Straight Double Inverted Pendulum System Control Based On Multiple Model Adaptive Control

Inverted pendulum system is multivariable, fast and absolute instability under strong coupling. Many concepts come from research work, such as stabilization or tracking resistance, can be presented clearly through inverted pendulum research. With the increase of pendulum number, the system will be more complexity and less controllability. The achievement of stability control for such system will be harder, which can be only achieved by creating innovative control algorithms continuously. Seen in this light, inverted pendulum system provides a platform for upgrading and optimization with a broad research prospects.Multiple model adaptive control(MMAC) refers to solve a complex problem by sub-dividing the related system model into simple ones and solve them separately. The solution for the initial complex system can be sought from those separated answers. In practice, it is mainly applied to solve the complex issues with nonlinear and uncertainty.In this paper, straight double inverted pendulum is treated as the research object. System nonlinear mathematical model is built up based on Lagrange equations. According to the state equations around the balance point, by doing the analysis of step response stability, observability and controllability, straight double inverted pendulum system can be determined as absolute unstable, but controllable and observed around the balance point. During multiple model adaptive controller design, taking the system character of unique balance point into account, using swing angles as the standard to divide sub- models for the system. This paper built up four MMAC controllers with four different angle control scopes and different sub- model set capacities. The real positons of the two swing angles mentioned above are used as the signal of sub- model switchover. Feedback control algorithm, which is simple and staple, is used in sub-controllers, which will improve system performance. MATLAB here is used as the simulation software. The differences of performance between these four controllers are presented clearly by simulation figures. After analyzing, it can be known that relative small angle control scope and a bigger sub-model set can lead to better performance, but if the angle control scope is too much small, vibrate will appear, which influence the stable of the controlled system.