Behind and beyond the Matlab ODE suite

Ashino, Ryuichi; Nagase, Michihiro; Vaillancourt, Rémi

doi:10.1016/s0898-1221(00)00175-9

Cited by 116 publications

(64 citation statements)

References 7 publications

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“…Integration formulas of different complexity can be found in the control literature, see for instance, the trapezoidal rule employed in optimal control algorithms [28]; and the collection of algorithms for nonstiff and stiff problems available in MATLAB [29]. Because ZOH sampling is not capable of filtering out the possible undesirable oscillations caused by bounded disturbances [17], we use an L-stable integrator originated by Rosenbrock [26].…”

Section: A Linearly Implicit L-stable Time Integratormentioning

confidence: 99%

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

Bursi

Stoten

Tondini

et al. 2010

Numerical Meth Engineering

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SUMMARYAdaptive control techniques can be applied to dynamical systems whose parameters are unknown. We propose a technique based on control and numerical analysis approaches to the study of the stability and accuracy of adaptive control algorithms affected by time delay. In particular, we consider the adaptive minimal control synthesis (MCS) algorithm applied to linear time-invariant plants, due to which, the whole controlled system generated from state and control equations discretized by the zero-order-hold (ZOH) sampling is nonlinear. Hence, we propose two linearization procedures for it: the first is via what we term as physical insight and the second is via Taylor series expansion. The physical insight scheme results in useful methods for a priori selection of the controller parameters and of the discrete-time step. As there is an inherent sampling delay in the process, a fixed one-step delay in the discrete-time MCS controller is introduced. This results in a reduction of both the absolute stability regions and the controller performance. Owing to the shortcomings of ZOH sampling in coping with high-frequency disturbances, a linearly implicit L-stable integrator is also used within a two degree-of-freedom controlled system. The effectiveness of the methodology is confirmed both by simulations and by experimental tests.

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Section: A Linearly Implicit L-stable Time Integratormentioning

confidence: 99%

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

Bursi

Stoten

Tondini

et al. 2010

Numerical Meth Engineering

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“…A6c,d and A8c,d that generated them. Figure 2 compares the assembled perturbation solutions to ''exact'' numerical solutions 29,30 of the outer Eq. 15 for c 5 0.333, d 5 0.111, and e 5 0.110.…”

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confidence: 99%

A new perturbation solution to the Michaelis‐Menten problem

Dingee

Anton

2008

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).We develop a new dimensionless representation of the time-dependent mass balances for the Michaelis-Menten (MM) reaction mechanism; we identify several dimensionless parameters that control the fundamental nature of the solution; and we solve the scaled equations with a combined regular and singular perturbation expansion. Unlike several approximate solutions to the MM problem offered previously in the literature, each of which is valid only for some limited range of conditions, the new solution converges accurately for any combination of initial substrate concentration, initial enzyme concentration, and kinetic rate constants. We discuss the physical significance and interdependence of the dimensionless parameters that emerge from our scaling analysis; we use these parameters to categorize previous approximations for the MM problem and to delimit their accuracy; and we verify the accuracy of our solution via comparisons to an exact numerical solution and various approximations offered previously by others. 2008 American Institute of Chemical Engineers AIChE J, 54: [1344][1345][1346][1347][1348][1349][1350][1351][1352][1353][1354][1355][1356][1357] 2008 Keywords: mathematical modeling, reaction kinetics, bioengineering Introduction Homogeneous, enzyme-catalyzed reactions nearly always occur via a two-step process known as the ''MichaelisMenten'' (MM) mechanism. [1][2][3] In the first elementary reaction, the enzyme E attaches reversibly to the substrate molecule S to form a complex C, i.e.and in the second elementary reaction, the bound enzyme converts the substrate irreversibly to product P and releases it, which returns the enzyme to solution, i.e.,The parameters k 1 [units mol/vol-time], k 21 [time 21], and k 2 [time 21 ] are the kinetic rate constants for each elementary reaction as shown. 4 One frequently seeks to measure these rate constants (or combinations thereof) as accurately as possible for various enzyme/substrate combinations to compare their performance or for use in simulations of complex, multi-step, multi-component biochemical processes. 5,6 Four ordinary differential equations are required to describe the time-dependent concentrations E(t), S(t), C(t), and P(t) in a reactor where an MM reaction is occurring:From this point forward we use combined kinetics parameters that are preferred by the biochemistry community:Correspondence concerning this article should be addressed to A. B. Anton at aba6@cornell.edu. ; K D ¼ k À1 =k 1 is the dissociation equilibrium constant of the enzyme-substrate complex; andÞ=k 1 is the MM constant. 4 Each of these has units of concentration [mol/vol] and can range between zero and infinity for different enzymesubstrate combinations. They quantify in some sense the relative tendency of enzyme and substrate to distribute among initial, intermediate, and final states during the reaction. Typically, the reaction is carried out in a closed batch reactor charged with an initial concentration of enzyme (E T ) and subs...

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“…We will assume here the existence of event detection routines. For instance, in MATLAB (Higham and Higham, 2005) the event detection routines are built-in and can easily be used together with the likewise built-in ODE solvers in order to integrate trajectories and to locate events along them as precisely as the accuracy of MATLAB permits (for more details of the MATLAB ODE routines, see (Shampine and Reichelt, 1997;Ashino et al, 2000)). However, standard methods, for example, the so-called secant type methods, can easily be implemented and have proven to be fast and reliable.…”

Section: The Event-driven Simulation Methodsmentioning

confidence: 99%

Drilling Systems: Stability and Hidden Oscillations

Kiseleva

Kuznetsov

Леонов

et al. 2013

Discontinuity and Complexity in Nonlinear Physical Systems

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Esitetään Jyväskylän yliopiston informaatioteknologian tiedekunnan suostumuksella julkisesti tarkastettavaksi yliopiston Agora-rakennuksen Delta-salissa joulukuun 16. päivänä 2013 kello 12.Academic dissertation to be publicly discussed, by permission of the Faculty of Information Technology of the University of Jyväskylä, in building Agora, auditorium Delta, on December 16, 2013 at 12 o'clock noon. UNIVERSITY OF JYVÄSKYLÄ JYVÄSKYLÄ 2013Oscillations This work is devoted to the study of electromechanical models of induction motorpowered drilling systems. This is a current issue, as drilling equipment failures cause significant time and expenditure losses for drilling companies. Although there are many papers devoted to the investigation of these systems, equipment failures still occur frequently in the drilling industry. In this study, we continue investigations begun by researchers from the Eindhoven University of Technology, who introduced an experimental model of a drilling system. The model consists of two discs connected to each other by a steel string that experiences purely torsional deformation. The upper disc is connected to the driving part. The lower disc, representing the bottom end of the drill-string, experiences friction torque caused mainly by interaction with the shale. The key idea of the present study that distinguishes it from the previous model was the introduction of more complex equations of the driving part, in particular, considerations of the induction motor.Towards this end, two new mathematical models are considered. The first is a simplified one, its prototype being an electric hand drill. In this case it is assumed that the drill string is absolutely rigid and the friction torque acting on the lower part of the drill-string has asymmetric characteristics of the Coulomb type. The qualitative analysis of this model made it possible to obtain parameters on permissible loads (i.e., permissible values of the friction torque) in case the system remained in operational mode after the shale's type changes. Using computer modeling, analysis of sudden load appearance was also performed.The second mathematical model focuses on the torsional deformation of the drill during operation. For the friction torque with Coulomb type asymmetric characteristic, local analysis of the system is provided. The author carried out computer modeling of the friction model created by the researches at the University of Eindhoven. In this model, we found an interesting effect represented by hidden stick-slip oscillations.The results of the study have been published in 11 papers.

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Behind and beyond the Matlab ODE suite

Cited by 116 publications

References 7 publications

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

A new perturbation solution to the Michaelis‐Menten problem

Drilling Systems: Stability and Hidden Oscillations

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