Problem of stabilizing the nonlinear “seesaw” model object

Abstract

Abstract The objective of this paper is to discuss the problem of stabilizing the nonlinear type of oscillatory objects. The object under research is “Seesaw” model object which has many interpretations with different physical properties and mathematical models. Such a construction is used in biomechanics for implementing the “natural” gait of a human simulating the knee joint, for instance. This object can be stabilized by well-known techniques such as relay control, transitions controller, PI-regulator and others. Such a model has a lot of nonlinearities that makes the process of constructing the mathematical model and designing the stabilizing system more complicated. One of “Seesaw” models that consists of a mass suspended by an inelastic fiber was stabilized by methods of maximizing and minimizing the domain of attraction. The results of calculating and simulating the object within its stabilizing system show that the object can be successfully stabilized by relay control in case of minimizing the domain of attraction. However, the case of maximizing the domain of attraction leads to opposite transient process.