Page 46 - Modern Control Systems

Chapter 1 Introduction to Control Systems

As designers, we proceed to the first attempt to configure a system that will re-
sult in the desired control performance. This system configuration will normally
consist of a sensor, the process under control, an actuator, and a controller, as shown
in Figure 1.3. The next step consists of identifying a candidate for the actuator. This
will, of course, depend on the process, but the actuation chosen must be capable of
effectively adjusting the performance of the process. For example, if we wish to con-
trol the speed of a rotating flywheel, we will select a motor as the actuator. The sen-
sor, in this case, must be capable of accurately measuring the speed. We then obtain
a model for each of these elements.
Students studying controls are often given the models, frequently represented
in transfer function or state variable form, with the understanding that they repre-
sent the underlying physical systems, but without further explanation. An obvious
question is, where did the transfer function or state variable model come from?
Within the context of a course in control systems, there is a need to address key
questions surrounding modeling. To that end, in the early chapters, we will provide
insight into key modeling concerns and answer fundamental questions: How is the
transfer function obtained? What basic assumptions are implied in the model devel-
opment? How general are the transfer functions? However, mathematical modeling
of physical systems is a subject in and of itself. We cannot hope to cover the mathe-
matical modeling in its entirety, but interested students are encouraged to seek out-
side references (see for example [76-80]).
The next step is the selection of a controller, which often consists of a summing
amplifier that will compare the desired response and the actual response and then
forward this error-measurement signal to an amplifier.
The final step in the design process is the adjustment of the parameters of the
system to achieve the desired performance. If we can achieve the desired perfor-
mance by adjusting the parameters, we will finalize the design and proceed to docu-
ment the results. If not, we will need to establish an improved system configuration
and perhaps select an enhanced actuator and sensor. Then we will repeat the design
steps until we are able to meet the specifications, or until we decide the specifica-
tions are too demanding and should be relaxed.
The design process has been dramatically affected by the advent of powerful
and inexpensive computers and effective control design and analysis software.
For example, the Boeing 777, which incorporates the most advanced flight avionics
of any U.S. commercial aircraft, was almost entirely computer-designed [56, 57].
Verification of final designs in high-fidelity computer simulations is essential.
In many applications, the certification of the control system in realistic simulations
represents a significant cost in terms of money and time. The Boeing 777 test pilots
flew about 2400 flights in high-fidelity simulations before the first aircraft was even
built.
Another notable example of computer-aided design and analysis is the McDon-
nell Douglas Delta Clipper experimental vehicle DC-X, which was designed, built,
and flown in 24 months. Computer-aided design tools and automated code-generation
contributed to an estimated 80 percent cost savings and 30 percent time savings [58].
In summary, the controller design problem is as follows: Given a model of the
system to be controlled (including its sensors and actuators) and a set of design goals,
find a suitable controller, or determine that none exists. As with most of engineering