Ramp Function Research Articles

Event-triggered control for discrete-time piecewise affine systems

This work addresses the event-triggered control (ETC) of discrete-time piecewise affine systems. We propose a method to design a triggering strategy relying on an implicit representation of piecewise affine systems. Thanks to this implicit representation based on ramp functions, we propose a partition-dependent piecewise quadratic functions to define the trigger criterion and use a piecewise quadratic Lyapunov function candidate to derive conditions to certify the global exponential stability of the origin under the ETC strategy. Since the stability conditions can be expressed as linear matrix inequalities constraints, we propose a convex optimization solution to design the triggering function parameters and to compute the Lyapunov function to ensure the closed-loop stability and a reduction on the control updates. The approach is illustrated by numerical examples.

Nanoscale viscoelasticity characterization of engineered organometallic nanocomposite thin films for biomedical applications

This work is focused on nanoscale viscoelastic properties characterization of gold nanoparticles (AuNPs) reinforced chitosan nanocomposites using nanoindentation. Chitosan nanocomposite films reinforced with gold nanoparticles concentration (w/v) up to 0.25 mg/ml in chitosan were prepared via a solution evaporation technique. Creep and stress relaxation responses were modeled using the generalized Voigt model and the generalized Maxwell model, respectively. Nanoindentation experimental data were analyzed using these models to obtain model constants. Both displacement- and load-controlled ramp functions were used to indent the samples with a 100 µm conospherical indenter tip. The moduli increased with an increase in AuNPs concentration in chitosan. The plasticity index increased with an increase in AuNPs concentration indicating that the deformation became more plastic with an increase in the filler. The results also show the time-dependent viscous response of the nanocomposite is mainly governed by the response of the matrix because the characteristic time scales of the nanocomposite films are independent of the AuNPs concentration.

An implicit representation for the analysis of piecewise affine discrete-time systems

This paper presents a new framework for stability assessment of discrete-time piecewise affine systems. An implicit representation for piecewise functions based on ramp nonlinearities is proposed. Instead of the usual sector inequalities adopted in the study of Lurie systems, we directly exploit properties of the ramp function, which are given by a particular set of identities and inequalities. These properties are then used to derive stability conditions associated to piecewise quadratic Lyapunov functions. These functions are implicitly defined from quadratic forms involving ramp functions. These conditions can be cast as LMIs and their numerical solution is illustrated by examples highlighting the advantages of the proposed method over existing stability analysis methods for PWA systems.

Step, Ramp, Delta, and Differentiable Activation Functions Obtained Using Percolation Equations

This paper presents two new analytical equations, the Two Exponent Phenomenological Percolation Equation (TEPPE) and the Single Exponent Phenomenological Percolation Equation (SEPPE) which, for the proper choice of parameters, approximate the widely used Heaviside Step Function. The plots of the equations presented in the figures in this paper show some, but by no means all, of the step, ramp, delta, and differentiable activation functions that can be obtained using the percolation equations. By adjusting the parameters these equations can give linear, concave, and convex ramp functions, which are basic signals in systems used in engineering and management. The equations are also Analytic Activation Functions, the form or nature of which can be varied by changing the parameters. Differentiating these functions gives delta functions, the height and width of which depend on the parameters used. The TEPPE and SEPPE and their derivatives are presented in terms of the conductivity (<img src=image/13428023_01.gif>) owing to their original use in describing the electrical properties of binary composites, but are applicable to other percolative phenomena. The plots in the figures presented are used to show the response <img src=image/13428023_02.gif> (composite conductivity) for the parameters <img src=image/13428023_03.gif> (higher conductivity component of the composite), <img src=image/13428023_04.gif> (lower conductivity component of the composite) and <img src=image/13428023_05.gif>, the volume fraction of the higher conductivity component in the composite. The additional parameters are the critical volume fraction, <img src=image/13428023_06.gif>, which determines the position of the step or delta function on the <img src=image/13428023_07.gif> axis and one or two exponents <img src=image/13428023_08.gif>, and <img src=image/13428023_09.gif>.

Digital Control and Readout of MEMS Gyroscope Using Second-Order Sliding Mode Control

Microelectromechanical system (MEMS) is a kind of MEMS that has been utilized to monitor the angular speed of moving objects on several occasions and has attracted the interest of several organizations across the globe. This type of sensor has the benefits of excellent integration, cheap cost, and low power utilization. This study begins by describing the research and development of silicon MEMS gyroscopes since the 1980s, including the work of several universities, such as Draper Laboratory and UC Berkeley, as well as various design ideas, control systems, and architectures. Matching resonance frequencies of the driving and sense mechanical resonators may significantly improve the efficiency of MEMS gyroscopes. In a closed-loop readout circuit, however, exact control of the resonance frequency is difficult. Because of their inexpensive production costs in large numbers, MEMS gyroscopes are gaining appeal. Because of substantial nonstationary noise processes in the output of MEMS gyros, such as 1/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}$ </tex-math></inline-formula> noise, this creates difficulty for navigation system designing. In the implementation, relative error in ramp and step function is determined through the proposed methodology. Furthermore, the second-order sliding mode control (SoSMC) is used in the sliding mode of the gyroscope to minimize the chattering effect.

Ramp approximations of Michaelis–Menten functions in a model of plant metabolism

In 2019, Adams, Ehlting, and Edwards showed that in a model of plant phenylalanine metabolism following Michaelis–Menten kinetics, there are two mechanisms by which primary metabolism is prioritized over secondary metabolism when synthesis rates of shikimate, a precursor to phenylalanine, are low: the Precursor Shutoff Valve (PSV), a form of metabolic regulation effected by a series of reactions called the Shikimate Ester Loop (SEL), and threshold separation. They found that the SEL is completely effective in prioritizing primary metabolism when shikimate production is low, but when the SEL is absent, this prioritization is only seen when the threshold constant associated with the secondary pathway is sufficiently larger than that of the primary pathway. Since nonlinear terms can make analysis difficult, here we replace the Michaelis–Menten terms in Adams and colleagues’ model with piecewise approximations we call ramp functions. We show that the ramp function model behaves the same as the original model under low shikimate conditions; the SEL effects PSV type regulation regardless of threshold constants, while without the SEL, primary metabolism is only prioritized when the threshold constant of the secondary pathway is sufficiently large. This is in contrast to a step function version of the model studied by Edwards and Wood in 2021 where the SEL did not effect PSV type regulation on its own.

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed u–p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

A new enrichment scheme for the interfacial crack modeling using the XFEM

A new enrichment scheme is proposed for the interfacial crack modeling in the framework of extended finite element method (XFEM), in which the approximation of displacement in the element including the crack tip is reconstructed by only the Heaviside function and the material interface enrichment function. The proposed enrichment scheme can model not only the discontinuity of displacement across the crack surface but also the discontinuity of displacement gradient across the material interface in the crack tip element with the weight functions. In addition, no blending elements are introduced and it is unnecessary to define the ramp function in the new XFEM formulation. The static and dynamic stress intensity factors (SIFs) of interfacial cracks are analyzed by the new enrichment scheme and the results show that the effect of material interface in the crack tip element plays a significant role in the accuracy of fracture mechanics parameters and the proposed method can predict the deformation more accurately and obtain a more stable dynamic SIFs. The proposed new enrichment scheme can be extended to three dimensional crack modeling in future works.

Investigation of the torque transmission time constant of a multi-disc magnetorheological clutch in the case of ramp function excitation

In this work the torque transmission time constant of a multi-disc magnetorheological (MR) fluid clutch is presented. The self-built clutch contains six layers of MR fluid and it is excited by an external electromagnetic coil. The transmitted torque is measured by a torque sensor using a self-developed LabVIEW software. Torque transmission is measured using ramp excitation with different slopes. The time constant of the clutch is derived from the time delay of the torque response. Our measurements showed the time constants as a hyperbolic function of the slope of the ramp excitation.

Inventory optimization model of deteriorating items with nonlinear ramped type demand function

Inventory models for deteriorating items of a supply chain is of critical essence to the maritime industry. This study proposes a real and economically efficient multicriteria inventory policy of inventory models for deteriorating items of a supply chain with nonlinear ramp functions and permissible delay in payment under inflation, two conditions Shortages Followed by Inventory (SFI) and Inventory Followed by Shortages (IFS) have been considered for the formulation of models. Both the models consist of ordering cost, unit cost, deterioration cost, shortage cost and holding cost with replenishment where delay in payments is allowed. The development of these models is to minimize the total average cost per unit time. In order to validate the models, numerical examples have been considered and the sensitivity of several major parameters of exponential and quadratic functions is analyzed. From the numerical result, it is clear that the cost per unit time of IFS model decreases with the increment of the values of parameters of the quadratic function and holding cost whereas, with the increment of the values of parameters of the exponential function as well as holding cost per unite time, the cost per unit time of SFI model decreases. However, if the values of the parameters of the exponential functions as well as ordering cost and shortage cost increase, the cost per unit time of IFS model increases. On the other hand, it will also increase considering SFI condition, if the values of parameters of the quadratic function as well as ordering cost and shortage cost increase. Finally, it is observed that the model considering IFS case works better than SFI model up to a certain level. &#x0D;

Chemometrics optimized microencapsulation of ergocalciferol using emulsification technique and its physico-chemical characterization

The study reports the microencapsulation of ergocalciferol (vitamin D2) by emulsification technique, the experimental process parameters being chemometrically optimized by d-optimal mixture design approach followed by physico-chemical characterization of the resultant emulsion. Basing on desirability ramp function graph and lab experimentation results, the percentages of Ca stearate (0.124), Ca carbonate (0.385), Ethanol (5.0), Tween 80 (4.16), Span 80 (0.25) showed a maximum of 94.1% encapsulation efficiency. The optimized ergocalciferol emulsion showed particle size in the range of 469–493 nm, polydispersity index 0.23–0.24, zeta potential (ζ) value ranging from -15.27 to -15.35 mv; viscosity and interfacial tension was determined to be 1.401±0.02 mPaS and 23.1 mNm−1 respectively. The resultant emulsion showed no visual change in physical appearance, consistency, and color on keeping undisturbed for 7 days. Results of accelerated stability studies have shown that the initial ergocalciferol or (vitamin D2) content (83.75±0.03%) in the emulsion after storage at (55 °C, 75% RH) was found to be 83.05±0.01% and after storage at (75 °C, 80% RH) is 82.91±0.05%. From the results of accelerated stability studies it can be concluded that vitamin D2 emulsion is comparatively stable at high temperature storage conditions (75 °C, 80% RH). The devised optimized procedure of microencapsulation by emulsification of ergocalciferol was found to be effective with high encapsulation efficiency and significant stability of the emulsion system.

COVID-19 and the prevalence of drug shortages in Canada: a cross-sectional time-series analysis from April 2017 to April 2022.

Background:In March 2020, the Government of Canada introduced measures to reduce intensifying shortages of prescription drugs during the beginning of the COVID-19 pandemic. We sought to assess the extent to which a decline in drug shortages was observed in the months after this policy change.Methods:Our data source was the Drug Shortages Canada Database, which reports shortages by drug product, including shortage start and duration. Using a cross-sectional design, we tracked shortage rates of drug products using a 30-day moving average from Apr. 15, 2017, to Apr. 1, 2022. We used autoregressive integrated moving average modelling with a ramp function to determine the significance of trend changes after policy implementation.Results:We found that of the 13 329 drug products at risk for shortage, 44.7% (n = 5953) had at least 1 shortage event in the past 5 years. Average daily shortage prevalence rates rose from 901 in April 2017 to a peak of 2345 by April 2020. Significant declines (p = 0.02) ensued shortly thereafter, dropping to a rate of 1611 shortages by the end of the first year after policy implementation. However, we did not observe a significant reduction in shortage rates in the second year (p = 0.2), with rates plateauing below 1500 and then rising back above 1600 by the end of March 2022.Interpretation:Drug shortages are common in Canada, including during the initial months of the COVID-19 pandemic. We observed substantial improvements after the implementation of the new measures, but gains appear to have plateaued. Continued vigilance is needed to sustain improvements.

Central composite rotatable design for optimization of trihalomethane extraction and detection through gas chromatography: a case study

Central composite rotatable design (CCRD) was employed to optimize initial temperature (ºC), ramp function (ºC/min) and salt addition for trihalomethane extraction/quantification from the drinking water distribution network in Ratta Amral, Rawalpindi., Pakistan. Drinking water samples were collected from the treatment plant, overhead reservoir and consumer’s taps. The USEPA method for trihalomethane detection 551.1 via gas chromatography was applied using liquid–liquid extraction. The experiments with input variables for sample preparation and operational conditions were performed in a randomized order as per design of experiment by central composite rotatable design and responses were evaluated for model development. A significant (p = 0.005) two-factor interaction model was optimized. Initial temperature was observed to be insignificant (p = 0.64), while ramp function (p = 0.0043) and salt addition (p = 0.04) were significant. Product of salt addition and ramp was significant (p = 0.004), while product of initial temperature and salt addition was insignificant (p = 0.008). With a desirability function of 0.97, an initial temperature of 50 ºC, 6 ºC rise/min to 180 ºC and 0.5 g salt were optimized. It was found that development and optimization of the analytical methods for rapid trihalomethane detection would improve optimization of the current treatment practices in the country.

Improved capillary rheometry for viscous Newtonian filaments

The efficacy of the kinematic differential analysis of McCarroll et al. [“Differential analysis of capillary breakup rheometry for Newtonian liquids,” J. Fluid Mech. 804, 116 (2016)], expanding on McKinley and Tripathi [“How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer,” J. Rheol. 44, 653 (2000)], to evaluate the surface tension to viscosity ratio for Newtonian filaments is examined. The analysis is valid during and after stretch, while the latter is traditionally applied after cessation of stretch as the midfilament radius approaches zero. Through numerical simulations, the evaluation of viscosity is investigated for two common stretch histories: (a) the ramp function and (b) the modified step strain. The challenges with stretch are twofold: rapid stretch (large capillary number) results in a nearly cylindrical filament with a rapid change near the plate that challenges the one-dimensional (1D) approximation, while slow stretch results in a nearly static solution with limited viscous information. We examine the capillary number-aspect ratio parameter space and find the ramp function with small stretching speeds optimal. Hence, the most accurate measurements are taken while the filament is being stretched.

Hydrodynamic Analysis of a Breakwater-Integrated Heaving-Buoy-Type Wave Energy Converter with an Optimal Artificial Damping Scheme

A three-dimensional frequency-domain numerical wave tank (FR-NWT) based on the Rankine panel method was developed. An optimal artificial damping zone (ADZ) scheme was first applied to the FR-NWT to prevent reflection waves from the end walls. Parametric studies of ramp function shape with artificial damping coefficients and damping zone length were conducted to find a proper damping scheme for the frequency domain program. Applying both the Sommerfeld radiation condition and the ADZ scheme to the frequency domain program can reduce the length of the ADZ to less than one wavelength. The FR-NWT developed by the authors was used to calculate the hydrodynamic response of a hemispherical-heaving buoy wave energy converter (WEC) integrated with a seawall-type breakwater of infinite length. A linear power take-off system was used to calculate power generation of the WEC. The global motion of the WEC combined with the breakwater was up to 1.85 times greater than that of the WEC without the breakwater. Moreover, the capture width ratio of the WEC increased approximately 3.67 times more than that of the WEC without the breakwater.

Mechanism Analysis of a Subsequent Commutation Failure and a DC Power Recovery Speed Control Strategy

A subsequent commutation failure (SCF) of the Line-Commutated Converter–High-Voltage Direct Current (LCC-HVDC) may occur during the recovery after the clearance of an AC fault, seriously threatening the safe and stable operation of the LCC-HVDC and the entire post-fault AC/DC hybrid power system. In this study, the mechanism of an SCF as affected by the transient stability was analyzed, and a DC power recovery speed control strategy is proposed as an additional form of control to prevent the occurrence of SCFs. First, the sending-end and receiving-end power systems were modeled as synchronous generators instead of ideal voltage sources, and the mechanism of an SCF as affected by the transient stability was analyzed and verified. Second, the ramp function was adopted to describe the recovery characteristic of DC power, and a model of its recovery was established. Then, the recovery speed control strategy is presented based on the mechanism analysis of SCFs, which can not only be used to avoid the occurrence of SCFs but also increase the transient stability margin of the sending-end power system. Finally, the effectiveness and robustness of the proposed control strategy were validated by using a hybrid electromechanical–electromagnetic model and the full electromagnetic model of the IEEE 39-bus asynchronous interconnection test power system. With the implementation of the proposed control strategy, the safe and stable operation of the LCC-HVDC and AC/DC hybrid power system can be guaranteed. The adaptive DC power recovery speed control strategy will be further investigated in future research work.

Vibration analysis of permanent magnet synchronous motor using coupled finite element analysis and optimized meshless method

Conventional finite element analysis (FEA) performed in electromagnetic-vibration coupling calculation of motor suffers from several significant drawbacks, such as large memory space, high computational cost and heavy reliance on mesh quality for accurate solution. With the traditional meshless method, special attention needs to be paid to correctly impose the boundary condition like FEA. Besides, the matrix is easily prone to be ill-conditioned due to introducing large amount of higher-order basis functions. We propose a novel multi-physical coupling method combining FEA and optimized meshless method. The proposed methodology is further evaluated on the vibration analysis of a 12-slot 10-pole permanent magnet synchronous motor (PMSM). Firstly, 2D stator electromagnetic force is simulated and derived based on the local Jacobian derivative method through FEA. The electromagnetic force spectrum is calculated using FFT analysis and further imported into commercial meshless structural simulation software SimSolid for stator harmonic response analysis. Correct force boundary condition and data mapping between meshless and FEA simulation interface are key to the accuracy of the proposed combined multi-physical modeling methodology. This is achieved by introducing new high-dimensional ramp function in the transition region between FEA and meshless domains, which are defined with the shape functions composed of the FEA and meshless method. This function satisfies the continuity and consistency of the displacement function and ensures the convergence of coupled FEA-meshless method. Subsequently, construction of basis function is key to the establishment of convention meshless discrete equation for the elastic problem of rotating machinery. This is designed by using moving least square theory in cylindrical coordinate system. A harmonic response with meshless method is analyzed by using the mode superposition method to obtain detailed mode shape data, acceleration and displacement distribution of stator. Finally, the tangential continuity and robustness are not well considered in the traditional simulation with FEA coupled meshless method. To mitigate this problem, we propose an optimized meshless method based on modified local basis functions to recalculate the harmonic response motion. Then, the coupling electromagnetic-vibration simulation results of traditional coupled FEA-meshless method, optimized coupled FEA-meshless method and complete FEA coupled method are compared. It is worth noting that the optimized method significantly improves accuracy, robustness and computational speed at the same time. In short, the proposed electromagnetic-structure coupling calculation method provides a novel alternative for the multi-physical coupling calculation of rotating machinery combining FEA and meshless simulation methods.

An analytical heat exchanger model to study dynamic behavior in the case of simultaneous inlet variations

The work aims to improve the accuracy of an analytical heat exchanger dynamic model published recently in the International Journal of Heat and Mass Transfer. As shown in that paper, an analytical model to predict the dynamic performances is useful in some specific problems such as the heat exchanger network design. The proposed model illustrated considerable progress compared with the original one in the dynamic performance prediction aspect through a case problem. In which the accuracy of the time response prediction was improved more than 80%. In addition to increasing the accuracy, the new model also allows reaching the outlet temperature in the time domain with an analytical solution and free of convergence issues. As is the original model, the improved one is still capable of dealing with simultaneous inlet variations and various inlet temperature change forms, such as step, exponential or ramp functions.

Gel Textural Characteristics of Hair Gel with Cocoa Shell Extract by Using Mixture D-optimal Method

This study was used a mixture design to optimize the spreadability and viscosity of topical hair gel incorporates cocoa shell extract. The factor of the hair gel ingredient was thickener (0.2 – 0.8%), styling polymer A (2-5%), styling polymer B (2-6%), and solvent (84.63-91.63%) were studied on two responses selected spreadability and viscosity. The data collected were fitted to the model with high coefficient determination (R2= 0.994 for the spreadability and 0.9937 for the viscosity). The model can be predicted by showing the good lack of fit test result not significant with the p-value bigger than 0.05. From the ramp function simulation, the optimized formulation was selected and established at thickener (0.55%), styling polymer A (3.61%), styling polymer B (3.72%), and solvent (88.55%) with the spreadability and viscosity at 353.77 g.s and 39.91 pa.s respectively. The benefit of using mixture design in this experiment, it can help a formulator to understand the complex interaction between factors and can easily modify the formulation through ramp function simulation to obtain the desired result. The predicted validation test shows that both values were comparable. Under this condition showed that the model development could be used to predict future observations within the design range thickener (0.2 – 0.8%), styling polymer A (2-5%), styling polymer B (2-6%), and solvent (84.63-91.63%).

Modeling the transient dynamic fracture and quasi-static crack growth in cracked functionally graded composites by the extended four-node gradient finite elements

This paper presents numerical simulations of transient dynamic fracture behaviors and quasi-static crack growth in cracked functionally graded composites using the enhanced extended consecutive-interpolation quadrilateral element (XCQ4). The mechanical properties of functional composites are assumed to vary continuously in spatial coordinates. In terms of XCQ4 modeling, only one function of ramp type (either linear, quadratic or cubic order), alternatively to the usual four branch functions, is used as crack-tip enrichment, somewhat reducing the complexity in implementation. Another advantage of employing the ramp function, which is not derived from asymptotic solutions, lies in the less additional degrees of freedom (DOFs) required for the branch functions, saving the computational effort. The merits of the developed approach are demonstrated through our numerical experiments, which are devoted to both dynamic loading with stationary cracks and quasi-static crack growth simulation in FGMs composites. The accuracy of the developed model is verified by comparing the computed results with respect to reference solutions derived from analytical solution, other numerical methods, and experimental data.