Nonlinear dynamics

Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., Internal Combustion Engine) is one of the most important challenging works. This paper focuses on the design of a robust backstepping adaptive feedback linearization controller (FLC) for internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, feedback linearization controller is selected. Pure feedback linearization controller can be used to control of partly unknown nonlinear dynamic parameters of IC engine. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure feedback linearization controller. The results demonstrate that the error-based fuzzy feedback linearization controller is a model-free controllers which works well in certain and partly uncertain system. Pure feedback linearization controller and error-based feedback linearization like controller with have difficulty in handling unstructured model uncertainties. To solve this problem applied backstepping-based tuning method to error-based fuzzy feedback linearization controller for adjusting the feedback linearization controller gain ( ). This controller has acceptable performance in presence of uncertainty (e.g., overshoot=1%, rise time=0.48 second, steady state error = 1.3e-9 and RMS error=1.8e-11).