Page 44 - Anatomy of a Robot

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CONTROL SYSTEMS 29
We might be led to believe that making the actuator gain as large as possible is
desireable. Just be aware that increasing the gain of the actuator adds expense and
will adversely affect the dynamic (nonsteady state) behavior of the control system
as we will see later. In the worst case, a large actuator gain can make the system
unstable and lead to failures. Whenever altering the gain, remember to reevaluate
and retest the dynamic performance of the control system.
Realize that these equations model a general-purpose closed-loop control system. If
the control system is meant to control the robot’s position, then the variables a, b, and
d are measured in distance. If the control system is meant to control the robot’s speed,
the variables are measured in speed. If the control system is meant to control the robot’s
acceleration, the variables are measured in acceleration. The fundamentals of the math
are still the same; only the units change. We can use the equations herein to control any
of the aforementioned systems without further investigation.
We leave it up to the reader to investigate the mathematics of calculus that hold that
acceleration is the derivative of velocity, and velocity is the derivative of position.
Suffice it to say that positive acceleration builds up speed, negative acceleration (brak-
ing or accelerating in reverse) decreases speed, positive speed accumulates distance
(position), and negative speed (moving backwards) decreases distance (position).

DYNAMIC RESPONSE
When a control system sees a changing input, it generally changes the output. A stan-
dard test of a control system is to give it what’s called a step input. For a robot, such an
input might call for it to move from its present postion to a new position and stop there.
The classic input used to test a control system is a step input and is of the following
form (see Figure 2-8).

Position

Desired Final Position

Time
Initial Position Step Input

FIGURE 2-8 The classic step input function