Design and frequency analysis of continuous finite-time-convergent differentiator

In this paper, a continuous finite-time-convergent differentiator is presented based on a strong Lyapunov function. The continuous differentiator can reduce chattering phenomenon sufficiently than normal sliding mode differentiator, and the outputs of signal tracking and derivative estimation are all smooth. Frequency analysis is applied to compare the continuous differentiator with sliding mode differentiator. The beauties of the continuous finite-time-convergent differentiator include its simplicity, restraining noises sufficiently, and avoiding the chattering phenomenon

On fraction order modeling and control of dynamical systems

This paper demonstrates the feasibility of modeling any dynamical system using a set of fractional order di®erential equations, including distributed and lumped systems. Fractional order differentiators and integrators are the basic elements of these equations representing the real model of the dynamical system, which in turn implies the necessity of using fractional order controllers instead of controllers with integer order. This paper proves that fractional order differential equations can be used to model any dynamical system whether it is continuous or lumped

Pressure model of a four-way spool valve for simulating electrohydraulic control systems

An equation that relates the pressure flow characteristics of hydraulic spool valves was developed. The dependent variable is valve output pressure, and the independent variables are spool position and flow. This causal form of equation is preferred in applications that simulate the effects of hydraulic line dynamics. Results from this equation are compared with those from the conventional valve equation, whose dependent variable is flow. A computer program of the valve equations includes spool stops, leakage spool clearances, and dead-zone characteristics of overlap spools

System for measuring three fluctuating velocity components in a turbulently flowing fluid

A system is described for measuring fluid velocity in a turbulently flowing fluid including a sensing apparatus for dynamically sensing the mainstream and two orthogonal cross velocity components of the fluid. A transducer operative is included to provide three electrical output signals representative of the velocity components in the mainstream, and in the cross directions. Signal processors can be utilized to derive the Reynolds stress wave and the Reynolds stress

Design and analysis of continuous hybrid differentiator

In this paper, a continuous hybrid differentiator is presented based on a strong Lyapunov function. The differentiator design can not only reduce sufficiently chattering phenomenon of derivative estimation by introducing a perturbation parameter, but also the dynamical performances are improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating sliding mode items and the linear filter. Frequency analysis is applied to compare the hybrid continuous differentiator with sliding mode differentiator. The merits of the continuous hybrid differentiator include the excellent dynamical performances, restraining noises sufficiently, and avoiding the chattering phenomenon

Long-Period Fiber Gratings in Active Fibers

Traditionally, long period fiber gratings (LPG) are made in passive optical fibers that have negligible loss. However, loss or gain that can be controlled via optical pumping adds a new degree of freedom and - as will be shown in this chapter - brings many new and interesting properties. From the historical perspective, the first attempt to combine the fiber gain and LPG filtering characteristics was for gain flattening of an Erbium-doped fiber (EDF) amplifier by inscribing LPG directly into the active fiber [1]. At the same time, theoretical studies [2,3] showed that a proper level of loss/gain in the fiber core or cladding can modify the LPG transmission characteristics. Significant theoretical and experimental body of work has been published since with new emerging applications appearing. In this chapter, we investigate the new phenomena brought by the presence of the loss/gain [2,3]. Following this, we look on practical possibilities how to obtain required gain in active optical fibers and show how to analyze such structures, in which (incoherent) noise from an amplifying fiber is simultaneously generated and diffracted at the LPG [4]. Finally, we discuss possible application of the LPG in active fibers

Design and analysis of genetic feedback architectures for synthetic biology

Synthetic Biology seeks to design and assemble novel biological systems with favourable properties. It allows us to comprehend and modify the fundamental mechanisms of life and holds significant promise in revolutionizing current technologies ranging from medicine and biomanufacturing to energy and environmental protection. Biological processes constitute remarkably complex dynamical systems operating impeccably well in messy and constantly changing environments. Their ability to do so is rooted in sophisticated molecular control architectures crafted by natural evolutionary innovation over billions of years. Such control architectures, often blended with human-engineering approaches, are the key to realizing efficient and reliable synthetic biological systems. Aiming to accelerate the development of the latter, the present thesis addresses some fundamental challenges in biomolecular systems and control design. We begin by elucidating biological mechanisms of temporal gradient computation, enabling cells to adjust their behaviour in response to anticipated environmental changes. Specifically, we introduce biomolecular motifs capable of functioning as highly tunable and accurate signal differentiators to input molecular signals around their nominal operation. We investigate strategies to deal with high-frequency input signal components which can be detrimental to the performance of most differentiators. We ascertain the occurrence of such motifs in natural regulatory networks and demonstrate the potential of synthetic experimental realizations. Our motifs can serve as reliable speed biosensors and can form the basis for derivative feedback control. Motivated by the pervasiveness of Proportional-Integral-Derivative (PID) controllers in modern technological applications, we present the realization of a PID controller via biomolecular reactions employing, among others, our differentiator motifs. This biomolecular architecture represents a PID control law with set point weighting and filtered derivative action, offering robust regulation of a single-output biological process with enhanced dynamic performance and low levels of stochastic noise. It is characterized by significant ease of tuning and can be of particular experimental interest in molecular programming applications. Finally, we investigate efficient regulation strategies for multi-output biological processes with internal coupling interactions, expanding previously established single-output control approaches. More specifically, we propose control schemes allowing for robust manipulation of the outputs in various ways, namely manipulation of their product/ratio, linear combinations of them as well as manipulation of each of the outputs independently. Our analysis is centered around two-output biological processes, yet the scalability of the proposed regulation strategies to processes with a higher number of outputs is highlighted. In parallel, their experimental implementability is explored in both in vivo and in vitro settings

Report of the NASA seminar on pilot-vehicle systems identification

Comparison of cross correlation and orthogonalized exponential analyses by regression analysis for identification of human pilot dynamic response characteristic