Sensitivity analysis of eigenvalues for an electrohydraulic servomechanism
Abstract
Electrohydraulic 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 flightcontrol 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 electrohydraulic 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 statespace system with respect the parameters. These are obtained using a modal approach based on the eigenvectors of the statespace 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.
 Publication:

9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012
 Pub Date:
 November 2012
 DOI:
 10.1063/1.4765605
 Bibcode:
 2012AIPC.1493..977S