Time and frequency domain analysis of sampled data controllers via mixed operation equations

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods

Hybrid Systems and Control With Fractional Dynamics (II): Control

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help the system designer. It is part II of two companion papers and focuses on fractional-order hybrid control. Specifically, two types of such techniques are reviewed, including robust control of switching systems and different strategies of reset control. Simulations and experimental results are given to show the effectiveness of the proposed strategies. Part I will introduce the fundamentals of fractional-order hybrid systems, in particular, modelling and stability of two kinds of such systems, i.e., fractional-order switching and reset control systems.Comment: 2014 International Conference on Fractional Differentiation and its Application, Ital

Fractional Repetitive Control of Nanopositioning Stages for High-Speed Scanning Using Low-Pass FIR Variable Fractional Delay Filter

This work was supported by the National Natural Science Foundation of China under Grant 51975375, the Binks Trust Visiting Research Fellowship (2018) (University of Aberdeen, UK) awarded to Dr. Sumeet S. Aphale and the SJTU overseas study grant awarded to Linlin Li. The authors would like to thank Mr. Wulin Yan for his assistance with the experiments.Peer reviewedPostprin

MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

In this chapter, we explore a mathematical modelling that describes the nonlinear dynamic behavior of atomic force microscopy (AFM). We propose two control techniques for suppressing the chaotic motion of the system. The proposed model considers the interatomic interactions between the analyzed sample and the cantilever. These acting forces are van der Waals type, and we add a mathematical term that is a simple approximation to the viscoelasticity that possibly occurs in biological samples. We analyzed the behavior of the initial conditions of the proposed mathematical model, which showed a degree of complexity of the basins of attraction that were detected by entropy and uncertainty parameter, both detect if the basins have a fractal behavior. Numerical results showed that the nonlinear dynamic behavior has chaotic regions with the Lyapunov exponent, bifurcation diagram, and the Poincaré map. And, we propose two control techniques to suppress the chaotic movement of the AFM cantilever. First technique is the optimal linear feedback control (OLFC), which does not consider the nonlinearities of mathematical model. On the other hand, the control state dependent Riccati equation (SDRE) considers the nonlinearities of mathematical model. Both control techniques for a desired periodic orbit proved to be efficient

Resonance as the Mechanism of Daytime Periodic Breathing in Patients with Heart Failure

Rationale: In patients with chronic heart failure, daytime oscillatory breathing at rest is associated with a high risk of mortality. Experimental evidence, including exaggerated ventilatory responses to CO2 and prolonged circulation time, implicates the ventilatory control system and suggests feedback instability (loop gain > 1) is responsible. However, daytime oscillatory patterns often appear remarkably irregular versus classic instability (Cheyne-Stokes respiration), suggesting our mechanistic understanding is limited. Objectives: We propose that daytime ventilatory oscillations generally result from a chemoreflex resonance, in which spontaneous biological variations in ventilatory drive repeatedly induce temporary and irregular ringing effects. Importantly, the ease with which spontaneous biological variations induce irregular oscillations (resonance “strength”) rises profoundly as loop gain rises toward 1. We tested this hypothesis through a comparison of mathematical predictions against actual measurements in patients with heart failure and healthy control subjects. Methods: In 25 patients with chronic heart failure and 25 control subjects, we examined spontaneous oscillations in ventilation and separately quantified loop gain using dynamic inspired CO2 stimulation. Measurements and Main Results: Resonance was detected in 24 of 25 patients with heart failure and 18 of 25 control subjects. With increased loop gain—consequent to increased chemosensitivity and delay—the strength of spontaneous oscillations increased precipitously as predicted (r = 0.88), yielding larger (r = 0.78) and more regular (interpeak interval SD, r = −0.68) oscillations (P < 0.001 for all, both groups combined). Conclusions: Our study elucidates the mechanism underlying daytime ventilatory oscillations in heart failure and provides a means to measure and interpret these oscillations to reveal the underlying chemoreflex hypersensitivity and reduced stability that foretells mortality in this population