State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

Abstract

In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of a backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are formulated and discussed. The question on the optimal control of the system under consideration is also discussed and the corresponding theorem is considered.

Stabilization of coupled inverted pendula: From discrete to continuous case

“…The presented paper continues investigations started in the works Semenov et al (2014, 2015a, 2015b, 2016, 2018), devoted to the solution to the problem of inverted pendulum stabilization in the cases of rigid (Semenov et al, 2014) and flexible rod (Semenov et al, 2015a; 2015b) and in the case of the system of two coupled inverted pendula (Semenov et al, 2018). Particularly, we present the generalization of results obtained in Semenov et al (2018) to the case when the number of pendula is arbitrary.…”

“…Stabilization of discrete system (8) can be implemented by standard principles of feedback control (Semenov et al, 2014, 2015a, 2015b, 2016, 2018). Summing all equations in (8), we obtain the total deviation of pendula relative to their vertical position.…”

“…After many scientists have solved a whole range of problems considering simple inverted pendulum control (Aranovskiy et al, 2019; Boubaker, 2012; Chang and Lee, 2007; Citro et al, 2015; Dadios et al, 2006; Li and Liu, 2010; Lozano et al, 2000; Semenov et al, 2014, 2015a, 2015b, 2016, 2018, 2019; Tang and Ren, 2009; Wang, 2011; Wang and Kumbasar, 2018; Yan and Fei, 2011), the interest has shifted toward a more complicated problem of a coupled pendula (including inverted pendula systems) control. These can be a system of many joined (double and triple) pendula (Zhong and Rock, 2001), coupled oscillators with various nonlinear parts (Krack et al, 2016), and coupled inverted pendula.…”

Dynamic Model of Optimal Production Control in a Hysteretic Behaviour of Economic Agents

“…The properties of systems with hysteresis are significantly different from those with functional non-linearities . This can be explained by the complexity and non-linear structure of the hysteresis quantizer state space (Semenov, Grachikov et al, 2014). Beyond that point, mathematical models of hysteresis quantizers are generally not smooth, and this increases the difficulty of applying classical methods to analyse the corresponding systems.…”