Computation of the instantaneous frictional losses in internal combustion engines using estimated variables

The (P -- o) method is a model-based approach developed for determining the instantaneous friction torque in internal combustion engines. This scheme requires measurements of the cylinder gas pressure, the engine load torque, the crankshaft angular displacement and its time derivatives. The effects of the higher order dynamics of the crank-slider mechanism on the measured angular motion of the crankshaft have caused the (P -- o ) method to yield erroneous results, especially, at high engine speeds. As a first step in alleviating this problem, estimated rather than measured angular displacement of the crankshaft and its time derivatives have been used in the implementation of the (P -- o) method. This was done by developing a nonlinear sliding mode observer to accurately estimate the rigid and flexible motions of the crank-slider mechanism. The simulation results demonstrate that the reliance on estimated rather than measured state variables can significantly improve the accuracy of the ( P -- o) method at low engine speeds. However, this method fails to yield acceptable results at high engine speeds. To tackle this problem, the formulation of the (P -- o) method has been modified to account for the structural deformations of the crankshaft. The implementation of the modified (P -- o) method based on estimated state variables has lead to a superior performance over the original version of the (P -- o) method in yielding reasonable predictions of the instantaneous engine friction torque at high engine speeds. However, the accuracy of both versions of the ( P -- o) method has suffered from the approximations used in the elimination of the superfluous coordinates. To avoid this problem, the differential-algebraic form of the equations of motion of the crank-slider mechanism has to be retained. This necessitates the development of new robust observers that are suitable for handling nonlinear constrained systems. Three new robust observers have been designed herein. Their capabilities in accurately estimating the state variables of constrained systems have been demonstrated in the presence of both structured and unstructured uncertainties. The successful implementation of the new observers has lead to the development of an inverse dynamics scheme for the computation of the instantaneous frictional losses of engine components. Its formulation is based on the differential-algebraic form of the equations of motion. The implementation of this scheme in conjunction with the proposed observers has been proven to be a viable approach for determining the instantaneous frictional losses of engine components over a wide range of engine speed.