Page 43 - Anatomy of a Robot

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28 CHAPTER TWO
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Input Signal a Actuator Output Signal d
+ Gain = C
b
FIGURE 2-7 A closed-loop system with an actuator and error signal b

b, then signal d can be extremely large and negative. The system is designed to func-
tion with signal b being very small, nearly zero. The actuator usually provides the horse-
power and amplification to drive signal d. To be precise,

d C b
Substituting for b in the previous equation, we get

d C 1a d2
d C a C d
d C d C a
d 11 C2 C a

Finally, we have the relationship between the input a and the output d:

d a 1C>1 C2

This equation predicts that the steady state error of this sort of closed-loop control
system is governed by C. The output d will be off by the ratio of C/(1 C). This fac-
tor is also termed the steady state error coefficient. Note that it cannot be zero; a steady
state error always exists. Note also that the larger the gain, C, of the actuator, the smaller
the steady state error. As C tends toward infinity, the steady state error tends toward
zero. What practical things can we do with this math?
Expect the closed-loop control system to exhibit some steady state error. Don’t be
surprised if the system does not exhibit a perfect output. It is bound to have some
error.
Recognize that the steady state error is very likely to depend upon the gain of the
actuator. Use the steady state error coefficient to estimate what that error will be
in advance and design the robot to allow for an error of that size. If the system has
too much steady state error, consider revising the actuator gain to correct it.