This paper considers the discrete model of the cart-pendulum system modeled by discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. We first sum up basic concepts on discrete mechanics and discuss the explicitness of the linear approximation of the discrete Euler-Lagrange Equations. Next, the discrete cart-pendulum system is derived and analyzed from the viewpoint of solvability of implicit nonlinear control systems. We then show a control algorithm to stabilize the discrete cart-pendulum based on the discrete-time optimal regulator theory. Finally, some simulations are shown to demonstrate the effectiveness of the proposed algorithm.

In this paper, we consider a stabilization problem for the cart-pendulum system based on discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. First, the continuous and discrete cart-pendulum systems are explained. We next propose a transformation method that converts a discrete-time input derived from the discrete-time optimal regulator theory into a continuous-time zero-order hold input, and carry out some simulations on stabilization of the cart-pendulum system by the transformation method. Then, we apply not only our proposed method but also existing methods to an experimental laboratory of the cart-pendulum system and perform some experiments in order to verify the availability of the proposed method.

This letter is devoted to derivation of a transformation law which converts a class of nonlinear affine control systems with n-states and 2-iputs into simpler systems with chained structure. First, we give a problem formulation that we consider throughout this letter. We next introduce a transformation law and gives its mathematical certification. Then, we apply the transformation method to an example and consider control design based on chained structure for the example in order to confirm the effectiveness of our approach.