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Based on the general structure of mechanical systems described by their state-space representation, the Takagi–Sugeno fuzzy modeling, and the controllability property of fuzzy systems, an algebraic and practical approach to computing the fuzzy gain capable of ensuring the stability property of the Takagi–Sugeno fuzzy model is proposed in this article. The main idea consists of finding a continuous fuzzy gain such that any linear behavior, defined by the adequate selection of eigenvalues, is induced in the closed-loop fuzzy system. Therefore, by continuity, if the fuzzy model is an approximation sufficiently close to the mechanical system, then such a nonlinear system is also stabilized by the fuzzy controller. A notable advantage of the proposed method, when compared with similar approaches, is the simplicity of the resulting gain. The validity of the approach is illustrated through the numerical simulation of a sufficiently complex nonlinear system. [ABSTRACT FROM AUTHOR]

This study presents the design of a feedback-based smooth and continuous control action, for the movement stabilization of a mechanical system consisted of a dampen pendulum mounted on a cart. the designs assumes that the pendulum is initialized in the upper-half plane. Also assumes that the involved viscous friction force is known. The control strategy is based on some nonlinear transformation that allow to rewrite the system as if it were an simple chain of integrator of fourth degree, perturbed by a nonlinear function. This nonlinear function, which models the dynamics of the original system, vanishes at the origen. Once the system has been transformed, the simple control action, consisted of two parts, one linear and other nonlinear or linear by parts (saturation function), is applied. After that, the linear part of the control action brought the pendulum near to the origin. Subsequently, the quasilinear part slowly brought the cart to the origin, assuring the desired behaviour in closed-loop. The stability analysis, which supports the feedback control action, follows an approach known a the Lyapunov method. Convincing numerical simulations and laboratory experiments that were included. [ABSTRACT FROM AUTHOR]

The main contributions of this paper are as follows: 1) a proportional-derivative controller with inverse dead-zone is addressed for the regulation of robotic arms, where the inputs dead-zone is cancelled with the inverse dead-zone, 2) stability of the mentioned technique is assured, and 3) the considered strategy is validated by two examples. [ABSTRACT FROM PUBLISHER]