倒立振子に対する出力レギュレーション制御実験（中心多様体近似計算法による非線形制御）

概要

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This paper reports experimental verification of nonlinear output regulation for an inverted pendulum system. The output regulation problem, which is alternatively referred to as servo system design problem, is posed so that the cart of the pendulum tracks an arbitrarily given sinusoidal signal while holding the pendulum up above. To solve the problem, it is necessary to solve the so-called nonlinear regulator equation and the computation for its solution is based on a newly proposed theory to approximate center manifolds in a system of ordinary differential equations. This computation theory, which was proposed by the authors previously, provides an iterative algorithm that enables one to obtain higher order approximations. The algorithm is suitable for computer implementation and a 7-th order polynomial state feedback law is obtained. The experiments show that the cart of the pendulum tracks sinusoidal signals with different frequencies. The paper also reviews the general theory of nonlinear output regulation as well as the theories of center manifold and its approximate computation.