To improve the stability of nonminimum-phase characteristics for nonlinear mechanical systems with 2 DOF (Thai)

Abstract

This paper describes our preliminary research in analyzing a mechanical structure and improves stability of zero dynamics for a simple mechanical system with 2 degrees of freedom. Zero dynamics occur in mechanical systems that have fewer actuators than the number of degrees of freedom. In general, control of unstable zero dynamics or nonminimum-phase systems are complicated problems. In this paper, we introduce a new method for improving the stability of zero dynamics and control by using mechanical structures. That is the internal dynamics part is controlled by the action of counter force/moment proceeding along two basic stages. First, there is an energy shaping stage where we modify the potential energy of the system in such a way that the new potential energy function has a global and unique minimum in the desired equilibrium. Second, there is a damping injection stage where we now modify the dissipation function to ensure asymptotic stability. We demonstrated this method for the inverted pendulum on a cart. Consequently the nonminimumphase system became a minimum-phase system. In addition, we have proposed conditions to prove that in these systems with exclusively kinetic energy, the zero dynamics are unstable except for some rare situations.