active damping of engine speed oscillations based on learning control

7/26/2019 Active Damping of Engine Speed Oscillations Based on Learning Control

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Active Damping of Engine Speed Oscillations based on Learning Control

A.T. Zaremba, I.V. Burkov , R.M. StuntzAutomated Analysis Corporation, 2805 South Industrial, Suite 100

Ann Arbor, MI 48104-6767, U.S.A., email: [email protected]

St.Petersburg Technical University, 9-3-67 Hlopina str.,

St.Petersburg 194021, Russia, email: [email protected]

Ford Motor Company, P.O.Box 2053, MD 1170-SRL

Dearborn, MI 48121-2053, U.S.A., email: [email protected]

Abstract

In this paper, we present a learning control scheme foractive damping of engine crankshaft oscillationsusing a sup-plemental torque source. The scheme comprises a linearfeedback controller and a learning feedforward term whichpredicts the engine crankshaft torque. The proposed schemeis computationally efficient and it does not use an accelera-tion signal in the learning procedure.

1. IntroductionThe using of the supplemental torque source (STS) for

control improvement of the engine idle speed and reducingof crankshaft speed pulsations have been investigated ac-

tively in recent years [1][5].In [1] the auxiliary control loop providing the external

supplemental torque via an automobile reversible alternatoris used to prevent engine stalling and improve its perfor-mance during idling. The idea of an active flywheel is em-ployed in [3] based on the reversible alternator for reducingof engine speed oscillations and improving engine idle. Arepetitive learning control is used in [4] to reduce engine vi-brations at idle basedon the estimations of the angular veloc-ity and angular acceleration. The PI control of the STS is an-alyzed in [5] for active idle speed regulation and damping ofcrankshaft speed oscillations. In paper [6] an original learn-ing scheme based on analysis of the steady-state oscillations

is proposed for iterative identification of state-dependentdis-turbance torque for high precision electric motors.

In this paper, we utilize a learning control strategy foractive damping of engine crankshaft oscillations using theSTS. The periodicity of engine processes with respect to thecrank angle results in a periodic engine output torque andcrankshaft speedoscillations [7]. This naturallymotivates usto use the learning control strategy when control is adjustedwith each crankshaft rotation utilizing information obtainedfrom the previousrotation. We consider an asynchronous in-duction machine (IM) placed on the engine crankshaft as the

source of the control torque. This machine combines alter-nation function with active flywheel operation which resultsin better drivelinenoise, vibration and harshness (NVH), im-

proved idle and better fuel economy.

There have been a lot of research eorts in developinlearningcontrol of robotic manipulators[8][12]. Fora mordetailed survey of the literature on this topic the reader ireferred to [13]. The effects of state disturbances, outpnoise, and errors in initial conditions on a class of learnincontrol algorithmsare investigated in [14].

The learning control design is based on the periodicity of the external disturbance torque acting on the systeThe learningfeedforward torque is estimated using estimatelearning term from the previous cycle and the speed errterm from the current iteration. In discrete time implementationthe second termof the learningprocedure hasderivativelike action. The simulation results demonstrate the effective

ness of the proposed learning controland its robustness witrespect to speed nonzero initial conditions and variations othe system parametersand external disturbances.

The paper is organized as follows. In Section 2 wdiscuss the dynamic model and control problem statementMain results on the learning control synthesis are given iSection 3 with system simulation results being presented iSection 4.

Earlier relevant results obtained by authors on thadaptive and optimal control of dynamic systems are givein [15, 16].

2. System dynamic model and control probleformulation

We consider the dynamic model of the engine rotatincrankshaft under the action of the engine torque and texternal torque fromthe supplemental torque source (STSdevice

where are crankshaft position andspeed, respectively;is the lumped inertia of the flywheel and the alternator roto

and is the effective damping coefficient.The engine torque is the source of cranksha

speed pulsations and has complexnonlinear dynamics. Con

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sidering the engine processes at steady state the enginetorque can be characterized as a cyclic function in thecrankshaft angle domain. Utilizing the hypothesize that allengine processes are band-limited the cyclic functioncan be expressed in terms of a truncated Fourier series ex-pansion [7]

where is the number of harmonics, and is a numberof engine firing per revolution ( =2 for a four-stroke cycle

engine).The control torque is generated by the induction ma-

chine which has also complexnonlineardynamics. The prin-

ciples of IM control are well understood and the reader isreferred to [17] for details on direct and indirect field ori-entation control schemes based on rotor position measure-ments. In recent years, there are also a lot of research onadvanced control schemes for IM without rotational trans-

ducers [18, 19, 20] which have potential to achieve high dy-namic performance preservinglowcost, highendurance,andease of maintenance. At this stage we neglect detailed dy-namics of the electric drive and make an assumption that itcan provide the control torque with required amplitude andbandwidth.

We perform transformation of system equations (1) tothe crank angle domain

The model (3) is a natural choice for controller developmentas the engine torque is a function of the crank angle and thespeed signal is sampled at discrete crank angle intervals aswell.

For dynamic system (3) we consider the problem of ac-tive damping of crankshaft oscillations around desired idlespeed where ac components of torque pulsations are dom-inant.

Linearizing the system (3) around the idle speed , weobtain the followingequation

where is the crankshaft speed pulsation.At idle the engine controller regulates the engine torque

in such a way that the average (or dc) component ofthe engine torque compensates for the steady-state load anddamping, and (4) can be rewritten

where is time-varying (or ac) componentsof the engine torque. Henceforth we omit the tilde and con-sider as havingonly ac components.

The equation (5) defines crankshaft speed pulsationaround the idle speed at each crankshaft rotation under periodic disturbance with a zero average over the perioof rotation.

Thecontroller design problem is as follows: fordynamisystem (5) find a control law such that the crankshaspeed tracks the desired idle speed

where

and is the rotation number.The controller we design comprises a linear feedbac

controller and a learning feedforwardterm

Here

where is a positive feedback gain.The learning feedforward term predicts ac component

of the engine torque and it is computed at each cranksharotation according to the learning rule. It is selected to beperiodic function of the crankshaft angle

Substituting (7),(8) into (5) yields

where

and notation is used to definethe kinetic momentum of the system at the idle speed.

Let tobe a set ofallfunctionswhich are -periodi( ) and n times continuously diferentiable. For the functions we define the nor

and inner product, respectively, as

Next, we show that dynamic system (10) under periodic disturbance and control (7)-(9) has steady-state periodisolution .

Theorem 1 For any positive gainand each

a) the system (10) has a periodic solution ;b) any solution of (10) exponentially approache

trajectory as where is the rotation number.

The proof is given in Appendix A.
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5. ConclusionsWe present a learning control scheme for engine

crankshaft speed oscillations damping at idle which usesonly information about control from the previous cycle foradjustment of the learning feedforward term. The controllerdesign is based on the system linearized model and it com-prises the feedback controller and the learning term. Simu-lation experiments showed that crankshaft speed pulsationsapproached zero when the learning control was applied.

The learning term provides adequate estimationof theengine disturbance torque.

To avoid reproducing torque spikes at the beginningof each rotation the learning scheme was modified to pro-

vide smooth transition between rotations. Simulations inFigures 2 and 3 demonstrate that engine acceleration from

zero to idle speed does not eect learning torque estimationand dampingof pulsations.Learning control shows high robustness with respect

to system parameter variations, especially flywheel inertia,a parameter which is critical for design of passive flywheel

systems. Further work is under way to evaluate the eectsof actuator dynamics and crankshaft position sensor noise onlearning control performance. Test stand engine experimentsare also being conducted.

6. AcknowledgmentThe authors gratefully acknowledge the financial sup-

port and motivation provided by Ford Motor Company and

constructive discussions with our colleagues: Roy Davis,Rich Hampo, and others.

7. Appendix AConsider a family of solutions of the dierential equa-

tion (10)

Let to be a steady state solution of (A1)

where

and

From (A2) follows that is -periodic

Next, taking limit of (A1) as , where is a rotationumber, we can conclude that all solutions of (10) exponentially converges to which completes the proof.

8. Appendix BUsing (11) we can rewrite (13)as

From (B1) follows

Using (10) and applyingintegration by parts the second terin (B2) yields

Substituting (B3) into (B2) we get

From (B4) using (14) we can conclude that sequence imonotonically decreasing and

From (B5) it is clear that

which, in turn, leads to statement a) of Theorem 2.To prove second statement we represent periodic func

tions and in the form of Fourier series expansion

where are complexFourier coefficients.Substituting (B7) into (10) we get

and accounting for well-known relations from functionaanalysis


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then, from (B8),(B9) and (B6) follow

Second equality (B10) yields

where is a minimal integer which is greater than a band-width of the low pass filter .

This proves the statement b) of Theorem 2.

References[1] Kouadio, L.K., Bidan, P., Valentin, N., and Berry,P., S.I. engine idle control improvement by using automo-tive reversible alternator, IFAC Preprints for 13th TriennialWorld Congress, San Francisco, CA, pp. 93-98, 1996.

[2] Kolmanovsky, I.V., Gilbert, E.G., and Cook, J.A.,ReferenceGovernorsfor SupplementalTorque Source Con-trol in Turbocharged Diesel Engines, Proceedings of the

American Control Conference, pp. 652-656,1997.

[3] Gusev, S.V., Johnson, W., and Miller, J.,Active fly-wheel control based on the method of moment restrictions,Proceedingsof the American Control Conference, 1996.

[4] Kadomukai, Y., Yamakado, M., Nakamura, Y., Mu-

rakami, K., and Fukushima, M., Reducing Vibration inIdling Vehicles by Actively Controlling Electric MachineTorque, Trans. Jpn. Soc. Mech. Eng., vol. 59, No. 560, C(1993), pp. 1023-1030.

[5] Zaremba, A.T., and Burkov, I.V., PI control for en-

gine speed oscillations damping, Ford internal report, Dear-born, March 1997.

[6] S.-H. Han, Y.-H. Kim, and I.-J. Ha, Iterative Iden-tification of State-Dependent Disturbance Torque for High-Precision Velocity Control of Servo Motors,IEEE Trans. on

Automatic Control, vol. 43, No. 5, May 1998, pp. 724-728.

[7] Rizzoni, G., Estimate of Indicated Torque from

Crankshaft Speed Fluctuations: A Model for the Dynamicsof the IC Engine, IEEE Transactions on Vehicular Technol-ogy,vol. 38, No. 3, pp.168-179, 1989.

[8] Arimoto,S., Kawamura, S., and Miyazaki, F., Better-ing operation of robots by learning, J. Robot. Syst., vol. 1,No. 2, pp. 440-447, 1984.

[9] Craig, J.J., Adaptive control of manipulators throughrepeated trials, in Proc. Amer. Contr. Conf., San Diego, CA,

June 1984, pp. 1566-1573.

[10] Togai, M., and Yamato, O., Analysis and Design ofan optimal learning control scheme for industrial robots:

A discrete system approach, Proc. of 24th IEEE Confer-ence on Decision and Control, Ft. Lauderdale, FL, 1985, pp.1399-1404.

[11] Pervozvanskii, A., and Avrachenkov, K., LearninControl Algorithms: Convergence and Robustness, Proc.

Austral. Control Conference, 1997.

[12] Kue, T., Nam, K., and Lee, J., An Iterative LearninControl of Robot Manipulators, IEEE Trans. on Roboticand Automation, vol. 7, No. 6, December 1991,pp. 835-841

[13] Moore, K., Dahleh, M., and Bhattacharyya, S., Itera

tive Learning Control: A Survey and New Results, Journof Robotic Systems, vol. 9, No. 5, July 1992, pp. 563-594.

[14] Heinzinger, G., Fenwick, D., Paden,B., andMiyazaki

F., Stability of Learning Control withDisturbances and Uncertain Initial Conditions, IEEE Trans. on Automatic Con

trol, vol. 37, No. 1, January 1992, pp. 110-114.

[15] Zaremba, A., Adaptive Control of Flexible Link Manipulators Using a Pseudolink Dynamic Model, Dynamicand Control, 6, 179-198 (1996).

[16] Zaremba, A., Hampo, R., and Hrovat, D., OptimaActive Suspension design using constrained optimization,Journal of Sound and Vibration(1997), 207(3), 351-364.

[17] Leonhard, W., Control of Electric Drives, SpringeVerlag, 1984.

[18] Khalil, H.K., Strangas, E.G., and Miller, J.M., torque controller for induction motors without rotor position sensor, Intern. Conf. on Electric Machines (ICEM96)

Vigo, Spain, 1996.

[19] Yoo, H.S., and Ha, I.J., A polar coordinate-orientemethod of identifying rotor flux and speed of induction motors without rotational transducers, IEEE Transaction oControl System Technology,vol. 4, No. 3, May 1996.

[20] Jansen, P.L., Corley, M.J., and Lorenz, R.D., Fluxposition, and velocityestimation in AC machines at zero anlow speed via tracking of high frequency saliencies, in 5t

European Power Electronics (EPE) Conf. Rec.,vol. 3, p154-160, Sevilla, Spain, Sept. 19-21, 1995.

C P

L

uai

Te

d

d

+

+

+

+

- -

Fig. 1. Learning control scheme for engine crankshaft speedamping.


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 28

6

4

2

0

2

4

Feedback control alpha=10

Speedoscillations

rad/sec

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24

3

2

1

0

1

Speedoscillationsrad/sec

Time sec

Learning control

Fig. 2. Speed oscillations for feedback and learning control.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220

10

0

10

20

30

Engine Torque Nm

Ten

gineNm

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 230

20

10

0

10

20

30

Tle

arningNm

Time sec

Learning Torque Nm

Fig. 3. Engine torque and learning feedforwardtorque.


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active damping of engine speed oscillations based on learning control

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