No abstract

The gramian-based approach is proposed for estimation of control costs. The inputs of object are considered to be finite-dimensional. Authors proposed to consider the norm of control vector as a measure of system power consumption, which could be estimated by upper and lower bounds. These control cost bounds are calculated by means of singular values of control costs gramian and the norm of initial state vector while control costs gramian is calculated from Lyapunov equation. The algorithm and numerical example for harmonic exogenous impact are attached.

The purpose of the article is to develop a mathematical model of the power regulator using an A11VO axial-piston pump (Bosch Rexroth) as an example and determine the effect of pressure on the control process parameters. A mathematical model of the regulator was developed; a scheme for its solution in the Matlab-Simulink environment was suggested; dependencies of the spool movement (x1), piston (x2), transition time (t) and other parameters on the pressure in the pressure line (p) have been determined. The mathematical model of the regulator establishes the effect of pressure on control process parameters. When the pressure increases from 30 to 45 MPa, the regulator spool moves at a distance varying from 0.4-2.8 mm. The spool movement is proportional to the pressure. The piston movement is more sensitive to the change in pressure. It changes within the range of 3-19 mm, while the relationship is non-linear. The cylidner pressure and the ratio of rocker arms are proportional to the pressure and increase 1.5 times; the transition time of is expressed by a non-linear dependence and decreases twofold .

A mathematical model of the regulator was developed; a scheme for its solution in the Matlab-Simulink environment was suggested; dependencies of the spool movement (x1), piston (x2), transition time (t) and other parameters on the pressure in the pressure line (p) have been determined. The mathematical model of the regulator establishes the effect of pressure on control process parameters. When the pressure increases from 30 to 45 MPa, the regulator spool moves at a distance varying from 0.4 - 2.8 mm. The spool movement is proportional to the pressure. The piston movement is more sensitive to the change in pressure. It changes within the range of 3–19 mm, while the relationship is non-linear. The cylidner pressure and the ratio of rocker arms are proportional to the pressure and increases 1.5 times; the transition time is expressed by a non-linear dependence and decreases two-fold.