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Closed-loop swing-up and stabilization of inverted pendulum by finite-horizon LQR applied in 2-DOF concept

Docekal Tomas, Ozana Stepan, Pal Singh Abhaya, Kawala-Sterniuk Aleksandra

Control and Cybernetics

2020

Vol. 49, No. 1

109--122

The general framework of this paper is the control design of complex nonlinear systems. The proposed approach is demonstrated with the use of a case study regarding a typical mechatronic system - control design of inverted pendulum on the cart. The methodology used for the solution of this problem is based on two- degree of freedom control structure (2-DOF) with feed-forward and feedback terms. Feed-forward term represents a solution of trajectory generation problem and feedback term stands for a state controller. Both of these parts generally fall into the category of optimal control problems. The article focuses on the design of a finite-horizon linear quadratic controller and its application in 2-DOF structure with the use of customized LQR computation procedure, showing all necessary steps of the design, including source codes. It is proposed that the developed methodology is general and can be adopted for most of other nonlinear mechatronic systems, including unstable or non-minimum phase systems. This has been already tested successfully for models of both double and triple inverted pendulums. The functionality of the concept under real conditions can also be seen in Ozana (2018a) and Ozana (2018b) showing preliminary experiments with real apparatus.