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Applied Sciences OPEN ACCESS

Mathematical Model and Adaptive Mechatronic Control Algorithm for A Passenger Car Engine Cooling System

A.I. Yangibaev
Islam Karimov Tashkent State Technical University, Tashkent, Uzbekistan
DOI Crossref DOI 10.37547/tajas/Volume08Issue05-46
tajas 2026
VOL. 8 / NO. 5 MAY
FULL TEXT PP. 326-338
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VOLUME 8
ISSUE 5
YEAR 2026
PAGES 326-338
RESEARCH OVERVIEW

Abstract

A mathematical model of the thermal state of a passenger-car internal combustion engine cooling system is constructed and investigated in the form of a system of nonlinear ordinary differential equations with a discontinuous (relay-type) and piecewise-linear right-hand side reflecting the operation of the thermostat and the electric fan. Based on linearization of the model in the characteristic operating modes of the thermostat and the fan, a local stability analysis is carried out and estimates of the time constants of the transient processes are obtained. An adaptive mechatronic control algorithm is proposed that forms a stepwise voltage for the main and auxiliary fans depending on the engine temperature and the ambient air temperature. It is shown that the standard explicit fourth-order Runge-Kutta method with a fixed step (used, in particular, by the ode4 solver in MATLAB/Simulink) accumulates a significant phase error during long-time integration of the relay system: small local errors arising near the switching instants lead to a systematic drift of the predicted relay-triggering instants amounting to tens of seconds after several dozen oscillation cycles. To eliminate this effect, an event-driven modification of the Runge-Kutta method is proposed and implemented, which accurately localizes the instant of crossing the relay threshold within the integration step by means of a nested bisection procedure. A computational experiment shows that, for the same nominal step size, the proposed scheme reduces the maximum solution error by one to two orders of magnitude and reduces the error in determining the switching instants by more than a factor of 60 compared with the classical scheme without event localization. The results of simulation in the MATLAB/Simulink environment confirm that the proposed adaptive mechatronic control algorithm provides smoother stabilization of the engine operating temperature and a reduction in the amplitude of temperature oscillations compared with conventional two-position control.

RESEARCH TOPICS

Keywords

ICE cooling system mechatronic control nonlinear dynamical system with a discontinuous right-hand side

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