An Optimal Control Approach to Preventing Marine Diesel Engine Overloading Aboard Karel Doorman Class Frigates

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Copyright © IF AC Control Applications in Marine Systems, Glasgow, Scotland, UK, 2001

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AN OPTIMAL CONTROL APPROACH TO PREVENTING MARINE DIESEL ENGINE OVERLOADING ABOARD KAREL DOORMAN CLASS FRIGATES P.J. van Spronsen * R.L. Tousain **

* Royal Netherlands Navy, PO box 10000, 1780 CA Den Helder,

the Netherlands ** Mechanical Engineering Systems and Control Group, Delft

University of Technology, Mekelweg 2, 2628 CD Delft, the Netherlands

Abstract: The aim of this research is to analyse and find possible solutions for the occurence of diesel engine overloading aboard the Karel Doorman class frigates in high sea states and during acceleration. In this paper an Hoc control approach is used to include the knowledge on the model, the disturbances and the performance criteria (disturbance suppression and preventing overloading) in the controller design in a systematic way. If only the fuel rack position is used for control, then the effect of wave disturbances on the shaft revolutions cannot be reduced significantly without causing overloading of the engine. The incorporation of a second control degree of freedom, the propeller pitch angle, makes it possible to meet all the control objectives. A constrained, time optimal control approach is taken to solve the servo problem, i.e. acceleration and deceleration of the vessel. The main benefit of this approach is that constraints on the operation of the propulsion plant, such as the overloading criterion, can be taken into account explicitly. The optimal controls derived from the constrained optimization are combined with the tracking controller in a reference model tracking configuration. Copyright ©2001 IFAC Keywords: marine propulsion diesel engine, dynamic overloading, MIMO pitch control, H 00 optimal control, time optimal control.

1. INTRODUCTION

initial research showed that the regulatory control currently in use is not capable of dealing properly with the external disturbances that act on the diesel engine (see Figure 2). The governor causes overloading of the engine during the operation in high sea states and during acceleration and manoeuvring. The problem of diesel engine overloading in marine engineering, and especially the role of speed governors therein, has received a lot of attention in literature. Faber (1993) summarizes and discusses the prevailing thoughts on the subject. He quotes many expert's opinions, amongst which a few 'historical' ones, to support his concluding statement that there are more

The Karel Doorman Class frigates were first introduced in the Royal Netherlands Navy (RNIN) in 1994. These vessels use the so-called COmbined Diesel Or Gasturbine (CODOG) propulsion concept. The gas turbine delivers power for high speed manoeuvring, while the fuel-efficient diesel engine is used at cruising speeds. One prime mover drives a shaft at a time. Over the past years, maintenance costs of the diesel engines have exceeded the predicted costs. This has lead to an investigation into the operation of these engines aboard the Karel Doorman Class. An outcome of

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drawbacks than advantages to the use of governors for speed control. Kyrtatos (1997) supports this notion though he stresses the importance of improved control of the machinery during transient phenomena, such as acceleration and manoeuvring. Despite the convincing arguments against speed-governing given by the above-mentioned authors, many ships are currently equipped with such controllers and a lot of research is conducted to improved control algorithms. Lam et al. (1993) propose an adaptive revolution control algorithm for the case of a fixed-pitch propeller. The authors consider the operation of the engine in heavy sea state as well as during acceleration and deceleration however the design approach is not ver~' systematic and diesel overloading is only partly taken into account. Another adaptive control algorithm is proposed by Itoh et al. (1990). An optimal controller is proposed by Guillemette and Bussieres (1997). Their simulations shov.· improved speed control at the expense of increased fuel rack fluctuations for sea state 4. Whether or not overloading is expected to occur for higher sea states is not mentioned. In this paper, we describe an optimal-controlbased analysis and design of the control system for the diesel propulsion system in the Karel Doorman Class frigates. Our research first aims to analyze in a systematic manner the presumed inherent trade-off between speed variations and fuel rack fluctuations for the traditional single input single output (SISO) speed governor. To this end we explore the maximum achievable control performance of such a SISO control system by means of Hoo design. Next, in search for alternative control solutions to overcome the limitations of the SISO controller we will consider the use of a second degree of freedom, the propeller pitch, in the control system design. Our research focuses foremost on those situations in which diesel overloading occurs in practice: acceleration and heavy sea state (state 6). The control approach that we use will take the diesel overloading explicitly into account in both situations.

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Fig. 2. The overloading criterion plotted in the phase plane. able propeller pitch. This was originally installed to achieve ship velocities congruent with engine speeds lower than idling speed. At present, pitch variations are used in a heuristic manner to reduce overloading (similar to the situation described in (Guillemette and Bussieres 1997)). With the hydraulic system currently installed, the pitch can vary at a rate up to 2.4 [degjs]. The associated torque variations may hence be quick enough to compensate the torque variations caused by external disturbances. Overloading criterion An overloading criterion defines, together with minimum and maximum shaft revolutions, the preferred operating region of the diesel engine. The criterion is defined in terms of the engine revolutions and the fuel rack position and it connects operating points for which a Reduced Time Between Overhaul (RTBO) can be expected. For practical reasons , the engine revolutions are translated to propeller shaft revolutions. The overloading criterion can be visualized in a phase plane with the fuel rack position on the vertical axis, and the shaft revolutions on the horizontal axis, see Figure 2. The grey area defines the region of operating points for which RTBO holds. The steady state operating points of the propulsion system are projected onto the same phase plane for different pitch angles. The overloading margin is smallest at 80 [rpm] and 31 degrees. The remainder of this paper will focus on this critical operating point. The operating margins resulting from applying the static overloading criterion to this operating point are used in all dynamic control studies presented in this paper. Results

2. THE PROPVLSION PLANT Plant layout The mechanical components of the propulsion system that are relevant to this investigation are the diesel engine, the gearbox, the propeller shaft and the propeller. Figure 1 shows a schematic diagram of the propulsion system. The fuel rack position controls the amount of fuel injected into the engine per cycle. This power drives a gearbox reduction, which in turn drives the propeller shaft. At a constant propeller pitch, the shaft revolutions are directly proportional to ship velocity. The Karel Doorman frigates are equipped with a hydraulically activated, vari-

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desired change in speed

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Fig. 4. Two-degrees of freedom design. the fluctuations in the shaft revolutions lead to a violation of the overloading criterion in the open loop (= uncontrolled) case. Therefore, our control problem is defined as to (i) minimize the effect of the sea state on the engine speed (hereafter: the regulatory control problem) and (ii) enable fast acceleration and deceleration of the ship (hereafter: the servo control problem), while (iii) preventing the engine from entering the overloading region. All operating requirements are to be met for sea states up to state 6.

Frequency (rad/sec)

Fig. 3. Frequency response of the open loop linear model. from a more thorough analysis into the physical background of overloading, see e.g. (Grimmelius and Stapersma 2000) may be included in a later stage.

External disturbances The propulsion plant is subject to external disturbances. The most significant disturbance is the sea state. The waves act on the propeller, and induce torque variations on the propeller. These variations propagate through the propulsion plant to the diesel engine. Variations in engine revolutions are the result. The governor that is currently installed on the engine attempts to counteract these disturbances. Its control effort causes excessive variations in the fuel rack position, which causes violations of the RTBO criterion. Design specifications require normal operating up to sea state 6. Real-life measurements confirm the overloading phenomenon. Figure 2 shows measurements for a sea state 6. Wave spectra are readily available in the literature, hence the dynamics of the external effects are more or less known.

3. CONTROLLER CONFIGURATION The control problem formulated in the previous section contains many more or less conflicting objectives. The trade-off between preventing overloading and reducing the speed variations is well known and intuitive. Another trade-off is present in the extent to which servo and regulatory performance requirements can be met. A two-degree-of-freedom (2-dof) controller design can be applied to avoid this trade-off to some extend. The classical 2-dof approach is to design a LTI pre-compensator which filters the reference before it enters the loop, see e.g. (Maciejowski 1989). However, in our servo problem constraints on system inputs and outputs, imposed by the RTBO criterion, play an essential role and we want to take these into account in the solution of the servo problem. In this paper the design of an input shaper is considered which computers, for a certain desired change of engine speed, a control input which optimizes the transient behavior according to some performance objective (in our case: minimal time) while satisfying all constraints. The 2-dof control structure that we propose is depicted in Figure 4; it can be referred to as a reference model tracking configuration. The design consists of finding a feedback controller K and an input shaper such that all control objectives are met.

Model of the propulsion plant A non-linear model of the propulsion plant which was available from previous studies was linearised at the most critical operating point of 80 [rpm] and 31 degrees pitch angle. The open loop frequency response of the linear model is shown in Figure 3. Neither fuel rack nor the external disturbance acts on the propeller pitch. A linear filter was used to approximate the nonlinear disturbance spectrum which was taken from (Pierson and Moskowitz 1964). The frequency response of the filter is displayed in Figure 7 as the open loop sensitivity.

Control Problem Although the benefits of engine speed control have often been questioned (see the introduction of this paper), the necessity to prevent the engine from racing in case of heavy sea is undisputed. Further, it is important to note that

3.1 Feedback controller design using Hoo optimization

The design of feedback controller K will be done using Hoo optimal control. The big advantages of

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HOG control is that it naturally allows to combine different , possibly conflicting, performance requirements and that it provides for a systematic way to include knowledge on disturbances. For details on HOG control we refer to (Zhou et al. 1996).

3.2 Time-optimal servo control A naval vessel may find itself in a situation were acceleration is of vital importance. A time optimal response is then desirable. Hence, the servo control can be seen to be a constrained, time-optimal control problem. Time optimal control problems often lead to bang-bang control solutions, however not in this case. First, the plant is not normal because the propeller pitch cannot be controlled through by the fuel rack position. Second, the trajectories of the shaft revolutions and the pitch variations are subject to bounds and the overloading criterion.

S1S0 design To explore the possibilities for using the fuel rack position to control the engine speed, we will first consider the SISO HOG design. In this SISO design we consider only the transfer function from the fuel rack position (input 2) to the shaft revolutions (output 2) . The performance channels that we introduce are indicated in Figure 6. By weighting the transfer from w to Z2 we can shape the closed loop sensitivity function. Weighting the transfer from w to Z4 enables to prevent excessive fluctuation of the control. Also, using this weighting we enforce the controller gain to go to zero for high frequencies. Performance channel Z5 is introduced to prevent overloading. The measure Z5 =:; Wx (sin(a)e2 + cos(a)u2) is chosen such that fluctuations perpendicular to a direction parallel to the RTBO criterion are penalized. This is illustrated graphically in Figure 5. The direction L1 is parallel to the RTBO criterion, hence oscillations of U (fuel rack pos.) and y (shaft revs.) in the direction L1 are save. The closed loop behaviour of the plant is shaped through a proper selection of the weight functions T-Fp2 , TVu2 , lrx and 11'8' details are omitted.

To take all constraints into account we formulate a discrete time optimal control problem. We consider the following discrete time representation with sampling interval T8 (the notation Xk =:; Xk.Ts is used) Xk+l

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MIMO design The SISO design is done in the first place to verify the presumed inadequacy of using the fuel rack position for speed control. A 1\111\10 design is done to test the potential benefits of using the pitch variation as a second control input in the engine speed control problem. For the MIMO design, the control configuration in Figure 6 is expanded to include the propeller pitch as a control variable. Also, two new performance channels Zl and Z3 are introduced. The weightings HOp 1 and Tl"u1 weight respectively the sensitivity of the pitch and the pitch set point with respect to the disturbance w.

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4. SIMULATION RESULTS SISO sensitivity reduction control

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on Z 5, i.e. the 'overloading' channel. The projection of the closed loop time responses onto the diesel operating chart were perfectly aligned with the RTBO line, hence overloading was prevented. However, the closed loop sensitivity was worse than the open loop sensitivity, see Figure 7, which confirmed our suspicion, and that of many authors before us , that using the fuel rack position for speed control is not a good idea.

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A simple analysis of the conflicting control requirements explains the simulation results. To align the closed loop responses with the RTBO line the controller must, at the dominant wave frequency w, satisfy K(jw) = - tan(a) which means positive feedback! A quick analysis into the gain and phase of the propulsion plant learns that this will always lead to a deterioration of the output sensitivity. This result has a clear physical interpretation: for safe operation the fuel rack position should be reduced to compensate for the increased load. Compare this with the traditional governor which will increase the fuel rack to compensate for the decreased speed of the engine! Weighting Wx was relaxed to attempt to find a compromise between overloading and speed reduction, however no satisfactory compromise could be achieved.

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Fig. 9. Projection of a MIMO controlled time response onto the phase plane. 99, 95 and 90 [%] confidence interval are plotted as well.

Time-optimal servo control To test the benefits and the applicability of the input shaper to the acceleration problem we solved problem (2) for a desired change in shaft revolutions of 5 [rpm] and a related change in the ship's velocity of 0.86 [kts]. The constraints that we included were the margin to the overloading criterion, a maximum overshoot of the fuel rack position of 50 [%] and a maximum rate change of the pitch of 0.6 [deg/s]. The time-optimal solution reaches the new steady-state operating point in 30.0 [sec]. The time response of the system to this optimal input is displayed in Figure 10. Only deviations from the steady state operating point are shown. The time response consists of three phases. During the first phase, which lasts for 5 [sec], the propeller pitch is reduced at its maximum rate. The opposing torque to the engine is thereby reduced while the shaft revolutions increase to maximum overshoot. Fuel rack is increased simultaneously. In the second phase, the ship accelerates to its final velocity, while the propeller pitch and fuel rack position are controlled such that neither the overshoot nor the overloading margin is violated. This phase

MIMO sensitivity control The MIMO control approach uses the variable pitch as an extra control degree of freedom. The weightings were chosen such that a maximum rate of change of the pitch of 1.8 [deg/s] was obeyed. The frequency response of the resulting closed loop sensitivity function in Figure 8 shows a significant output sensitivity reduction at the relevant frequency range. More important, engine overloading is prevented as well. Figure 9 shows the projection onto the phase plane of a simulated response of the MIMO controlled system to a wave disturbance.

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olutions cannot be satisfactorily controlled without causing diesel engine overloading. The inclusion of a second control degree of freedom, the variable propeller pitch angle, via a multi-input multi-output Hoo design gave very promising control performance. The effect of the sea state on the shaft revolutions was significantly reduced whereas overloading was prevented. Time optimal acceleration of the vessel was considered as well. A discrete time, constrained optimal control problem was formulated to compute the optimal open loop controls and the related reference signals. These control trajectories can, together with the Hoo feedback controller be combined in a 2-dof control scheme which provides a complete solution to the control of the propulsion plant. The usefulness of the proposed control solution was demonstrated in simulations.

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6. REFERENCES

o 5 10 15 20 25 Variations in shaft revolutions (rpm], nominal value;;; 80 [rpm).

Faber, E. (1993). Some thoughts on diesel marine engineering. SNAME Transactions 101, 537582. Grimmelius, H. and D. Stapersma (2000). Control optimisation and load prediction for marine diesel engines using a mean value simulation model. ENSUS 2000, Conference Proceedings pp. 212 - 229. Guillemette, J.R. and P. Bussieres (1997). Proposed optimal controller for the canadian patrol frigate. Ship Control Systems Symposium 1,219-236. Itoh, M., T. Okawa, H. Mizuno, N. Mizuno, M. Horigome and K. Ohtsu (1990). Dynamic control of the engine of ships. International Symposium on Marine Engineering (ISME) 2, 1-6. Kyrtatos, N.P. (1997). Propulsion control optimization using detailed simulation of engine/propeller interaction. Ship Control System Symposium 1, 507-530. Lam, W.C., T. Katagi and T. Hashimoto (1993). Design of an adaptive electronic governor for better control of marine diesel engine. Maritime technology 21st century 2, 1-12. Maciejowski, J. (1989). Multivariable feedback design. Addison-Wesley Publishers Ltd .. Wokingham, England. Pierson, W.J. and L. Moskowitz (1964). A proposed spectral form for fully developed wind seas based on the similarity theory of s. a. kitaigorodskii. Journal of Geophysical Research 69, 5181-5190. Zhou, K., J.C. Doyle and K. Glover (1996). Robust and optimal control. Prentice-Hall. New Jersey.

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Fig. 11. Simulation results projected on the phase plane for the time optimal acceleration of the vessel during sea state 6 (desired change in revolutions: 15 [rpm]). continues for 27.5 [sec]. In the third and final phase pitch and fuel rack position are adjusted such that the system continues to operate at the desired steady state operating conditions.

Acceleration during heavy sea state In the final simulations we consider the acceleration of the vessel in sea state 6. A step of 15 [rpm] in shaft revolutions is demanded during a simulated sea state 6. The simulation results are projected onto the phase plane in Figure 11. The stochastic nature of the disturbances is represented by the 99 [%] confidence intervals plotted at three vital operating points. The overloading criterion is not violated at any time.

5. CONCLUSIONS This paper describes an optimal control approach to the control of diesel engines aboard the Karel Doorman Class frigates. The disappointing results of a single-input (fuel rack position) single-output (shaft revolutions) Hoo controller confirm our suspicion and that of other authors that the shaft rev-

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