Simulation and control design of hybrid propulsions in boats

Simulation and control design of hybrid propulsions in boats

8th IFAC Conference on Control Applications in Marine Systems Rostock-Warnemünde, Germany September 15-17, 2010 Simulation and control design of hybr...

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8th IFAC Conference on Control Applications in Marine Systems Rostock-Warnemünde, Germany September 15-17, 2010

Simulation and control design of hybrid propulsions in boats Johann Wilflinger, Peter Ortner, Luigi del Re: Johannes Kepler Universität , Linz, Austria * Michael Aschaber Steyr Motors, Steyr, Austria ** *Institute for Design and Control of Mechatronical Systems Johannes Kepler Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austria (e-mail:[email protected]) ** STEYR MOTORS GmbH, Im Stadtgut B1, 4407 Steyr, Austria (e-mail: [email protected]) Abstract: This paper concerns the implementation of hybrid drive lines in marine applications with the main aim to improve the longitudinal dynamics during acceleration. The main concern is the optimal use of the combination between internal combustion engines and electric motors limited by battery capacity and thermal load. We use physical and data based modelling to derive a suitable model for control design. Based on a chosen cost function we finally compute a control law to assist the combustion engine during acceleration phase while battery charge conditions and thermal constraints can be taken into account via a cost function parameter. Keywords: Control functions, Performance drives, Propulsion control, Internal combustion engine, Electrical motors Additionally, hybrid drives can be used to supply current for the other uses on the boat, and can allow a purely electrical operation in suitable places. In order to obtain a smoother performance during acceleration, two elements are needed: a peak torque supply unit, in this case an electrical motor able to supply an additional torque for a few seconds, and a model based control strategy able to control it. Figure 2 shows the hybrid system, Figure 3 the test boat which has been the source of the in Figure 1 shown acceleration profile as well. The control setup is different from standard road applications, on one side for the different emission regulations, but even more for the difficult repeatibility on water with respect to the road (besides the lack of a fixed coordinate system) and the small number of production lots which makes the determination of extensive physical models hardly viable.

1. INTRODUCTION Hybrid drivelines have been proposed over decades for road vehicles, see e.g. [Sciarretta 2007] for a recent overview. However, they are not yet as popular in ships and boats, up to some special uses, mostly pure electrical, like in submarines or other essentially military applications, see [Skinner 2007] for one of the few examples. This is surprising, because they could strongly improve the environmental acceptance in harbours or inland waterways, and also offer dynamic advantages during acceleration phases. Indeed, during acceleration, fast boats go through a series of changes of assets which cause a reduction of the acceleration in a certain time interval which is perceived negativily by the passengers (see Figure 1, where the bolded curve shows the acceleration with the clearly distinguishable drop between 12 and 20 seconds.

Figure 2: hybrid unit (1 electric unit (motor/generator), 2 Hybrid Control Unit, 3 battery set, 4 combustion engine, 5 external controls, 6 electric propulsion inputs, 7 hybrid sensor inputs) This paper is concerned with the modelling of the system using easily available physical understanding, but using as much identifications as possible (Ljung 1999), as this strongly reduces the time demand for modelling and is more suitable to the bad variants/performance ratio of ship industry. To improve this aspect, the model is build up

Figure 1: Typical acceleration profile of a sport boat

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CAMS 2010 Rostock-Warnemünde, Germany, Sept 15-17, 2010

modulary and uses torque estimators to determine parameters during the actual boat operation.

Figure 3: test boat

Figure 4: Diesel engine model

The result is a multi-physics modular model with a constant engine and changing boat design and use profile, which has been used to design a compensation law which allows to use the available boost power of the electrical motor. The model has been designed as a combination of physical understanding, experiments and/or data on components (in particular the combustion engine and the electrical drive) and dynamical identification steps.

Diesel engines are complex systems, but for torque control a simplified Linear Parameter Varying first order model with an operating point dependent dynamic behaviour was used here. This has allowed a fast and easy identification of the main dynamic behaviour. In the model, different kinds of parametrized drivelines have been included to allow the a priori estimation of the final dynamical behaviour for different configurations. The track resistance of the standard car model has been simplified to get an alterable model of the boat behaviour.

The paper is structured as follows: In section 2 we explain the mathematical model of the hybrid drive train for the sport boat. In section 3 we introduce our control algorithm based on a cost function and in section 4 we show the simulation results for a boost supported acceleration phase using different control laws. Finally section 5 concludes.

Tdyn = − ρ (Tdyn , ω )Tdyn + ρ (Tdyn , ω )Tstat

(1)

On the engine test bench we first measure the static engine torque Tstat for several engine speeds and injection amounts

2. Mathematic Model

e.g. acceleration pedal position α to obtain the first map in Figure 4. Therefore we remain in each operating point for at least 30 seconds to guarantee the steady state. Afterwards using ramp profiles for several fixed injection amounts it is possible to determine the dynamic engine torque Tdyn

2.1 Diesel engine model Diesel engine modelling has been of great interest in the research community in the last few years, see [Jung 2003] and [Ortner 2007] for a good overview. We decided to model the Diesel engine as a Linear Parameter Varying (LPV) first order model with an operating point dependent dynamic behaviour shown in Figure 4 and in equation (1). We are able to use such a simple structure because of the absence of an exhaust gas recirculation and variable geometry turbocharger usually occurring in Diesel engines for automotive applications. The only inputs are the engine revolution speed ω and the throttle position α.

Tdyn = Tmeasured − θ Eω E where

θ E is

(2)

the engine inertia and ω E is the slope of the

speed ramp profile. After filtering Tdyn its derivative Tdyn can be computed and with these quantities it is finally possible to compute the dynamic parameter ρ (Tdyn , ω ) according to

ρ (Tdyn , ω ) =

41

Tdyn Tstat − Tdyn

(3)

CAMS 2010 Rostock-Warnemünde, Germany, Sept 15-17, 2010

Figure 7: “Z-drive” application The “fixed shaft” approach has the advantage to be very simple and an electric motor can easily be added. The losses are much less than in the “Z-drive” approach. But the latter has the advantage that the propeller angle can be adjusted and therefore the pitch angle of the boat can be actively influenced.

Figure 5: Diesel engine model validation We divided the speed from 800 rpm to 4500 rpm into 20 regions and the torque into 13 regions covering the whole possible operating range of the engine, which lead to 260 values for the dynamic parameter ρ(Tdyn, ω). Finally Figure 5 shows the validation results of our Diesel engine model with data not used for the identification, which shows a very good approximation quality even though it is a simple first order model. Since in this work we consider a hybrid boat and not only a Diesel engine driven boat we have to add an electric motor which is done quite simple by adding an ideal torque provider to the dynamic torque provided by the Diesel engine.

Tsum = Tdyn + Telectric

Figure 8: drive train model

(4)

Figure 8 shows the basic model of the drive train suitable for both approaches mentioned above. The equations for this two mass oscillator are

This is a suitable simplification due the fast torque response time of an electrical motor compared to a combustion Diesel engine.

θ Eω E = Tdyn + Telectric − TW θ Pω P = TW − TP ∆ϕ = ωE − ωP TW = c∆ϕ + d ∆ϕ

2.2 Drive train model The two most common drive train approaches for sport boats are the “fixed shaft” (Figure 6) and the “Z-drive” (Figure 7) approach. Both are usually equipped with only one forward and one reverse gear, whereby only one transmission is available for the whole drive line calibration, which makes things much more complicated compared to automotive applications.

(5)

θ E is the inertia of the Diesel engine and the electric motor, θ P is the inertia of the propeller, Tw is the shaft torque, c the stiffness of the shaft and d the damping coefficient of the shaft. 2.3 Propeller model Combustion engines in a power range of about 250 hp are usually combined with fixed propeller of 30 to 70 cm diameter, where the diameter for high speed application gets smaller. In contrary to propeller with adjustable blades, for fixed propeller the run-up behaviour is of great interest. The steep pitch angle which allows high top speed of the boat transfers at small slip a huge torque which can provide the

Figure 6: “fixed shaft” application

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CAMS 2010 Rostock-Warnemünde, Germany, Sept 15-17, 2010

The model for the boat itself is based on the standard car model and simplifies, due to the absence of variable transmissions, road inclination and tire friction, to [Wilflinger 2007]:

engine from accelerating. With newer geometries this effect can be reduced where different pitch angles along the diameter are used. Near the top speed most of the thrust is produced at the very outer surface of the propeller. We model our propeller with the help of a so called “open water” diagram. A propeller is mounted on an “open water” vehicle, driven with a constant rotation speed n at a driving speed v. Thereby the thrust THR and torque Q are measured. The basic quantity in the open water diagram is the advanced number J [Krüger 2005].

J=

v nD

mv = THR(1 − t ) − ( ρ LcwL (v) AL (v) + ρ F cwF (v) AF (v))

v2 2

(11)

with cwL(v) the resistance parameter in the air, and cwf(v) in the fluid. Both parameters depend on the speed since the effect from the displacement drive into the sliding drive is considered via look up tables. AL(v) is the speed dependent front surface projection in the air and AF(v) the speed dependent front surface projection in the fluid, t the thrust deduction number.

(6)

where D is the diameter and n the revolution speed of the propeller. The advanced number can be interpreted as the ratio between the water speed and the speed of the blade tips. The pitch of the swirls of the propeller (see Figure 9) can be approximated by arctan (J /π).

3. Control Algorithm The amount of electric energy on board is limited. A second limit is the thermal behaviour of the electric motor. To get the maximum advantage of the hybrid system, the control strategy of the electric motor has to guarantee the optimal use of the available battery capacity in the thermal limits of the electric unit. In order to evaluate a control algorithm we need a cost function to quantify the performance of it. Therefore we have chosen the following cost function which penalizes the deviation from the actual drive train acceleration torque from an optimal one.

Figure 9: Propeller swirls With the density of the fluid ρF and the thrust coefficient kT [Krüger 2005]:

kT ( J ) =

THR ρF n2 D 4

GBoost = (

(7)

(8)

With the torque coefficient kQ [Krüger 2005]:

kQ ( J ) =

Q ρ F n2 D5

(9)

The torque of the propeller can be modelled as:

Q = kQ ( J ) ρ F D(nD 2 ) 2

(12)

The optimal ratio between the engine torque TE and the propeller torque TP vopt, is chosen to be 2, which is a standard value. The cost function takes the following form when neglecting negative values and taking into account a saturation (Figure 10 is saturated at the value 20).

The thrust of the propeller can finally be modelled as:

THR = kT ( J ) ρ F ( nD 2 ) 2

TE − vopt ) TE − TP

(10)

2.4 Boat model

Figure 10: Cost function 43

CAMS 2010 Rostock-Warnemünde, Germany, Sept 15-17, 2010

values of GBoost and cE according to the engine revolution have been stored in the boat as fixed values to avoid online calculation.

The cost function is now directly used to control the electric motor. The higher the cost function gets the more electric torque is necessary to support the engine and keep the cost function low. In Figure 10 the cost function is saturated with a value of 20, but we allow a sliding saturation depending on the charge condition of the battery and the thermal condition. In order to determine the actual value of the cost function, both the actual engine torque and the propeller torque are needed. The engine torque is calculated as Tdyn shown in Figure 4 while the propeller torque must be estimated via a Kalman filter. Engine control units often provide a torque signal for TE which can be used as well. The model for the estimator takes the following form

⎡ d ⎢− θ i 2 ⎡ω E ⎤ ⎢ E ⎢ω ⎥ ⎢ d ⎢ P ⎥ = ⎢ θ i2 ⎢ ϕ ⎥ ⎢ P ⎢ ⎥ ⎢ 1 ⎣ TP ⎦ ⎢ ⎢ i ⎢⎣ 0

d θ Ei 2

c θ Ei 2

d

c

θP

θP

−1

0

0

0



⎤ 0 ⎥ ⎡1⎤ ⎥ ⎡ωE ⎤ ⎢ ⎥ 1 ⎥ ⎢ ⎥ θE − ⎥ ⎢ωP ⎥ ⎢ ⎥ (13) + ⎢ 0 ⎥T θP ⎥ ⎢ϕ ⎥ ⎢ ⎥ E 0 ⎥⎢ ⎥ 0 ⎥ ⎣ TP ⎦ ⎢ ⎥ ⎢⎣ 0 ⎥⎦ ⎥ 0 ⎥⎦

Figure 11: Calculation of the cost function

where the unknown propeller torque TP is modelled as constant parameter and therefore a higher uncertainty in the tuning of the estimator has to be taken into account in the forth state. i denotes the possible transmission of the Z-drive. The engine speed ωE is used as update since it is the only available measurement on the boat. 4. Control law and stability The cost function shown in Figure 10 can be direct used for controlling the electric torque Telectric.

Telectric = GBoost (TE , TP )ce ( Emax )TE max

(14) Figure 12: Offline simulation of the control law

TEmax is the maximum available torque of the electric motor. The factor cE takes in account the maximum amount of energy Emax which can be delivered by the motor. The maximum amount of energy is limited by the capacity of the batteries or (more often) by the thermal limit of the electric motor. Of course Telectric computed by TEmax multiplied by GBoost.ce is limited with 100% TEmax. When computing the GBoost online, the start value of the factor cE should be chosen very conservative but can be increased with a learning control during driving until the motor reaches a certain limit of temperature after the acceleration phase. Figure 11 shows the computed values for GBoost in the test boat (Figure 3). Because of the trim regulation and the aggressive acceleration of the boat the online values of the cost function have been very noisy. To get good values for the torque control the signal has been filtered offline. With the original rpm signal, the engine and torque estimation of the previous chapters the energy amount of the motor has been simulated and the factor cE has been decreased until a certain limit (see Figure 12 where the red line shows the final values). The

Adding Telectric (14) to the static torque Tstatic in formula (1) while replacing TEmax with:

TE max = f PTdyn were fP is the power factor between the electric motor and the combustion engine the closed loop occurs as:

Tdyn = − ρ (Tdyn , ω )Tdyn (1 + f pGBoost ce ) +

ρ (Tdyn , ω )Tstat with

(15)

f pGBoost ce > −1 and ρ > 0 (combustion engine is

stable) as a constraint to have a negative eigenvalue and to be stable. GBoost (Figure 10) and cE are positive via definition while a positive fP is guaranteed through positive torque values of both power supplies. 44

CAMS 2010 Rostock-Warnemünde, Germany, Sept 15-17, 2010

propeller and a boat body model. Simulation results claim that there is a big advantage in using small electric units to assist during the acceleration phase, and to take into account the constraints of the electric unit – the battery capacity and the thermal constraints.

5. Boost – Mode in simulation

REFERENCES Jung M. (2003), Mean Value Modelling and Robust Control of the Airpath of a Turbocharged Diesel Engine, Department of Engineering: University of Cambridge Krüger S. (2005), Schiffspropeller, Hamburg Ljung L. (1999), System Identification: Theory for the User – second edition, Prentice Hall Ortner P. and Re L. (2007), Predictive Control of a Diesel Engine Air Path, presented on IEEE Transactions on Automatic Control Sciarretta A. and Gazzella L. (2007), Control of Hybrid Electric Vehicles, IEEE Control Systems Magazine Skinner B.A., Palmer P. R., and Parks G.T. (2007), Multiobjective design optimisation of submarine electric drive systems, presented at IEEE-Electric-ShipTechnologies-Symposium Wilflinger J. (2007), Momentenregelung am Steyr M-1 Hybridmotor, presented as diploma thesis in Linz

Figure 13: Acceleration for different control strategies We tested the control strategy in simulation to verify its suitability for acceleration support. Figure 13 shows the resulting boat acceleration for different control strategies. We see a clear advantage of control algorithm based on the cost function compared to full boost with shutting off strategy which would be the first idea to use in a real boat.

Figure 14: Cost function of different control strategies Figure 14 shows the cost function for the different strategies, showing that the cost function based controller best minimizes the cost function, except the full boost, but this scenario does not take into account the constraints and is not feasible in reality. 6. CONCLUSIONS We have developed a modular simulation model of a hybrid drive train for a sport boat, consisting of a data based engine model, a parameterized drive train model, a diagram based 45