Numerical simulations for stabilization of underactuation mechanical systems of degree one, using IDA-PBC method: the TORA system example
Abstract
The problem of the stabilization of not linear systems underactuation has attracted the attention of the community of control in the recent years. The so called IDA-PBC method (Interconnection and Damping Assignment Passivity Based Control), from the theoretical point of view, it has been achieved to describe the dynamic behavior of a wide class of the above mentioned systems, obtained a port controlled Hamiltonian form, the controller stabilizes globally and asymptotically the equilibrium point. The general objective of this study is to analyze the stabilization of mechanical systems underactuation degree one using IDA-PBC method. In this method, in order to achieve the control objective, the stabilization mechanism follows two basic stages: (1) energy holding stage, which consists on shaping the total energy function of the system in order to assign the desired equilibrium state, and (2) damping introduction stage, necessary to achieve asymptotic stability. The success of the application of this method resides in the possibility of solving the set of equations in partial derivatives, which solutions provide the assignable functions of energy to the system in closed loop. The TORA system (“translational oscillator with rotational actuator”) is a prototype of a underactuated mechanical system widely studied by the non linear control community. In this paper, a controller is designed taking into account the port controlled Hamiltonian approach based on the total energy of the system, considered as the sum of kinetic and potencial energies, the controller stabilizes globally and asymptotically the equilibrium point, showing an excellent preformance. The numerical simulations con#rm this appreciation.
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