Control of mechanical motion systems with non-collocation of actuation and friction: A Popov criterion approach for input-to-state stability and set-valued nonlinearities

Input-to-state stability of Lur’e systems

“…Traditionally, Lyapunov approaches to the stability theory of systems of the form (1.1) consider unforced Lur'e systems (i.e., v = 0 in (1.1)), whilst Lur'e systems with forcing (usually acting through B, that is, B e = B) have been studied using the input-output framework initiated by Sandberg and Zames in the 1960s, see, for example [27]. More recently, forced Lur'e systems have been analysed in the context of input-to-state stability (ISS) theory, see [1,2,12,13] (and [22] for discrete-time systems). In [1], an ISS result is obtained for Lur'e systems (1.1) under the assumptions that B e = B, the underlying linear system has the positive real property and the nonlinearity (which may have superlinear growth) satisfies a suitable cone condition.…”

“…In [1], an ISS result is obtained for Lur'e systems (1.1) under the assumptions that B e = B, the underlying linear system has the positive real property and the nonlinearity (which may have superlinear growth) satisfies a suitable cone condition. Partial extensions of the classical Popov and circle criteria to an ISS setting can be found in [2] and [12,13], respectively. The concept of ISS (for a general controlled nonlinear system) appears first in [23] published in 1989.…”

Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert–kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits

“…Here, following [Kiseleva et al, 2012], on the examples of a two-mass model [de Bruin et al, 2009;Mihajlovic et al, 2004] of drilling system and its modified version, supplemented by equations of induction motor, we demonstrate that unique stable equilibrium state can coexist with a stable limit cycle (hidden oscillation) in both models. It is very possible that the breakdowns in real drilling systems happen due to the existence of hidden oscillations in such systems, which are difficult to find because of the limitation of the standard numerical procedure.…”

“…Below, the model studied in [de Bruin et al, 2009;Mihajlovic et al, 2004] will be considered. This model consists of an upper disc, actuated by a drive part, no-mass string, and lower disc.…”

Observer-based output-feedback control to eliminate torsional drill-string vibrations

“…[4], [5], [6]. In these models, it is generally assumed that the resisting torque at the bit-rock interface can be modeled as a frictional contact with a velocity weakening effect as reported in [7], [8].…”