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For now we will only look at the sum of the horizontal forces. Where b is the coefficient of friction on the between the car and the ground, and N is the reaction force on the cart. (The figure was take from Michigan University Control Tutorial page)įrom the Figure above we see that the sum of the horizontal forces acting on the cart give the following equation of motion: A simple inverted Pendulum attached to a wheeled cart is shown below:įigure 1: Illustration of a Simple inverted Pendulum loaded onto a cart In either case we will need to look at the dynamics of the system and resolve the forces acting on the Pendulum and cart, for an impulsive external force F. Two ways of representing the motion of the pendulum and cart in MATLAB are as transfer functions or in a state-space form. This is obviously far more math heavy than the Simulink approaches we will cover later on. We will model the inverted pendulum system directly using the MATLAB command window, by first deriving the necessary equations with which we can define the system and then inserting the equation/s into MATLAB, to allow the software to model the system for us. It is a particularly good exercise since the inverted pendulum problem is a practical practical problem which closely relates to a number of common place engineering problems. The modelling of an inverted Pendulum is a useful exercise to familiarise oneself with MATLAB and Simulink while applying your knowledge of dynamics. Four approaches will be outlined in the following posts, two in MATLAB and two in Simulink. There are a number of ways to model and control an inverted Pendulum using MATLAB and Simulink.