Page 130 - Mechatronics with Experiments

116 MECHATRONICS
θ cmd
Kva
θ
cmd
Kvf Umax
Friction compensation
Umin
θ
cmd e Notch u DAC
KP
filter
Deadband and limit
on error entering the
Integral
servo loop control KD
logic
u I max
KI Gravity
uImin
/d
compensation dt
f(g)= “mg Sinθ”
θ act
FIGURE 2.51: Practical implementation and various modifications of PID control algorithm:
(i) velocity and acceleration feedforward, (ii) deadband and limit on error passed on to the
servo loop, (iii) enable/disable integral action, (iv) friction compensation, (v) gravity
compensation, (vi) notch filters, (vii) control signal limit.

gets large. The acceleration feedforward (K ) term approximately tries to cancel or
af
reduce the inertial effects on the dynamic response.
2. Deadband, applied on the error that is allowed to enter into the servo control loop, is
sometimes useful in some applications, when a certain amount of error is acceptable
and it is more important to hold the output steady instead of trying to achieve perfect
zero error. Similarly, limiting the maximum value of the error passed on to the servo
loop that is multiplied with the PID gains further might improve transient response
and reduce overshoot.
3. In some cases, integral control maybe completely enabled or disabled. For instance,
we may disable the integral control while in transient response phase, that is derivative
of the command signal is not zero, and then enable it in steady-state condition when
derivative of command signal is zero. In motion control applications, if the closed
loop control variable is the position, then the derivative of the command signal is the
commanded velocity.
...
if ( (dot_theta_cmd) != 0)
Ki = 0.0
else
Ki = Ki_original
end

u_i = u_i + K_i * e * T_sampling
...
4. Friction is a common problem in motion control systems. If the friction force/torque is
known approximately as a function of speed and/or position, it can be compensated for
in the feedforward or feedback path. Compensating in feedforward is more reliable
in terms of stability. Compensating in the feedback block may lead to instability
due to the stick-slip type discontinuous nature and variations in the actual friction
conditions.