Torque imbalance in multicylinder spark-ignition (SI) engines leads to vibration, accelerated wear, higher fuel consumption, and efficiency loss. Conventional diagnostic methods either rely on prohibitively expensive, noise-sensitive in-cylinder pressure sensors or employ cycle-averaged Mean-Value Engine Models that lack the resolution and accuracy required for cylinder-specific torque estimation. Gray-box and discrete models improve fidelity but demand extensive parameter identification and computational effort, limiting their practicality for control-oriented applications facing diverse field conditions and production line spread. This study presents a nonlinear uniform Super-Twisting White-Box Observer for high-resolution, sensor less estimation of in-cylinder forces as direct indicators of torque imbalance. The observer models individual cylinder forces as unknown inputs to the torque production subsystem and reconstructs both cycle-to-cycle and cylinder-to-cylinder variations with high accuracy. The structure ensures fast convergence and robustness against torque imbalance conditions introduced through controlled variation of injected fuel mass across cylinders, enabling accurate force estimation under both normal and fault-induced operation. Validation against a high-fidelity GT-Power model of a 1300 cm 3 four-cylinder spark-ignition engine representative of a production vehicle shows high estimation accuracy, with Root Mean Square Error below 3%. The framework offers a robust, high-resolution basis for real-time fault detection and torque imbalance diagnosis in advanced engine control systems.
Farhan et al. (2026) studied this question.