**4.1 Modeling of transient state and pressure recovering in aircraft proportional hydraulic servo-actuators**

In the paper is presented computer analysis of hydraulic servo-actuator transient state between its engage and full pressure recovering. In different mathematical forms hydraulic actuator dynamic model is assumed without any geometrical and physical discontinuities and ambiguity of initial pressure conditions. Hydraulic actuator can be assumed with two serial connected compressible fluid flows controlled by supply and return variable fluid flow restrictors enclosed in control servo-valve and separated by actuator piston, expressed by equivalent mass, viscous damping and arbitrary external force. Presented mathematical model includes transient state of hydraulic actuator, which can be described and determined by ambiguity of the initial pressure conditions in actuator chambers as result of the final state of its previous operations and existing fluid leakage which can produce arbitrary value of initial pressure. Initial condition of pressure is primarily caused by external force, which is arbitrary value during actuator operations. Pressure surge in the moment of change direction of piston motion as result of geometric and flow asymmetry of actuator and its control servo-valve is included in the model also. Hydraulic actuator is usually assumed with compressible fluid flow including the effects of its viscosity. Fluid compressibility is assumed as quasi-static change of its density depending of static pressure. Each of the mentioned effects produces local pressure drop and surge and corresponding actuator operational time delay, which is the limiting factor of its cyclic velocity. Dominant influence on actuators time delay (less than 3% of unit step discrete control piston stroke time) is caused by fluid volumetric compressibility. In the paper following problems are treated: pressure discontinues changes in reverse of piston motion direction; nonlinear effects of actuator behavior; actuator dynamic model linearization.

Any direction change of actuator motion produces pressure discontinuity in its source and return pipelines. This is caused by inversion of fluid flow which produce connection change between supply pipeline and actuator chambers. In the moment of fluid flow direction change each of actuator chambers inter-change connections with system pump and return pipeline and produce corresponding discrete change of pressure in actuator chambers. Possible pressure drop or surge is also caused by geometric asymmetry of servo valve.
