Page 78 - Mechatronics with Experiments

64 MECHATRONICS
The response for the open loop control case is

y(s) = D(s)G(s) r(s) + G(s) w(s)
and for the closed loop control case is

D(s)G(s) G(s) D(s)G(s)
y(s) = r(s) + w(s) − v(s)
1 + D(s)G(s) 1 + D(s)G(s) 1 + D(s)G(s)
In real-world systems, the following issues exist and must be addressed:
1. Disturbances (w(s)): there are always disturbances which are not under our control.
They exist and cause error in the system response. For instance, the wind acts as a
disturbance on an airplane changing its flight direction. Low outside temperature and
the heat loss due to it from the walls of a heated house acts as a disturbance on the
control system since the outside temperature is not under our control, yet it affects
the temperature of the house.
2. Variations in process dynamics (ΔG(s)): the dynamics of the process may change
structurally or parametrically. Structural changes in the dynamics imply drastic sig-
nificant changes, such as the change in the dynamics of an aircraft due to loss of an
engine or a wing. Whereas parametric changes imply less significant, more smooth,
non-drastic changes, such as the change in the weight of an aircraft as the fuel is
being consumed, or due to opening of the wing control surfaces.
3. Sensor noise (v(s)): closed loop control requires the measurement of the actual
response (the controlled variable). The sensor signals always have some noise in the
measurement. The noise is included in the control decisions and hence affects the
overall performance of the system.

Let us consider the effect of these three groups of real-world problems in system perfor-
mance under open loop and closed loop control (Figure 2.14a). In open loop control, the
effect of disturbance is,

y (s) = G(s) w(s)
w
the effect of process dynamic variations is,

y(s) = (G (s) +ΔG(s)) r(s)
0
= G (s)r(s) +ΔG(s) r(s)
0
Since no feedback sensors are needed in open loop control, there is no sensor noise problem.
The responses due to disturbance G(s) ⋅ w(s) and due to process dynamic variations
ΔG(s) ⋅ r(s) are not wanted and are considered errors. Open loop control has no mechanism
to correct for these errors. The error is proportional to the disturbance magnitude and
the changes in the process dynamics. On the one hand, if the process dynamics is well
known and no variations occur, and there is no disturbance or the nature of disturbance
is well known, the open loop control can provide excellent performance. On the other
hand, if process dynamics vary or there are disturbances whose nature is not known or not
repeatable, open loop control has no mechanism to reduce their effect.
In closed loop control, there is an added component, the sensor, to provide feedback
measurement about the actual output of the process. By definition, feedback control action
is generated based on the error between desired and actual output. Hence, error is inherent
part of such a design.