Civil Engineering Reference
In-Depth Information
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Investigation of the roles of multi-modal (visual, vestibular, tactile) feedback on human manual
control behavior in virtual environments such as flight and driving simulators (Mulder et al., 2004).
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The design of haptic manipulators in applications like tele-operation or the development of force-
feedback systems in vehicular control (Van Paassen, 1994).
Investigation of vehicular control (aircraft, automobile) in general, including handling qualities
research.
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Investigation and evaluation of augmented systems, that is, the study of the interim between fully
manual and automated control.
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Studying human perception and action cycles in active psychophysics, for example, in the
determination and identification of a human's use of visual cues in multi-cue displays (Flach,
1991; Mulder, 1999).
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In this chapter we will provide a short introduction into some fundamentals of control theory. This
introduction is very limited, however, and for further study the reader is referred to the many good
textbooks that are available. A textbook geared towards human control is “Control Theory for
Humans,” by Jagacinski and Flach (2003). Others that are recommended for their “human engineering”
perspective are “Man-Machine Systems” by Sheridan and Ferrell (1974), and “Engineering Psychology and
Human Performance” by Wickens (1992). More engineering-oriented textbooks are “Control Systems
Engineering” by Nise (1995), “Control System Design” by Goodwin et al. (2001) “Modern Control
Systems” by Dorf and Bishop (2005) and “Feedback Control of Dynamics Systems” by Franklin et al.
(2002). Note that this selection is not exhaustive, and that many more excellent textbooks are available.
Furthermore, a historic overview of the modeling of human control behavior is given, followed by a
more detailed description of two of the most common and widely used approaches to describe human
behavior in control-theoretical terms, the COM, based on classical control theory, and the OCM, based
on optimal control theory.
12.2 Fundamentals of Systems and Control Theory
Systems and control theory is a branch of mathematics that studies dynamic processes, that is, things that
evolve in time. Examples of dynamic processes that are the subject of systems and control theory are
artifacts like airplanes, power plants, and cars, biological systems like the heart, chemical processes,
large-scale processes like economics, etc. These can be modeled, described and simulated with dynamical
systems theory, and their automated control systems are designed with control theory.
The building blocks of systems and control theory are differential equations, linear matrix algebra,
complex number theory, and probability theory. In this section we will focus on studying linear,
time-invariant (LTI), continuous time, single-input single-output (SISO) systems. We will briefly study
the response of these systems to deterministic signals, in later sections, we will also briefly address
stochastic signals.
Most of the physical processes in the real-world are nonlinear, time-varying, multi-input multi-output
(MIMO), stochastic systems. A deep understanding of SISO systems, however, is an important first step
for understanding more complex MIMO systems. Many of the intuitions gained from working with
simple control systems will generalize to more complex systems — even though it might not ever be poss-
ible to model the more complex systems with the same confidence that we can model the simpler systems.
12.2.1 Linear, Time-Invariant Systems
A useful definition of a system in systems and control theory is given by Olsder and van der Woude
(1994):
(A system is) a part of reality which we think to be a separated unit within this reality. The reality
outside the system is called the surroundings. The interaction between system and surroundings is
realized via quantities, quite often functions of time, which are called input and output.
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