Mathematical modeling of electromechanical steering gear with ball-screw actuator with account for nonlinearities of dry friction and backlash types
The paper addresses the multi-purpose mathematical model of the electro-mechanical actuator’s (EMA) dynamics. It contains the general description of the EMA, which was the object for the modelling, the description of the mathematical model developed and mathematical modeling results. The actuator was developed in the frame of the Russian-European project called RESEARCH for the elevator deflection of a regional passenger airplane. The mathematical model was implemented within MATLAB/Simulink software. The actuator model consists of four submodels of its physical constituent parts such as controller, power electronics block, electric motor and mechanical gearbox (ball screw transducer). Programmatically switchable models with various level of detail of physical processes were realized for each part. The electrics were realizedby the submodels of a single-phase DC motor and a simplified controller corresponding to it. It also contains three-phase induction motor with permanent magnets, regulated by a controller, realizing vector control in {p, q}-coordinates. Power electronics is modeled either by simplified dynamic elements, or on a physical level in detail (electronic components level). Special attention was payed to mechanical part of the actuator modeling, i. e. various submodels of non-linear mechanical effects of a “dry friction” and “backlash” were realized. Thus, we managed to ensure a balance between modeling accuracy and speed within the framework of a single model. Based on mathematical modeling results the paper demonstrates how the dry friction and backlash parameters, as well as software methods of their realization effect on the actuator’s regulation quality and its characteristics. It shows that program splitting of the actuator states (idle, motion, initiation) based on velocity smallness without using the sign function approximation is optimal method of dry friction effect accounting. It ensures reproduction of the necessary actuator motion pattern with acceptable integration step (10-4 s). The paper demonstrates also that accounting for linear stiffness of the actuator’s ball screw transducer has insignificant effect on the actuator’s frequency response within the frequency range of control surface control. It is shown that the replacement of the three-phase motor with a single-phase one while reducing the EMA model leads to different regulation character even while using the similar regulator structure and comparable PID-regulator coefficients. The developed model can be used while the electromechanical flight control systems design for various engineering tasks, characterized by significantly varyng requirements imposed on the model in use. These tasks include: 1) development of the actuator and its control system, including actuator digital regulator synthesis; 2) actuator static and dynamic characteristics express-analysis; 3) obtaining reference actuator characteristics including small control signals; 4) analysis of transient responses and stability margins of the closed “aircraft - flight control system - actuator” control loop, including in-line simulation; 5) study and optimization of actuator thermal conditions while operating in the closed bay of the outer wing.