Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism

Halanay, A.; Safta, Carmen-Anca; Ursu, Ioan; Ursu, Felicia

doi:10.1023/b:engi.0000032810.53387.d9

Cited by 29 publications

(17 citation statements)

References 11 publications

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“…The electrohydraulic servo system was examined by a close-to-reality mathematical model, taking into account the non-linear and dynamic behaviour of hydraulic elements and the leakage of hydraulic actuator [16]- [20].…”

Section: Mathematical Model Of the Electrohydraulic Positioning Systemmentioning

confidence: 99%

Effect of Leakage in Electrohydraulic Servo Systems Based on Complex Nonlinear Mathematical Model and Experimental Results

2015

APH

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Section: Mathematical Model Of the Electrohydraulic Positioning Systemmentioning

confidence: 99%

Effect of Leakage in Electrohydraulic Servo Systems Based on Complex Nonlinear Mathematical Model and Experimental Results

2015

APH

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“…The mathematical model that describes the dynamical behavior of the EHMSs is a nonlinear ordinary differential equation system composed by the mass and energy conservation equations, the actuator movement equations and the controller equation, [7,8]. Denoted with x 1 -the load displacement, x 2 -load velocity, x 3 and x 4 -pressures in the cylinder's chambers, x 5 -the valve position and u the control variable, the mathematical model of the controlled electro-hydraulic servomechanism is the following: °°°°°°¯°°°°°°®…”

Section: Mathematical Model Of Ehsmmentioning

confidence: 99%

“…The linear system stability and the linear controller design was discussed in previous papers , [7,8]. For 0 O we have the same critical case as in [7] and [8] and using the Lyapunov-Malkin's Theorem [9] it was demonstrated that the equilibrium is stable for every solution that starts close enough from the equilibrium point (y 10 = y 20 = y 30 = y 40 = y 50 = 0).…”

Section: Mathematical Model Of Ehsmmentioning

confidence: 99%

“…To calculate the eigenvalues and their sensitivity the system's Jacobian and its partial derivatives with respect the parameters are determined. The EHSM proposed in this study is described by the mathematical model developed in [7] and [8] where combining a four-dimensional nonlinear model for mecano-hydraulic servomechanism with a linear controller to stabilize the zero solution, a fivedimensional nonlinear model for an electro-hydraulic servomechanism is deduced.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity analysis of eigenvalues for an electro-hydraulic servomechanism

Stoia-Djeska

Safta

Halanay

et al. 2012

AIP Conference Proceedings

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Electro-hydraulic servomechanisms (EHSM) are important components of flight control systems and their role is to control the movement of the flying control surfaces in response to the movement of the cockpit controls. As flight-control systems, the EHSMs have a fast dynamic response, a high power to inertia ratio and high control accuracy. The paper is devoted to the study of the sensitivity for an electro-hydraulic servomechanism used for an aircraft aileron action. The mathematical model of the EHSM used in this paper includes a large number of parameters whose actual values may vary within some ranges of uncertainty. It consists in a nonlinear ordinary differential equation system composed by the mass and energy conservation equations, the actuator movement equations and the controller equation. In this work the focus is on the sensitivities of the eigenvalues of the linearized homogeneous system, which are the partial derivatives of the eigenvalues of the state-space system with respect the parameters. These are obtained using a modal approach based on the eigenvectors of the state-space direct and adjoint systems. To calculate the eigenvalues and their sensitivity the system's Jacobian and its partial derivatives with respect the parameters are determined. The calculation of the derivative of the Jacobian matrix with respect to the parameters is not a simple task and for many situations it must be done numerically. The system stability is studied in relation with three parameters: m, the equivalent inertial load of primary control surface reduced to the actuator rod; B, the bulk modulus of oil and p a pressure supply proportionality coefficient. All the sensitivities calculated in this work are in good agreement with those obtained through recalculations.

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“…(20) is rather a modelling hypothesis [20] than a direct consequence of physical laws and mathematical inference on these. The evading of this equation leads to an extended MM, involving the pressures p 1 ; p 2 as state variables; this MM was already introduced a long while ago by Wang [21], but only sporadically was taken back.…”

Section: Backstepping For An Extended Ehs MMmentioning

confidence: 99%