Internal Leakage Fault Detection and Tolerant Control of Single-Rod Hydraulic Actuators

Table 1

Nominal equivalent parameters of the considered hydraulic system.

Symbol	Parameter	Nominal value
𝑚	The total mass of the load	40 kg
𝐴1	The ram area of the cylinder	1.92×10^−4 m^2
𝐴2	The ram area of the cylinder	1.92×10^−4 m^2
𝐵	The coefficient of the viscous friction	45 N·s/m
𝑓𝑐	The Coulomb friction	52 N
𝑓𝑠	The stiction friction	78 N
𝑦̇𝑣	The Stribeck velocity	0.013 m/s
𝜎	The empirical parameter of the Stribeck effect	2
𝛽𝑒=𝛽1=𝛽2	The bulk modulus of the oil in the cylinder	200 Mpa
𝑉01	The original total control volume of the cylinder	1.76×10^−4 m^3
𝑉02	The original total control volume of the cylinder	1.76×10^−4 m^3
𝐶𝑙	The normal coefficient of the internal leakage	8.9×10^−12 m^5/Ns
𝑘𝑞=𝑘𝑞1=𝑘𝑞2	The flow gain of the servovalve	9.92×10^−6 m^4/(s·A·√𝑁)
𝑃𝑠	The supply pressure	7 Mpa
𝑃𝑟	The return pressure	0 Mpa
𝜔𝑣	The servovalve natural frequency	628 rad/s
𝜁𝑣	The servovalve damping ratio	0.7
𝑘𝑖	The gain of the servovalve	4×10^−3 A/V