Design and Experimental Evaluation of a Robust Position Controller for an Electrohydrostatic Actuator Using Adaptive Antiwindup Sliding Mode Scheme

Table 6

List of terms.

Notation	Description	Unit
A	Pressurized area of hydraulic cylinder of EHA	m^2
𝐵	Viscous friction coefficient	N/m/sec
𝐶𝑇	Equivalent leakage coefficient	m^3/sec/Pa
𝐷𝑝	Pump displacement	m^3/rad
𝑒	Position error	mm
𝑖	Current	Arms
𝐾pipe	Pipe coefficient relating pressure drop to flow	Pa/m^6/sec^2
𝐾𝑠	Angular velocity to voltage gain	—
𝐾𝑝	Proportional control gain	—
𝐾𝑖	Integral control gain	—
𝐾𝑑	Differential control gain	—
𝑘𝑎	Antiwindup gain	—
𝑘1, 𝑘2, 𝑘3,𝐷, 𝐾, 𝛾	Positive design parameters of adaptive PID sliding mode controller	—
𝐾𝑚, 𝑇1, 𝑇𝑚1, 𝑇𝑚2	Parameters of dynamic model for the BLDC motor with controller	—
L	Internal leakage coefficient of the cylinder	m^3/Pa/sec
M	Mass load of position control test rig of EHA	N
𝑝1, 𝑝2	Cylinder inlet/outlet chamber pressure	Pa
𝑝pipe	Pressure drop of pipe between the pump and the cylinder	Pa
𝑄1, 𝑄2	Cylinder inlet/outlet flow	m^3/sec
𝑠	Laplace operator	—
𝑇𝑚	Torque of BLDC motor	Nm/(rad/sec)
𝑇𝑠	Sampling time	sec
𝑉𝑎, 𝑉𝑏	Volumes of inlet/outlet pipe and cylinder chamber	m^3
𝑉0	Mean volume of pipe and cylinder chamber.	m^3
𝑣𝑒	Voltage signal of error for angular velocity of BLDC motor	V
𝑣𝑟	Voltage signal of reference angular velocity of BLDC motor	V
𝑣𝜔	Voltage signal of angular velocity	V
𝑥	Cylinder displacement	m
𝑦^𝑑step(𝑡)	Desired step response of the optimal PID and antiwindup PID control system	—
𝑦step(𝑡)	Step response by the identified transfer function	—
𝛽𝑒	Effective bulk modulus	Pa
𝜔𝑝	Pump angular velocity	rad/sec
𝜁	Sliding surface	—
𝜉	Pump cross port leakage coefficient	m^3/Pa/sec