maximum fuel injection value as a function of charge pressure p 1 slightly more conservative than (35), could be used to reduce thermal loading during this specific case. Then, the relationship would either have to be experimentally established or have to be determined with the simulation model used in this study using the engine model in isolation and fixing the charge pressure model input.
Alongside the maximum temperature that is reached during acceleration, the rate of change of the exhaust valve temperature dT dt / ev during an acceleration is also important for thermal stresses in the engine. Figs  dT dt / ev during the initial phase of the acceleration is similar to the baseline manoeuvre mode, but that the fluctuation due to waves does not occur for the adaptive pitch control strategy, due to the slow integration speed control. Moreover, close to the peak temperature, when the thermal stresses are highest, the increase rate of the temperature reduces, again without the fluctuation due to waves. While further research would be necessary to accurately determine the thermal stresses caused by the two control strategies, Figs. 27 and 28 suggest the behaviour of the adaptive pitch control strategy is more gradual and therefore less likely to cause thermal overloading.

Minimise acceleration time
The control objective to minimise acceleration time is a trade-off with the control objective to prevent engine thermal overloading. In order to reduce engine thermal loading during an acceleration manoeuvre, charge pressure needs to increase as fast as possible as a higher charge pressure provides a higher air excess ratio and scavenge flow increases at higher charge pressures. Increasing charge pressure during an acceleration can be best achieved by increasing engine speed and thus air flow in the engine. However, the fuel injection limitation of the baseline control strategy and the air excess ratio limitation of the proposed strategy limit the fuel injection during the acceleration manoeuvre and therefore the torque available for acceleration. Reducing pitch during the acceleration manoeuvre, which is an indirect effect of the effective angle of attack control strategy, helps increasing engine speed during an acceleration manoeuvre due to (1). Fig. 24 demonstrates how, with fast adaptive pitch control, engine speed is increased during intermediate sprints due to pitch reduction, well above the engine speed after reaching constant speed, and Fig. 29 shows that this engine speed increase leads to a faster increase in charge pressure than during an intermediate sprint with the baseline manoeuvre mode. During a slam start acceleration with adaptive pitch control, engine speed and charge pressure do rise faster than with the baseline manoeuvre mode, but the increase in engine speed then is limited by the air excess ratio limitations due to the turbocharge lag, as shown in Figs. 26 and 29. Acceleration is 32% faster with fast adaptive pitch control than with the baseline manoeuvre, as shown in Fig. 30, but a further increase in engine speed during the acceleration might enable even faster acceleration. If the propulsion engines would be supported by an electric machine in a hybrid propulsion configuration, as proposed in [92,93], engine speed potentially could be increased even more, further reducing the effect of the turbocharger lag and reducing acceleration time. [92] shows that a combination of speed control on the induction machine and torque control of the main engine would reduce acceleration time by 40% compared to acceleration time without the electric machine, when a fixed combinator curve is used. Future work should investigate how much acceleration time can be further reduced with the combination of the proposed adaptive pitch control strategy and parallel control of an electric drive and propulsion diesel engine.

Prevent engine overspeed and under-speed
The control objective to prevent engine over-and under-speed is achieved by hard over-and under-speed limitations defined in (36) and (37) and by switching from slow integrating speed control (34) to fast PI speed control (45). Fig. 35 shows that fuel injection is limited during speed fluctuations in design conditions at the maximum virtual shaft speed setting, limiting engine overspeed to below 1050 rpm. Moreover, it shows how during the crash stop deceleration, [94,89], engine underspeed is prevented by switching to fast PI speed control (45), and how the fuel rack limitation that prevents engine under-speed is not even used during the crash stop manoeuvre. While slow integrating speed control does cause a 50 % increase in speed fluctuation due to heavy seas, from 30 rpm to 45 rpm, as illustrated in Figs. 16 and 17, engine speed stability is maintained in all conditions.

Behaviour in waves and turns
The results in all operating envelopes above, Figs. 21, 22, 31, 32, 33 and 34, demonstrate that the adaptive pitch control strategy reduces the torque fluctuations due to waves, because slow integrating speed control attenuates torque fluctuations at the cost of a slight increase in engine speed fluctuations. Moreover, the adaptive pitch control strategy aims to maintain the angle of attack constant and tries to compensate     the wake speed fluctuations from waves. However, due to the slow response of pitch actuation, the angle of attack during waves is not kept constant. While faster pitch actuation might enable the adaptive pitch control strategy to better maintain a constant angle of attack during high frequency wake fluctuations, we expect that the adaptive pitch control strategy can compensate for the relative slow wake speed fluctuations due to turns, particularly in stabilised conditions, as reported in [23, Fig. 3]. Moreover, the method to establish the angle of attack as described in [33] also uses the assumption of constant propeller characteristics, which [23] suggests also to hold for estimating the effect in turns, even though effects such as non-uniform wake distribution and oblique propeller inflow due to turns will have an impact on the accuracy of this assumption. Therefore, future work should be performed, first with simulation models and subsequently with model or full scale trials, to establish whether the adaptive pitch control strategy can also maintain the angle of attack in turns, thus reducing cavitation noise and increasing propeller and propulsion efficiency.

Measures of performance
The MOPs of the proposed adaptive pitch control strategy with and without a limited air excess ratio can now be compared with the MOPs of the transit and manoeuvre mode of the baseline control strategy as discussed in [24]. The fuel consumption plot for trial and design conditions, the air excess ratio plot for trial conditions, the cavitation plots for trial and design conditions and the angle of attack plot for trial conditions are shown in Figs. 36, 37, 38, 14, 15 and 39, for the three control strategies. Moreover, the acceleration time, minimum air excess ratio and maximum angle of attack of the transit and manoeuvre mode of the baseline control strategy and the proposed adaptive pitch control strategy with a limited air excess ratio are presented in Table 4.
From the comparison of the MOPs, we can draw the following conclusions: • The adaptive pitch control strategy reduces fuel consumption in design conditions by 5-15% compared to the baseline transit mode in the ship speed range from 6 to 15 kts, and by 5-30% compared to the baseline manoeuvre mode in the speed range up to 15 kts. This is     achieved by running the engine at the theoretical propeller curve on the associated air excess ratio. When the air excess ratio is limited at 1.6, in the engine speed range from 600 to 800 rpm the engine torque is actually limited at a value below the theoretical propeller curve, causing a slight increase in fuel consumption of up to 2%, because the air excess ratio at 700 rpm on the propeller curve is 1.5, as shown in Fig. 9. Nevertheless, this would be a very conservative setting as the theoretical propeller curve lies well within the operating envelope of the engine.
• The adaptive pitch control strategy reduces acceleration time from 0 to 15 kts with the slam start procedure by 32% compared to the baseline manoeuvre mode and by 63% compared to the transit mode, while consistently maintaining the air excess ratio at a minimum value of 1.6. For an intermediate acceleration from 10 to 15 kts, acceleration time reduces by 84%. While faster acceleration can be achieved by using the slam start procedure [89], requesting maximum virtual start speed in stead of the virtual shaft speed associated with 15 kts, the adaptive pitch control strategy does provide a more consistent acceleration time, also for intermediate acceleration, without thermally overloading the engine.
• During acceleration, the angle of attack is kept around the design value of 10.5 deg, as shown in Figs. 14-17. The wake flow fluctuation causes the angle of attack to fluctuate with a similar amplitude as with the baseline control strategy.
In summary, the adaptive pitch control strategy accelerates much faster and much more consistently than the baseline manoeuvre mode, while also reducing fuel consumption significantly, without thermally overloading the engine and reducing cavitation risk for a propeller designed for low cavitation. Moreover, the control strategy does not need operator input to switch between fuel efficient or manoeuvrable operation.

Conclusions and future research
While shipping urgently needs to reduce its impact on the environment due to emissions and noise, multifunction ships also need to manoeuvre fast and accurate with a reliable propulsion plant to support more autonomous operation. This study has proposed an adaptive pitch control strategy for diesel mechanical or hybrid propulsion with slow integrating speed control and demonstrated the following: it robustly follows the requested virtual shaft speed; operates the propeller around its effective angle of attack; reduces fuel consumption and has the potential to improve NO x and particulate matter (PM) emissions; maintains the air excess ratio λ at its required minimum value, thus limiting engine thermal loading; reduces acceleration time particularly during intermediates sprints, due to its consistent acceleration behaviour; and robustly prevents engine over-and under-speed. For the case study patrol vessel, the adaptive pitch control strategy reduces fuel consumption by 5-15% compared to the baseline transit mode in the ship speed range from 6 to 15 kts, and reduces acceleration time from 0 to 15 kts with the slam start procedure by 32% compared to the baseline manoeuvre mode and by 84% for an intermediate acceleration from 10 to 15 kts, without thermally overloading the engine.
Future work should establish how much NO x and particulate matter (PM) emissions can be reduced with this strategy, as an initial analysis in this study suggests the proposed approach can be used to address the quasi-static trade-off between fuel consumption and NO x emissions based on static maps, and the smooth torque trajectory due to slow integrating speed control is expected to have a positive impact on PM emissions. Moreover, the exact relation between charge pressure and engine thermal loading, indicated by exhaust valve and exhaust receiver temperatures should be established with simulation studies verified by experiments, to improve the fuel injection limitation that prevents engine thermal overloading. Finally, the maximum acceleration improvement and fuel consumption reduction with hybrid propulsion should be established, with an electric drive assisting the engine during acceleration and allowing more freedom of control in operating the main engine at its best possible fuel consumption.
With the proposed adaptive control strategy and these additional improvements, the freedom of control provided by controllable pitch propeller can be optimally utilised to contribute to the urgently required reduction of the environmental impact of shipping, both due to emissions and noise, without operator input. Moreover, the improvements in acceleration performance and reduction in engine thermal loading ensure the ships can be used for its increasingly divers tasks without operator input and with minimum time in port for maintenance, thus supporting more autonomous operation. Table 4 Acceleration time, minimum air excess ratio and maximum angle of attack during acceleration with baseline control in manoeuvring (man) and transit (tran) mode compared with the proposed adaptive pitch control (apc) strategy (design condition).