Authors: TUĞÇE YAREN, SELÇUK KİZİR
Abstract: This paper is concerned with the modeling framework based on power and control for a mechanical system that has nonlinear, unstable, and under-actuated characteristic features, based on an analogy, which is developed by using the Brayton and Moser's (BM) equations between mechanical and electrical systems. The analogy is based on a mixed-potential function generalized for BM. The mixed-potential function for a cart - pole double inverted pendulum (CPDIP) system is used as a new building block for modeling, analysis, and controller design. The analogy allows for the exact transfer of results from electrical circuit synthesis and analysis to the mechanical domain. This paper focuses mainly on the development of the electrical equivalent circuit of CPDIP inspired by the power-based modeling framework. In this brief, a real time CPDIP experimental setup was modeled by using this framework and a linear quadratic regulator (LQR) controller was designed for the stabilization of the system. Experimental results validated that this framework can be used as a new and advantageous modeling method and is a convenient and practical alternative to the Lagrangian framework.
Keywords: Analogy, Brayton-Moser, double inverted pendulum, linear quadratic regulator, optimal control, real time control
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