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Control‐oriented modeling and deployment of tensegrity–membrane systems
Author(s) -
Yang Shu,
Sultan Cornel
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3708
Subject(s) - tensegrity , control theory (sociology) , underactuation , nonlinear system , lyapunov function , controller (irrigation) , linearization , coordinate system , ordinary differential equation , computer science , partial differential equation , lyapunov stability , control engineering , mathematics , differential equation , engineering , control (management) , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , agronomy , biology
Summary This study addresses control‐oriented modeling and control design of tensegrity–membrane systems. Lagrange's method is used to develop a control‐oriented model for a generic system. The equations of motion are expressed as a set of differential‐algebraic equations (DAEs). For control design, the DAEs are converted into second‐order ordinary differential equations (ODEs) based on coordinate partitioning and coordinate mapping. Because the number of inputs is less than the number of state variables, the system belongs to the class of underactuated nonlinear systems. A nonlinear adaptive controller based on the collocated partial feedback linearization (PFL) technique is designed for system deployment. The stability of the closed‐loop system for the actuated coordinates is studied using the Lyapunov stability theory. Because of system complexity, numerical tests are used to conduct stability analysis for the dynamics of the underactuated coordinates, which represents the system's zero dynamics. For the tensegrity–membrane systems studied in this work, analytical proof of zero dynamics stability remains an open theoretical problem. An H ∞ controller is implemented for rapid stabilization of the system at the final deployed configuration. Simulations are conducted to test the performance of the two controllers. The simulation results are presented and discussed in detail. Copyright © 2016 John Wiley & Sons, Ltd.