CONTROLLER SYNTHESIS FOR A LINEARIZED MODEL OBJECT "DOUBLE INVERTED PENDULUM ON A CART" BASED ON THE LOCALIZATION METHOD
O.A. Votrina, G.A. Frantsuzova, D.S. Hudjakov
Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: Double inverted pendulum on a cart, stabilization, localization method, controller synthesis, state estimation filter
Abstract
In this paper, the possibility of stabilizing algorithm application for a linearized system “Double inverted pendulum” by means of the localization method is discussed. In order to reduce the complexity of the controller calculation procedure, a preliminary transformation of the object definition to the canonical basis is provided. Moreover, the control algorithm formulation in the form of a function of the canonical variables is suggested. The controller definition in a primitive basis is obtained via an inverse transformation of the canonical variables. It provides a possibility of issuing recommendations for the physical implementation of the system. In addition, it is needed to estimate the entire list of variables for creating the controller, but only the part of internal variables of the object can be measured. With the purpose of the variables’ estimation, three similar differentiators are proposed, which provides the possibility of estimating the total state vector. The designed controller guarantees the pendulum’s stabilization in a vertical position with a small angle of deviation. The main features of the designed system are shown by simulating the model in the MatLab Simulink integrated environment.
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