Original Article Proc IMechE Part D: J Automobile Engineering 1–13 Ó IMechE 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0954407018820399 journals.sagepub.com/home/pid Cyclic torque imbalance detection in gasoline engines using a uniform second-order sliding mode observer Raheel Anjum 1 , Aamer Iqbal Bhatti 1 , Ahmed Yar 2 and Qadeer Ahmed 3 Abstract Engine torque imbalance is a wide-ranging problem which is caused due to variance of the combustion mixture in the engine cylinder. In this research work, cyclic torque imbalance detection is carried out by formulating a uniform second- order sliding mode observer using the First Principle–based Engine Model. Oscillations in the crankshaft angular speed were modeled in the novel First Principle–based Engine Model, which were suppressed in the Mean Value Engine Models. Cyclic torque imbalance is simulated at multiple instances by varying the injected fuel mass. Estimation of the net piston force is carried out for cyclic torque imbalance detection using rotational dynamics of the engine model. This force is treated as unknown input to the torque production subsystem of the model. Cyclic torque imbalance detection is validated using the GT-Power engine model. Variations in the cyclic torque were detected proximate to actual values which demonstrated validity of the proposed technique. Keywords Gasoline engines, cyclic torque imbalance, second-order sliding mode observer, net piston force Date received: 22 April 2018; accepted: 26 November 2018 Introduction The torque balancing approach comprises of detecting the torque imbalance in an engine and subsequently tun- ing it to generate equal torque contribution by the engine cylinder. Torque imbalance is one of the important fea- tures that describes performance of the internal combus- tion (IC) engines. It is further classified as cyclic torque imbalance and cylinder-to-cylinder torque imbalance. Cyclic torque imbalance in a cylinder occurs due to differ- ence between work output of the consecutive combustion cycles, producing inconsistent varying profile of the out- put torque. It is also termed as cyclic torque variations. Combustion in the IC engines has variations due to different factors. The term cyclic torque imbalance cov- ers various types of variations in the engine cylinder. It includes variations of the gaseous mixture’s motion in the engine cylinder during combustion; variance in the air, fuel mass; variation in the residual or recirculated exhaust gases in the engine cylinder; and inconsistent spark duration and energy. 1 Schematic diagram of the engine cylinder is shown in Figure 1. Cyclic torque imbalance acts as a limiting factor to enhance engine performance as these variations affect fuel economy and exhaust emissions, 2 degrade vehicle drivability by causing fluctuations in engine output tor- que, and vibrations in the driveline. 3 Variations in the cyclic torque also effects wear and degradation of the engine parts due to excessive periodic loading of engine components. Thus, cyclic torque imbalance lead to loss of thermal efficiency, reduced power contribution by the engine cylinder, increase in engine harshness, 4 and rise in indicated torque fluctuations at a given operating point. Objectives of cyclic torque balancing are diverse. A common target is to minimize the torsional vibrations arising from unbalanced torque contributions from the 1 Department of Electrical Engineering, Capital University of Science and Technology (CUST), Islamabad, Pakistan 2 Controls and Signal Processing Research Group (CASPR), Capital University of Science and Technology (CUST), Islamabad, Pakistan 3 Center for Automotive Research, Ohio State University, Columbus, OH, USA Corresponding author: Raheel Anjum, Department of Electrical Engineering, Capital University of Science and Technology (CUST), Kahuta Road, Islamabad, 44000, Pakistan. Email: ranjum342@gmail.com