Confirming Pages
484 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies
we need to use feedback from sensors (e.g., an encoder or a tachometer). By sub-
tracting a feedback signal from a desired input signal (called the set point value), we
have a measure of the error in the response. By continually changing the command
signal to the system based on the error signal, we can improve the response of the
system. This is called feedback or closed-loop control. The goal of this section is to
introduce the basics of feedback control system design.
The theory and practice of control system design can be very complicated and
may involve some mathematical techniques and software tools with which you
might not be familiar. However, it is important for the reader to understand the
approach to control system design, first to appreciate the value of its application
and second to develop a desire to learn more about the field of controls (e.g., via
follow-on coursework). In the subsections that follow, we explore the concepts of
feedback control through a basic but important example of controlling the speed of
a DC motor.
Before continuing, you may want to view Video Demos 11.4 and 11.5. They
demonstrate two laboratory experiments that illustrate various control system topics.
These examples might help you better relate to the material presented in this sec-
tion. Video Demo 11.3 does a particularly good job of explaining some of the basic
principles of proportional-integral-derivative (PID) control, which forms the basis of
many control systems.
11.3.1 Armature-Controlled DC Motor
An important electromechanical device that is incorporated into many mechatronic
systems is a permanent magnet or field-controlled DC motor. In mechatronic system
applications, we might need to carefully control the output position, speed, or torque
of the motor to match design specifications. This is a good example where feedback
control is required. Our first problem, as in every mechatronic control system, is to
model the motor. The model of a physical system is often referred to as the plant.
Then we apply linear feedback analysis to the problem to help in selecting the design
parameters for a controller that will reasonably track the desired output (specified
input). We must create a good mathematical model of the motor (the system model)
before we continue with controller design.
The basic equations governing the response of a DC motor were presented in
Section 10.5, but we will take the analysis further here. A DC motor has an armature
with inductance L and resistance R, such that when it rotates in a magnetic field,
the armature will produce an output torque and angular velocity. Due to the motor
construction, a back emf (voltage) proportional to angular velocity is caused by the
armature coils moving through the stator magnetic fields. Figure 11.3 illustrates the
salient elements in the system. The shaft of the armature transmits torque T to a load
of inertia I
L
and damping c. The motor armature also has inertia, and we will call the
total moment of inertia of the armature and load l.
The model for the armature-controlled DC motor assumes that the motor pro-
duces a torque T proportional to the armature current i
a
:
T(t)=
t
i
a
(t)
(11.1)
Video Demo
11.4PID
control of the
step response
of a mechanical
system
11.5Inverted
pendulum
uprighting and
balancing with
linear cart motion
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