Nonlinear model of a servo-hydraulic shaking table with dynamic model of effective bulk modulus

In this paper, based on fluid mechanical expressions and a new modified effective bulk modulus model of hydraulic oil built upon IFAS model (developed at the Institute für Fluidtechnische Antriebe und Steuerungen, RWTH Aachen university), an empirical nonlinear model for a servo-hydraulic uni-axial shaking table is developed. This new model can precisely simulate the acceleration, velocity and position outputs of the system with respect to different kinds of inputs such as pulse and sinusoidal signals for a wide range of frequencies and different weights of the specimen. Therefore, it can be helpful for designing and optimizing the parameters of a model-based controller for tracking reference force or acceleration signals, which is the goal of the shaking table with only position sensor. In the new modified IFAS model, the effective bulk modulus of hydraulic oil on both sides of the piston has been considered as two nonlinear springs, which are connected serially. The minimum stiffness of the spring effect of the hydraulic oil in a symmetric double-acting hydraulic cylinder occurs, when the piston is in the center of its travel, which can be characterized with differential pressure on its both sides. When the differential pressure is less than a specific threshold pressure, these springs have the minimum stiffness and reserve energy in themselves. Based on the experimental observations, this effect has been modeled with a function, which multiplies the IFAS model. The experimental acceleration output of the system demonstrates the dynamic behaviors of the effective bulk modulus of hydraulic oil, which occurs in the center of the piston travel. The parameters of the simulated model are estimated with the nonlinear least square method in MATLAB. Finally, the accuracy of the proposed model for simulating the motion states of the shaking table, by comparing the experimental and simulated results in different ranges of amplitudes and frequencies with respect to the new and the previous model of the hydraulic servo-systems have been shown.