COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2000; 16:505–517 Numerical inversion of the dynamic model of a single-cylinder diesel engine Yahya H. Zweiri, James F. Whidborne * and Lakmal D. Seneviratne Department of Mechanical Engineering; King’s College London; Strand; London WC2R 2LS; U.K. SUMMARY This paper presents a numerical technique to invert the dynamic model of a single-cylinder diesel engine. The method is employed to estimate the parameters of an engine from the data of crankshaft angular velocity, indicated torque, dynamometer angular velocity and applied load. The numerical inversion is performed during both the transient and steady-state responses of the dynamic model. The method is developed with the aim of giving the designer information about the engine parameters which achieve a required performance characteristic (crankshaft velocity, indicated torque and applied load) and for tuning the parameters which play an important role in dynamic modelling. The model is implemented in MATLAB= SIMULINK, and simulation results are presented. The simulation predictions of the engine and dynamometer parameters are compared with physical values, and they are in excellent agreement. Further, a comparison between the measured crankshaft velocity with simulated engine velocity calculated from the inverted parameters is presented, showing very good agreement. Copyright ? 2000 John Wiley & Sons, Ltd. KEY WORDS: diesel engine; dynamic modelling; numerical inversion; Newton–Raphson method; transient response; parameter tuning 1. INTRODUCTION Inversion of an engine dynamic model has been established as an eective tool for studying engine performance and contributing to design evaluation and new developments. Previous eorts in the area of inverting a dynamic engine model can be found in References [1–3]. The main aim of these works is to use the engine dynamic model to describe the relationship between the combustion pressure and engine angular velocity. This allows engine torque and cylinder pressure to be estimated from a measurement of crankshaft angular velocity which is more easily measured than cylinder pressure. The work of Zhang and Rizzoni [2] concentrates on the discrete frequencies corresponding to the periodic rotation of the crankshaft; so it is only necessary to compute the engine dynamic model at the discrete frequencies, thus decreasing the computational time. * Correspondence to: J. F. Whidborne, Department of Mechanical Engineering, King’s College London, Strand, London WC2R 2LS, U.K. Contract=grant sponsor: Mu’tah University, Hashemite Kingdom of Jordan Received 23 April 1999 Copyright ? 2000 John Wiley & Sons, Ltd. Accepted 12 January 2000