Page 574 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
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5. Different damping in the cylinder and load dynamics, c .
p
6. Gains of PID controller; especially K value since velocity can reach large values for
d
very short periods of time due to high frequency content.
Remark on “Dither” Signal in Hydraulic Control There are two physical
sources of hysteresis in a hydraulic valve:
1. stiction friction,
2. electromagnetic hysteresis.
Electromagnetic materials have hysteresis. Let us assume that current is zero and magnetic
field is zero in a solenoid. When current is applied from zero to a finite value, a magnetic
field will develop approximately proportional to the current magnitude. When the current
is reduced back to zero, the magnetic field will not be exactly zero, but some residual field
will be left. This is the nature of electromagnetism and materials used in electromagnetic
actuators such as solenoids.
Stiction friction presents a position control problem for valves. Due to stiction friction,
when the control signal (current) is small, the spool movement may be prevented. In order
to avoid this, it is very common in hydraulic circuits to add (“superimpose”) a dither signal
to the regular control signal in order to keep the valve spool moving about a nominal
operating condition.
The dither signal is a periodic signal (i.e., sinusoidal) with a frequency typically in
the range of 100 Hz to 300 Hz, and its magnitude is in the range of 2–10% of the maximum
current signal,
i dither = A dither ⋅ sin(2 w dither t) (7.638)
where A dither = 0.02 ∼ 0.10 ⋅ i max , and w dither = 100 ∼ 300 Hz. The frequency and magni-
tude of the dither and its magnitude selection depends on the specific type of valve appli-
cation and is mostly determined by experimentation. The key is that the dither frequency
should be large enough not to affect the normal position response within the bandwidth
of the valve, but small enough still to cause some motion to break the stiction friction.
The dither signal can either be generated digitally in software or by an analog operational
amplifier circuit and added to the normal current signal.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Filename: EH_Servo_Sim.m
global D_p w_shaft p_max
global Q_rv x_vmax T_vmax p_r c_v w_n tau_a K_a K_t i_v x_v
global beta V_hose_pv V_hose_va V_hose_vb A_a A_b l_cyl m_p c_p m_l
F_load

global Q_p Q_v Q_r
global p_p p_a p_b p_t
global y_d ydot_d y ydot K_fb K_p K_i K_d u_i i_cmd

% Parameters of the components of the EH hydraulic circuit

D_p = 20 ∗ 10ˆ-6 ; % mˆ3/rev
p_max = 20.685 ∗10ˆ6 ; % [N/mˆ2] = Pa
x_vmax = 10 ∗ 10ˆ-3 ; % m