UDC 621 MODELING AND ANALYSIS OF AN INVERTED PENDULUM © Krishna Murari, Graphic Era University, Dehradun, Uttarakhand, India Faraz Ahmed, Graphic Era University, Dehradun, Uttarakhand, India Pushpendra Kumar, Graphic Era University, Dehradun, Uttarakhand, India Abstract. <...> Mathematical modeling of the physical systems is important to describe their dynamic behavior. <...> Furthermore, mathematical model of a physical system enables to apply model-based control on the system. <...> In the present work, an inverted pendulum mounted on a cart is modeled using different mathematical modeling approaches and the dynamic behavior of the system is analyzed. <...> Equations of motion (EOM) for the inverted pendulum system are obtained using Newton-Euler formulationand Lagrange-Euler formulation. <...> Control strategies are developed for the system to control the angular motion of the pendulum. <...> The developed model is analyzed through simulation results. <...> Inverted pendulum is a nonlinear and unstable system, therefore it is very useful problem to study and apply di f ferent control strategies. <...> Dynamic model of the system can be derived based on physics laws [1–2]. <...> In inverted pendulum system, position of inverted pendulum (or bar) is controlled to keep it upright by applying various control strategies. <...> Many researchers proposed different control strategies for various configurations of inverted pendulum system including sliding mode control [1], fuzzy control [3], classical PID control [4], etc. [1–7]. <...> In the present work, an inverted pendulum (bar) mounted on a cart is analyzed for planar case. <...> Dynamic model of the system is derived based on Newton-Euler formulation and Lagrange-Euler formulation. <...> Model-based control strategies are developed for the system to control the motion of the bar. <...> The present paper is arranged in five sections; first section is about introduction of the inverted pendulum system; second section describes the mathematical modeling of the system; control schemes are described in third section; simulation and results are discussed in fourth section; finally conclusion and future work are given in fifth section. 2. <...> Dynamic model of the system is developed using two approaches namely, Newton-Euler formulation Fig. 1 <...>