Time-periodic Systems Research Articles

Reliability and Robustness Analysis of the Masinga Dam under Uncertainty

Kenya’s water abstraction must meet the projected growth in municipal and irrigation demand by the end of 2030 in order to achieve the country’s industrial and economic development plan. The Masinga dam, on the Tana River, is the key to meeting this goal to satisfy the growing demands whilst also continuing to provide hydroelectric power generation. This study quantitatively assesses the reliability and robustness of the Masinga dam system under uncertain future supply and demand using probabilistic climate and population projections, and examines how long-term planning may improve the longevity of the dam. River flow and demand projections are used alongside each other as inputs to the dam system simulation model linked to an optimisation engine to maximise water availability. Water availability after demand satisfaction is assessed for future years, and the projected reliability of the system is calculated for selected years. The analysis shows that maximising power generation on a short-term year-by-year basis achieves 80%, 50% and 1% reliability by 2020, 2025 and 2030 onwards, respectively. Longer term optimal planning, however, has increased system reliability to up to 95% in 2020, 80% in 2025, and more than 40% in 2030 onwards. In addition, increasing the capacity of the reservoir by around 25% can significantly improve the robustness of the system for all future time periods. This study provides a platform for analysing the implication of different planning and management of Masinga dam and suggests that careful consideration should be given to account for growing municipal needs and irrigation schemes in both the immediate and the associated Tana River basin.

Self-contained, low-cost Body-on-a-Chip systems for drug development.

Integrated multi-organ microphysiological systems are an evolving tool for preclinical evaluation of the potential toxicity and efficacy of drug candidates. Such systems, also known as Body-on-a-Chip devices, have a great potential to increase the successful conversion of drug candidates entering clinical trials into approved drugs. Systems, to be attractive for commercial adoption, need to be inexpensive, easy to operate, and give reproducible results. Further, the ability to measure functional responses, such as electrical activity, force generation, and barrier integrity of organ surrogates, enhances the ability to monitor response to drugs. The ability to operate a system for significant periods of time (up to 28 d) will provide potential to estimate chronic as well as acute responses of the human body. Here we review progress towards a self-contained low-cost microphysiological system with functional measurements of physiological responses. Impact statement Multi-organ microphysiological systems are promising devices to improve the drug development process. The development of a pumpless system represents the ability to build multi-organ systems that are of low cost, high reliability, and self-contained. These features, coupled with the ability to measure electrical and mechanical response in addition to chemical or metabolic changes, provides an attractive system for incorporation into the drug development process. This will be the most complete review of the pumpless platform with recirculation yet written.

Robust Generation of Limit Cycles in Nonlinear Systems: Application on Two Mechanical Systems

This paper studies inducing robust stable oscillations in nonlinear systems of any order. This goal is achieved through creating stable limit cycles in the closed-loop system. For this purpose, the Lyapunov stability theorem which is suitable for stability analysis of the limit cycles is used. In this approach, the Lyapunov function candidate should have zero value for all the points of the limit cycle and be positive in the other points in the vicinity of it. The proposed robust controller consists of a nominal control law with an additional term that guarantees the robust performance. It is proved that the designed controller results in creating the desirable stable limit cycle in the phase trajectories of the uncertain closed-loop system and leads to induce stable oscillations in the system's output. Additionally, in order to show the applicability of the proposed method, it is applied on two practical systems: a time-periodic microelectromechanical system (MEMS) with parametric errors and a single-link flexible joint robot in the presence of external disturbances. Computer simulations show the effective robust performance of the proposed controllers in generating the robust output oscillations.

Linear Time Invariant Approximations of Linear Time Periodic Systems

Several methods for analysis of linear time periodic (LTP) systems have successfully been demonstrated using harmonic decompositions. One method recently examined is to create a linear time invariant (LTI) model approximation by expansion of the LTP system states into various harmonic state representations, and formulating corresponding linear time invariant models. Although this method has shown success, it relies on a second order formulation of the original LTP system. This second order formulation can prove problematic for degrees of freedom not explicitly represented in second order form. Specifically, difficulties arise when performing the harmonic decomposition of body and inflow states as well as interpretation of LTI velocities. Instead this paper will present a more generalized LTI formulation using a first order formulation for harmonic decomposition. The new first order approach is evaluated for a UH-60 rotorcraft model, and is used to show the significance of particular harmonic terms; specifically that the coupling of harmonic components of body and inflow states with the rotor states has a significant contribution to the LTI model fidelity in the prediction of vibratory hub loads.

VARIOUS FORMULATION VARIABLES EFFECTING FLOATATION BEHAVIOUR OF SINGLE UNIT GASTRORETENTIVE CAPSULES OF OFLOXACIN

<p><strong>Objective: </strong>Objective of the present study was to prepare simple single unit gastro-retentive capsules of ofloxacin with the aim to have the gastric retention of the system for longer periods of time (12h) and to study the effect of various polymers on floating behaviour of such single unit gastro-retentive capsules of ofloxacin.</p><p><strong>Methods: </strong>The method used for the preparation of gastro-retentive capsules was a simple physical blending of various low-density hydrophilic polymers alone and in combination with hydrophobic polymers and filling into capsules. These capsules were then subjected to <em>in vitro</em> floatation and matrix integrity study in 0.1N HCl using static volume beaker method and the United States pharmacopoeia (USP) type II dissolution apparatus method at 100rpm.</p><p><strong>Results: </strong>Two grades of hydroxypropyl methylcellulose (HPMC) K4M and K15M used were found suitable for the purpose. Results showed that increase in HPMC level increased colloidal gel barrier strength along with matrix integrity with consequently improved buoyancy. Lactose which was added as release rate modifier decreased matrix integrity and buoyancy. Eudragit a hydrophobic polymer was added so as to have intact, the buoyant formulation for 12 h with desired drug release characteristics. The addition of eudragit enhanced matrix integrity and floatation time to certain levels but higher levels showed negative results. Floatation time of more than 16 h was observed in the formulations containing 2:1 ratio of HPMC K15M and eudragit respectively. 3<sup>2</sup> factorial design was used to study the effect of various formulation variables on buoyancy and matrix integrity. Formulations containing zero level of HPMC were found buoyant for more than 12 h with all levels of eudragit S100 (i.e.,-1, 0,+1 level). It was also observed that matrix integrity consequently buoyancy increased with increase in eudragit with all levels of HPMC.</p><p><strong>Conclusion: </strong>The study concludes that eudragit S100 a hydrophobic polymer increased floatation time of the formulated capsules with all the three levels of HPMC K15M, but at the same time eudragit level should not exceed HPMC, while lactose a release rate enhancer decreased matrix integrity/floatation time of the formulated capsules.</p>

Realization of Actuator‐Fault Estimation for Distributed Wireless Networked Control Systems

AbstractThis paper addresses a study of fault estimation for distributed wireless networked control systems (WNCSs) with actuator multiple faults during industrial automatic processes. Firstly, the model of WNCSs is formulated as linear time periodic systems (LTPSs) according to the periodicity of subsystems in WNCSs. Afterwards, the distributed fault estimation (FE) method for LTPSs is concerned. The strategy of avoiding the problem of structure‐limitation in the FE gain and the realization of the proposed method in the real process are especially detailed. Finally, the proposed FE method is verified on a wireless network control (WiNC) platform.

Connecting orbits for a class of singular time-periodic second-order Hamiltonian systems

We show the existence of connecting orbits for a class of singular second-order Hamiltonian systemswhere, as opposed to most of the existing literature, we assume that the potential V has not one but any finite number of maxima of equal value. We use variational methods under the assumption that V (t, u) satisfies the so-called ‘strong-force’ condition at the singularity.

Computation of Lyapunov functions for nonautonomous systems on finite time-intervals by linear programming

We present an algorithm for numerically computing Lyapunov functions for nonautonomous systems on finite time-intervals. The algorithm relies on a linear optimization problem and delivers a continuous and piecewise affine function on a compact set. The level-sets of such a Lyapunov function give concrete bounds on the time-evolution of the system on the time-interval and for time-periodic systems they deliver an ultimate bound on solutions. Four examples of computed finite-time Lyapunov functions are given.

Fredholm alternative and solution regularity for time-periodic hyperbolic systems

This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n, $$ with periodicity conditions in time and reflection boundary conditions in space. We state a non-resonance condition (depending on the coefficients $a_j$ and $b_{jj}$ and the boundary reflection coefficients), which implies Fredholm solvability of the problem in the space of continuous functions. Further, we state one more non-resonance condition (depending also on $\partial_ta_j$), which implies $C^1$-solution regularity. Moreover, we give examples showing that both non-resonance conditions cannot be dropped, in general. Those conditions are robust under small perturbations of the problem data. Our results work for many non-strictly hyperbolic systems, but they are new even in the case of strict hyperbolicity.

An abstract theorem on the existence of periodic motions of non-autonomous Lagrange systems

In this paper, we established an abstract theorem on the existence of periodic solutions for Lagrange systems under Tonelli framework (strictly convex and superlinear, completeness of phase flow) which is based on the principle of least action in geometry and dynamics. An example of the application of the abstract theorem is given and the existence of periodic solutions for a class of time-periodic Lagrange systems will be proved.

Computations of Newtonian fluid flow around a square cylinder near an adiabatic wall at low and intermediate Reynolds numbers: Effects of cross-buoyancy mixed convection

ABSTRACTThe effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady for G = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed for G = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasing G and/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% at G = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value at G = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained.

Reduction model approach for linear time-varying systems with input delays based on extensions of Floquet theory

We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We also prove an analogue for discrete time systems, through a discrete time extension of Floquet theory.

Street Viewer: An Autonomous Vision Based Traffic Tracking System.

The development of intelligent transportation systems requires the availability of both accurate traffic information in real time and a cost-effective solution. In this paper, we describe Street Viewer, a system capable of analyzing the traffic behavior in different scenarios from images taken with an off-the-shelf optical camera. Street Viewer operates in real time on embedded hardware architectures with limited computational resources. The system features a pipelined architecture that, on one side, allows one to exploit multi-threading intensively and, on the other side, allows one to improve the overall accuracy and robustness of the system, since each layer is aimed at refining for the following layers the information it receives as input. Another relevant feature of our approach is that it is self-adaptive. During an initial setup, the application runs in learning mode to build a model of the flow patterns in the observed area. Once the model is stable, the system switches to the on-line mode where the flow model is used to count vehicles traveling on each lane and to produce a traffic information summary. If changes in the flow model are detected, the system switches back autonomously to the learning mode. The accuracy and the robustness of the system are analyzed in the paper through experimental results obtained on several different scenarios and running the system for long periods of time.

Exposing local symmetries in distorted driven lattices via time-averaged invariants

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wave functions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.

Symbolic Computation of Quantities Associated With Time-Periodic Dynamical Systems1

Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with periodic time-varying coefficients. The state transition matrix (STM) Φ(t,α), associated with the linear part of the equation, can be expressed in terms of the periodic Lyapunov–Floquét (L-F) transformation matrix Q(t,α) and a time-invariant matrix R(α) containing a set of symbolic system parameters α. Computation of Q(t,α) and R(α) in symbolic form as a function of α is of paramount importance in stability, bifurcation analysis, and control system design. In earlier studies, since Q(t,α) and R(α) were available only in numerical forms, general results for parameter unfolding and control system design could not be obtained in the entire parameter space. In 2009, an attempt was made by Butcher et al. (2009, “Magnus' Expansion for Time-Periodic Systems: Parameter Dependent Approximations,” Commun. Nonlinear Sci. Numer. Simul., 14(12), pp. 4226–4245) to compute the Q(t,α) matrix in a symbolic form using the Magnus expansions with some success. In this work, an efficient technique for symbolic computation of Q(t,α) and R(α) matrices is presented. First, Φ(t,α) is computed symbolically using the shifted Chebyshev polynomials and Picard iteration method as suggested in the literature. Then, R(α) is computed using a Gaussian quadrature integral formula. Finally, Q(t,α) is computed using the matrix exponential summation method. Using mathematica, this approach has successfully been applied to the well-known Mathieu equation and a four-dimensional time-periodic system in order to demonstrate the applications of the proposed method to linear as well as nonlinear problems.

Postnatal Cardiac Autonomic Nervous Control in Pediatric Congenital Heart Disease.

Congenital heart disease is the most common congenital defect. During childhood, survival is generally good but, in adulthood, late complications are not uncommon. Abnormal autonomic control in children with congenital heart disease may contribute considerably to the pathophysiology of these long term sequelae. This narrative review of 34 studies aims to summarize current knowledge on function of the autonomic nervous system in children with a congenital heart defect. Large scale studies that measure both branches of the nervous system for prolonged periods of time in well-defined patient cohorts in various phases of childhood and adolescence are currently lacking. Pending such studies, there is not yet a good grasp on the extent and direction of sympathetic and parasympathetic autonomic function in pediatric congenital heart disease. Longitudinal studies in homogenous patient groups linking autonomic nervous system function and clinical outcome are warranted.

Trigonometric spline and spectral bounds for the solution of linear time-periodic systems

Linear time-periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Examples include anisotropic rotor-bearing systems and parametrically excited systems. The structure of the solution to linear time-periodic systems is known due to Floquet’s Theorem. We use this information to derive a new norm which yields two-sided bounds on the solution and in this norm vibrations of the solution are suppressed. The obtained results are a generalization for linear time-invariant systems. Since Floquet’s Theorem is non-constructive, the applicability of the aforementioned results suffers in general from an unknown Floquet normal form. Hence, we discuss trigonometric splines and spectral methods that are both equipped with rigorous bounds on the solution. The methodology differs systematically for the two methods. While in the first method the solution is approximated by trigonometric splines and the upper bound depends on the approximation quality, in the second method the linear time-periodic system is approximated and its solution is represented as an infinite series. Depending on the smoothness of the time-periodic system, we formulate two upper bounds which incorporate the approximation error of the linear time-periodic system and the truncation error of the series representation. Rigorous bounds on the solution are necessary whenever reliable results are needed, and hence they can support the analysis and, e.g., stability or robustness of the solution may be proven or falsified. The theoretical results are illustrated and compared to trigonometric spline bounds and spectral bounds by means of three examples that include an anisotropic rotor-bearing system and a parametrically excited Cantilever beam.

On two-liquid AC electroosmotic system for thin films.

Lab-on-chip devices employ EOF for transportation and mixing of liquids. However, when a steady (DC) electric field is applied to the liquids, there are undesirable effects such as degradation of sample, electrolysis, bubble formation, etc. due to large magnitude of electric potential required to generate the flow. These effects can be averted by using a time-periodic or AC electric field. Transport and mixing of nonconductive liquids remain a problem even with this technique. In the present study, a two-liquid system bounded by two rigid plates, which act as substrates, is considered. The potential distribution is derived by assuming a Boltzmann charge distribution and using the Debye-Hückel linearization. Analytical solution of this time-periodic system shows some effects of viscosity ratio and permittivity ratio on the velocity profile. Interfacial electrostatics is also found to play a significant role in deciding velocity gradients at the interface. High frequency of the applied electric field is observed to generate an approximately static velocity profile away from the Electric Double Layer (EDL).

Fault‐tolerant control for wireless networked control systems with an integrated scheduler

SummaryThis paper addresses a study of fault‐tolerant control (FTC) for wireless networked control systems (WNCSs) in industrial automatic processes. The WNCSs is composed of many subsystems, which operate with different sampling cycles. In order to meet the real‐time requirements and ensure a deterministic data transmission, the time division multiple access (TDMA) mechanism is adopted in WNCSs. The data in WNCSs are transmitted following a TDMA‐based scheduler. According to the periodicity, WNCSs integrated with the scheduler is first formulated as discrete linear time periodic systems (LTPSs). Afterwards, a fault estimation method for LTPSs is developed under a H∞ performance specification with a regional pole constraint. With the achieved state observer and fault estimator, an FTC strategy for LTPSs is explored. Finally, the proposed methods are verified on a physical experimental WiNC platform. Copyright © 2016 John Wiley & Sons, Ltd.

Existence and asymptotic stability of periodic orbits for a class of electromechanical systems: a perturbation theory approach

In this work a class of time-periodic electromechanical system is investigated. This system is nonhyperbolic. By using Regular Perturbation Theory, results on existence and stability of periodic orbits are obtained. Moreover, the dynamics of this system can be approached in a mathematically rigorous way. These results generalize previous ones obtained for autonomous electromechanical systems.