Trajectory sensitivity analysis of first order and second order on position control system of highly integrated valve-controlled cylinder

Abstract

A Highly-integrated valve-controlled cylinder (HIVC) that has the advantage of large power weight ratio and fast response is widely applied in many fields. To ensure high performance of HIVC, control strategy selection and structure parameters optimization are essential; thus, performance-influenced main parameters and secondary parameters should be well-grasped to target control compensation and structure optimization. Trajectory sensitivity analysis (TSA), a branch of sensitivity analysis, can be adapted to research on the effects of control and structure parameter variation on system performance; the analysis conclusions can be used to improve system performance and the analysis has been applied in many applications in various fields. In this paper, based on the mathematical model of the First-order trajectory sensitivity analysis (FOTSA), the mathematical model of Second trajectory sensitivity analysis (SOTSA) is further derived; the general expression of the second-order trajectory sensitivity equations and the special expression that is applicable to each system parameter sensitivity analysis of HIVC are built respectively. Furthermore, based on the position control system of the nonlinear mathematical model of HIVC involved with servo valve dynamic characteristics, flow-pressure nonlinearity, initial piston position of servo cylinder, and friction nonlinearity, the coefficient items and the free items matrices of the special expression are calculated. Moreover, the First-order trajectory sensitivity function (FOTSF) and the Second trajectory sensitivity function (SOTSF) of the 17 main parameters in HIVC are computed on the MATLAB/Simulink platform under nine typical working conditions of the displacement step response. Then, the dynamic change rules and the differences and similarities of each parameter sensitivity analysis results are obtained through FOTSA and SOTSA under different working conditions with different parameter variations; each parameter sensitivity variation histogram based on the two kinds of sensitivity indexes, including the maximum value of the percentage absolute value and the absolute value summation within the sampling time, are given. Furthermore, differences and similarities of each parameter sensitivity index change rule and value are quantitatively analyzed. Finally, the sensitivity index change rules and values of the four parameters in the position control system of HIVC, including system supply oil pressure, proportion gain, initial piston position of servo cylinder, and load are experimentally verified. All above studies indicate that each parameter SOTSA result of HIVC vary under different working conditions. When parameter variation is significant, the differences in certain parameter sensitivity analysis between FOSTA and SOTSA are relatively significant; and SOTSA results are more similar to the test results, which illustrates that SOTSA results are more accurate.