I. IntroductionThe internal co mbustion (IC) engine is designed to produce power fro m the energy that is contained in its fuel. More specifically, its fuel contains chemical energy and together with air, this mixtu re is burned to output mechanical power. There are various types of fuels which can be used in IC engines namely; petroleum, d iesel, bio-fuels, and hydrogen [1]. Modeling of an entire IC engine is a very impo rtant and complicated process because engines are nonlinear, multi inputs-multi outputs (MIMO) and time variant.Controller design is the main parts in this paper as well as the majo r objectives in the controller design are stability and robustness. One of the significant challenges in control algorith ms is design a linear controller fo r nonlinear systems. When system works with various parameters and hard nonlinearit ies this technique is very useful in order to be implemented easily but it has some limitations such as working near the system operating point [9]. So me of IC engines which work in industrial processes are controlled by linear controllers, but linear controller design for IC engines is extremely difficu lt [1][2][3][4][5][6]. Co mputed torque controller (CTC) is a powerfu l nonlinear controller which it widely used in control of IC engine. It is based on feedback linearization and computes the required arm torques using the nonlinear feedback control law. This controller works very well when all dynamic and physical parameters are known but when the IC engine has variation in dynamic parameters, in this situation the controller has no acceptable performance [7][8][9][10][11][12][13][14]. In practice, most of physical systems (e.g., IC engine) parameters are unknown o r t ime variant, therefore, online tuneable gain co mputed torque controller used to compensate dynamic equation of IC engine [1,6]. Sliding mode controller (SMC) is one of the influential nonlinear controllers in certain and uncertain systems which are used to solved stability and robustness [10]. The main reason for this popularity is the attractive properties which SMCs have, such as good control performance for nonlinear systems, applicability to MIMO systems and well-established design criteria for discrete-time systems. SMC may emp loy unnecessarily large control signals to overcome the parametric uncertainties and difficulty in the calculat ion of what is known as the equivalent control [11][12][13][14][15][16][17]. In various dynamic parameters systems that need to be training online adaptive control methodology is used. Adaptive control methodology can be classified into two main groups, namely, t raditional adaptive method and fuzzy adaptive method [18][19][20][21][22]. Fu zzy adaptive method is used in systems which want to train ing parameters by expert knowledge. Trad itional adaptive method is used in systems which some dynamic parameters are known. In this research in order to solve disturbance rejection and uncertainty dynamic parameter, adaptive method are applied to slid ing mode controller and c...
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