Premium
Almost periodic motion planning and control for double rotary pendulum with experimental validation
Author(s) -
Wang Zeguo,
Freidovich Leonid B.,
Zhang Honghua
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2154
Subject(s) - control theory (sociology) , inverted pendulum , double pendulum , pendulum , controller (irrigation) , convergence (economics) , trajectory , stability (learning theory) , mathematical proof , motion control , mathematics , computer science , engineering , control (management) , nonlinear system , physics , robot , mechanical engineering , agronomy , geometry , quantum mechanics , artificial intelligence , astronomy , machine learning , economics , biology , economic growth
The aim is to develop a systematic procedure for planning feasible motions for a double rotary pendulum. This pendulum has one directly actuated horizontal link and two passive links, moving in a rotating vertical plane. We plan a nontrivial oscillatory motion for the passive links that is consistent with the horizontal link rotating at a given average speed and also design a stabilizing controller to approximately induce such a motion. For the motion planning, a numerical optimization procedure is proposed in the form of a sequence of three simpler problems to systematically derive initial guesses for the final optimization search. For the controller design, firstly the system is linearized along a nominal trajectory, and then a parametrized family of candidate stabilizing controllers is designed. For each set of parameters, a necessary and sufficient stability condition can be checked for the derived linear time varying periodic system. Therefore, a numerical optimization procedure is used to find the controller gain for the linear system based on the stability condition. The performance of the closed‐loop system is illustrated via numerical simulations and verified via experiments with an educational platform produced by PendCon, demonstrating achieving oscillations with required characteristics. However, the formal proofs for convergence and even for existence of almost periodic solutions are left for future studies.