Page 89 - Biosystems Engineering

70 Chapter Two

also known as the characteristic equation, determines its tracking
performance, disturbance rejection, and stability properties. Several
design criteria can be defined for the loop gain L(s):

1. Disturbance rejection: From Eq. (2.83) we can observe that
improved suppression of the negative influence of distur-
bances W(s) on the performance of the controlled system is
obtained when

|(Ljω>> 1 (2.88)
)|
The larger | (Ljω )|, the better the influence of W(s) will be
attenuated.
2. Noise filtering: From Eq. (2.84) we can derive that the influ-
ence of sensor noise V(s), which contaminates the measured
output signal Y (s), will be minimized when
m
|( ) ( )|<< 1 or |(jω )|<< 1 (2.89)
s
C
Gs
L
Hs
|( )|
The better the sensor noise V(s) is filtered out, the more accu-
rate the measured signal Y (s) becomes.
m
Apart from sensor noise, the measured signal Y (s) can also
m
be contaminated by unknown disturbance signals, generated
by unmodeled high-frequency dynamics of the system. The
better these are filtered out, the less influence these will have
on the controlled output Y(s). Badly filtered unmodeled high-
frequency dynamics can distort Y (s) so severely that the
m
feedback system becomes unstable. This phenomenon is
called observation spillover.
3. Reference tracking: From Eq. (2.81), the conditions can be calcu-
lated for which the output signal Y(s) will follow the reference
signal R(s) accurately:

| (Gjω )|≈ 1 or | (jω )|>> 1 (2.90)
L
c
4. Input limitation: The actuator signal, U(s), is sometimes
restricted (e.g., maximal available power, or maximal actua-
tor speed); therefore, U(s) has to be kept as small as possible.
From Eq. (2.85) we can derive that this is obtained when

Cj ( ω )
Cj ) ( ω
1+ Lj ( ω ) = |( ω S j )|<< 1 (2.91)