Page 131 - Mechatronics with Experiments

CLOSED LOOP CONTROL 117
5. Gravitational load can be compensated for as a function of the measured position
and inertia of the of the controlled axis. In nonlinear mechanisms and varying load
conditions, a conservative value of effective inertia may be used or a more detailed
inertia estimation algorithm may be used to support this control function.
6. Notch filters are used to reduce the likelihood of exciting the structural resonance
frequencies of the controlled sytem by minimizing the frequency content of the
control signal in the vicinity of the resonant frequencies. If there is only one resonant
frequency, then only a single second-order digital Notch filter would be sufficient.
If there are multiple resonant frequencies of concern, then multiple Notch filters in
series should be used.
7. Finally, the output magnitude of the control signal to the amplifier may be limited
at the controller level by a saturation function. In some cases, the maximum and
minimum values of the control signal may need to be different, that is the absolute
value of maximum and minimum values do not have to be same (i.e., u max = 10.0
and u min =−5.0).
8. Other practical aspects of PID control implementation are at the higher (supervisory)
level where an algorithm would set the maximum and minimum allowed limits on
the commanded position, commanded velocity, commanded acceleration, following
error to send a warning message to the user, following error to stop the closed loop
control (fatal error). The command signals would not be allowed to exceed these
limits. In addition, the maximum output control signal (u ) and root-mean-square
max
value (u ) value of the output signal can be monitored to protect the amplifier and
RMS
actuator from overheating. If these values are exceeded, the control logic may reduce
the control signal and/or send a warning signal to the user or shut-down the closed
loop control algorithm as a fault condition (i.e., when the maximum control signal
level is exceeded or the RMS control signal level is exceeded).

2.12.8 Time Delay in Control Systems

Time delay is a common problem in control systems. It typically occurs due to transport
delay or actuator response delay. A pure time delay example is in a fluid or thermal control
system. Consider a system where fluid moves with speed V, an actuator (heater) adds heat
at some location, and the measurement of the temperature is taken at some downstream
location at a distance l from where the actuator is located. Clearly, any effect of the actuator
l
action will be measured only after a time delay of t = V .
d
Pure time delay can be represented mathematically as follows (Figure 2.52),
u (t) = u (t − t ) (2.174)
d
2
1
u (s) u (s)
1 2
e d s
-t
u (t) u (t)
1 2

t t t 0 t
0 FIGURE 2.52: Time delay in control
t
d systems: pure time delay.