Repetitive Control for Lur’e-Type Systems: Application to Mechanical Ventilation

Abstract

Repetitive control (RC) has shown to achieve superior rejection of periodic disturbances. Many nonlinear systems are subject to repeating disturbances. The aim of this article is to develop a continuous-time RC design with stability guarantees for nonlinear Lur'e-type systems. Approximate output tracking is achieved by combining an internal model, consisting of a finite number of linear oscillators with frequencies at the reference frequency and at its multiples, with a stabilizer that guarantees a convergence property of the closed-loop system. The developed RC approach is applied to a nonlinear mechanical ventilation system for intensive care units (ICUs), which can be modeled as a Lur'e-type system. The experimental study confirms that the RC scheme is able to successfully follow the desired target pressure profile to properly support the ventilation needs of an adult patient.

Incremental Stabilization of Cascade Nonlinear Systems and Harmonic Regulation: A Forwarding-Based Design

“…. , γ) such that each couple (w φ, γ) is controllable, together with a stabilizer for the closed-loop ( 19), (22) (see [23], [28]). In the considered framework, we allow the external signals (r, d) to span the whole R ne × R nu and we look for a global result in the domain of attraction.…”

“…In this case, many practical examples can be found whose plant belongs to the classes of systems described by (26). Some examples are the mechanical ventilation machine in [28], a flexible link manipulator in [35] and the surge system considered in [36], [37]. For such a class of systems, we first assume that Assumption 1 is satisfied with respect to some constant metric P = P > 0.…”

“…The second group of results works in the "original" coordinates and follows a passivity-like approach. Within this approach, we recall for instance [14], where the problem is posed for incrementally passive systems coupled with a linear output, the work [7] where the problem is addressed under the notion of convergent systems with the control that is designed by explicitly solving the so-called regulator equations and, more recently, [28] for systems in Lur'e form having convergent properties.…”

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

“…Another control method for perfect tracking of repetitive trajectory is called Repetitive Control (RC). Recently, RC has been used for leg exoskeleton control [56], 1-DOF Lagrangian system [57], industrial wide-format printing [58], contouring control of micro-stereolithography [59], magnetically suspended rotor system [60], [61], [62], control of linear actuator [63], functional electrical stimulation [64], [65], grid-connected inverters [66], [67], [68], [69], [70], nanometer-order contouring [71], dynamical galvanometerbased raster scanning [72], atomic force microscopy (AFM) scanner [73], mechanical ventilation [74], permanent magnet synchronous motor (PMSM) [75]- [77], servo motor [78], plug-in electric vehicle (PEV) charger [79], piezoelectric nano positioning stage [80], hydraulic press system [81], robotic manipulator [82], [83], and electric spring [84]. The RC is based on the idea of internal model principle by Francis and Wonham [85] stated that by incorporating model of reference/disturbance then perfect reference tracking or disturbance rejection can be achieved.…”

LMI conditions for contraction, integral action, and output feedback stabilization for a class of nonlinear systems

“…Consider the example of a mechanical ventilation system presented in [27,36] and whose system dynamics is modeled as (28) with…”