Annotation: The use of Langrangian multipliers at solution of optimal control problems in linear statement with qua dratic quality criterion leads to the necessity of solving boundary value problem with conditions for multipliers at the right end of control interval. Solution of the obtained equations for the purpose of regulation synthesis in forward time in this case does not produce stabilizing effect, as a rule. For regulation synthesis, the met hod is widely used of analytical construction of optimal regulator based on stabilizing matrix, which is obtained by solution of algebraic Riccati equation. However, in this case, there are some difficulties ‒ the necessity of calculating the stabilizing matrix, impossibility of calculating this matrix in non-stationary problem. The article proposes the regulation synthesis method by way of solving boundary value problem on regulation cycle i nterval. For this purpose, the differential equations for state parameters and Langrangian multipliers are expressed in the form of finite-difference linear relations. Taking into account that the state parameters and Langrangian multipliers are equal to zero at the end of cycle, the Langrangian multipliers at the beginning of cycle are determined by known values of state parameters for the same moment through solving the above linear system. The obtained values form the regulation law. In consequence of small duration of regulation cycle, an amplifying coefficient is introduced in the regulation law. Its value is determined based on results of preliminary modeling. Efficiency of the proposed method was verified by the example of adopted dynamic system, including non-stationary. The amplifying coefficient is fairly simply selected by the type of stabilization process. The proposed method may be used in the control systems of rockets of various purpose for motion parameters regulation.

Annotation: During experimental investigation of the dynamic characteristics of a pneumatic test bench for testing liquid rocket engine high-flowrate automatic units, the effect was detected of 20-35% sound speed increase in the gas flow moving along the channel with corrugated wall (metal hose) which is a part of test bench drain system. The article presents the results of experiments and the task of theoretical justification of the effect is solved. It is indicated that its causes may be two mutually complementary factors – a decrease of gas compressibility at eddy motion and oscillations of metal hose wall. The physical model is considered that describes variation of gas elasticity and density in the conditions of high flow vorticity. It is supposed that in the near-wall layer of the channel, toroidal vortexes (vortex rings) are formed, which move into turbulent core of the flow where their size decreases and the velocity of rotation around the ring axis of torus increases. The spiral shape of the corrugation ensures also axial rotation, which increases vortexes stability. The intensive rotation around the ring axis creates considerable centrifugal forces; as a result, the dependence of pressure on gas density and the sound speed increase. The mathematical model has been developed that describes coupled longitudinal-lateral oscillations of gas and channel’s corrugated shell. It is indicated that in the investigated system, two mutually influencing wave types are present – longitudinal, which mainly transfer gas pressure pulses along the channel and lateral ones, which transfer the shell radial deformation pulses. As a result of modeling, it has been ascertained that because of the lateral oscillations of the wall, the propagation rate of gas pressure longitudinal waves (having the same wave length as in the experiments at test bench) turns out to be higher than adiabatic sound speed.

Annotation: Mission control of the orbital space plane is one of the actual and complicated applied problems of the theory of mobile objects control. Dynamic configuration of this plane as an object of control is described by the system of non-linear differential equations of higher order. Research of stability of such system is a difficult problem. However, thanks to known theorems of Lyapunov, often stability of the real system can be estimated by the roots of the characteristic equation of the linearized system. Thereupon the stability analysis in the linear setting is the necessary link in the process of orbital space plane control system development. Among the methods of synthesis of the automatic control linear systems developed to date one can emphasize the trend, which has become widely-spread in the engineering area. According to this trend the issues of synthesis of the dynamic regulator, observability and controllability for the orbital space plane are considered. Procedure of selection of the dynamic regulator parameters at the early phase of development of the control system for the orbital space plane motion about the center of mass is suggested. Observability and controllability of the orbital space plane are considered. It is shown that the considered control system of the orbital space plane is observable and controllable, i.e. it is possible to develop the stable dynamic regulator, which provides the required speed and accuracy of the angular position of the orbital space plane during the orbital flight. Factors selection procedure is offered for the factors being the part of the control laws for the control system actuators.

Annotation: The basic results of the design calculations and mathematical modelling of the control processes in the precision high-speed servo drive are presented, as well as results of experimental studies of the functional mock-up of this servo drive’s movable gears of the throttle and fuel flow regulator of the ILV main engine. Major task of the studies was theoretical and experimental verification of the required static and dynamic accuracy of the servo drive in the process of try-out of the command signals reception from the main engine’s controller. In the phase of development, theoretical study of the linearized servo drive with application of transformations and theorems of Laplace passages to the limit is conducted. Analytical dependences between servo drive circuit parametres, its elements and characteristics of the control signals are obtained. Instrument errors and servostatic elasticity of the servo drive are calculated. Calculation model including the basic nonlinearities of this servo drive is prepared. Mathematical modelling of the control processes is conducted according to the computational model, varying the circuit and design parameters of the electric drive. Results of the theoretical studies were taken as input data for the requirements specification document to develop the executive unit with the electromotor, reduction gear and output shaft position sensor, and the control box. Functional mockups of the executive unit, control box, as well as the computer-controlled technological test console were manufactured on the basis of the requirements specification documents. The required scope of the laboratory-development tests of the functional mock-up of the servo drive was conducted. Results of the conducted activities confirm the achievement of the required accuracies of the servo drive in the laboratory environment.