A class of discontinuous dynamical systems I. An ideal gas–liquid system

Moudgalya, Kannan M.; Ryali, Venkatarao

doi:10.1016/s0009-2509(01)00043-4

Cited by 17 publications

(19 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the approach of [1], a similar conclusion can be arrived at for M G G ≥ M L G . It can be shown that f + , f − and ϕ given by Equations 19, 20 and 21, respectively, satisfy Theorem 1.…”

Section: It Is a Straight Line That Passes Throughsupporting

confidence: 53%

“…All the above discussed properties hold good also in a closed loop configuration, such as, the one considered by [1]. The reason is that the controller strengthens self-regulation.…”

Section: Stability Of the General Nonlinear Systemmentioning

confidence: 94%

“…This system was studied by [1] with the hydraulic exponent n = 1 in Equations 12 and 16. In reality, however, there could be other functional forms.…”

Section: Gas-liquid System With Nonlinear Flow Modelmentioning

confidence: 99%

“…It is also well known that in the presence of friction, other exponents may also have to be used, see for example [5]. It has been shown by [1] that this system reaches a sliding mode, characterised by the simultaneous flow of both gas and liquid. The sliding process considered here is unusual in the sense that gas and liquid compete for access to the outflow tube.…”

Section: Gas-liquid System With Nonlinear Flow Modelmentioning

confidence: 99%

“…Such a system and its long time behaviour were studied by [1], who restrict their attention to the case when the outflow is a linear function of pressure drop. Their findings have been experimentally validated by [2].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sliding Motion and Stability of a Class of Discontinuous Dynamical Systems

2004

Self Cite

View full text Add to dashboard Cite

Abstract. A closed container with gas and liquid inflows and one outlet for outflow, described by a nonlinear hydraulic model, is shown to reach a state of sliding mode. Through a Lyapunov function, the sliding motion is shown to be stable for all positive exponents in the flow model. This property is independent of factors, such as, valve opening, valve coefficients, friction factor and initial states, making this device a suitable one to study two phase flow. The sliding solution of this system with square root hydraulic model is found using Filippov's equivalent dynamic approach. The discontinuous system is also solved using an accurate and efficient method that accounts for persistent discontinuity sticking. These two solutions are shown to be in exact agreement.Keywords: Discontinuous System, Sliding Mode, Lyapunov Function, Self Regulating System, Slug Flow, Two Phase Flow. Nomenclature:Di -Region in (MG, ML) phase plane; FG -Gas feed rate, mol/s; FL -Liquid feed rate, mol/s; kG -Valve coefficient for liquid flow; kL -Valve coefficient for gas flow; L -Liquid outflow rate, mol/s and subscript to indicate liquid; G -Gas outflow rate, mol/s and subscript to indicate gas; MG -Gas holdup in the system, mol; M * G -Gas holdup at the beginning of sliding motion, mol; MG,ss -Gas holdup at steady state, mol; M L G -Limiting value of gas holdup defined for sliding motion, mol; ML -Liquid holdup in the system, mol; P -System pressure, atm; PssSteady state pressure, atm; Pout -Outlet pressure, atm; R -Gas constant; SiSwitching/Sliding surface; T -Temperature, K; t -Time, s; t * -Time when sliding begins, s; V -Volume of the reactor, lit; V d -Volume of the reactor below the dip tube, lit; x -Extent of valve opening; α -Fraction time of applicability of liquid model while sliding; ϕ -Switching function; ϕ1 -Switching function restricted to MG > M L G ; ρL -Density of liquid in mol/lit.

show abstract

Section: It Is a Straight Line That Passes Throughsupporting

confidence: 53%

“…All the above discussed properties hold good also in a closed loop configuration, such as, the one considered by [1]. The reason is that the controller strengthens self-regulation.…”

Section: Stability Of the General Nonlinear Systemmentioning

confidence: 94%

“…This system was studied by [1] with the hydraulic exponent n = 1 in Equations 12 and 16. In reality, however, there could be other functional forms.…”

Section: Gas-liquid System With Nonlinear Flow Modelmentioning

confidence: 99%

Section: Gas-liquid System With Nonlinear Flow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sliding Motion and Stability of a Class of Discontinuous Dynamical Systems

2004

Self Cite

View full text Add to dashboard Cite

show abstract

Hybrid modeling and dynamics of a controlled reverse flow reactor

Mancusi¹,

Russo²,

Brasiello³

et al. 2007

AIChE Journal

View full text Add to dashboard Cite

in Wiley InterScience (www.interscience.wiley.com).A hybrid system approach is adopted to study the dynamic behavior of a controlled reverse flow reactor, where the occurrence of flow inversions is caused by a feedback control strategy. With this approach it is analyzed, theoretically and numerically a typical behavior of hybrid systems: Zeno phenomena. Hybrid system theory is also adopted to define a suitable Poincare`map that is a composition of two switching maps. Based on the Poincare´map an efficient methodology is developed for the continuation of limit cycles, and detection of local bifurcations as the set-point value, and inlet temperature are varied. This analysis shows that Zeno states can be coexisting with symmetric and asymmetric periodic regimes in a wide range of the parameters. The analysis of the nonlinear behavior and Zeno phenomena gives an insight on the limits of some model assumptions, and how these assumptions should be removed to avoid the unphysical response of Zeno executions. Considering a time delay due to the valves in the reactor, the unphysical Zeno state is removed, while Zeno like oscillations are shown to be still persistent.

show abstract