Civil Engineering Reference
In-Depth Information
Of course, most systems are not single integrator systems. However, the same principles can be
applied, that is, that a high gain at low frequencies is needed, and a sufficiently wide frequency range,
with a frequency response locally resembling a single integrator and having an acceptable phase
margin, can then be chosen for the cross-over frequency. This is summarized in the Primary Rule
of Thumb for frequency domain design, which says that near the cross-over frequency, the following
must hold:
v
c
jv
:
Y
OL
(jv)
¼
K(jv)G(jv)
¼
(12
:
15)
lead
network is usually chosen. Since a logarithmic scale is used in a Bode diagram, the frequency response
of the controller K( jv) can simply be added to the frequency response of the controlled system
G( jv). Diagrams of the most common “compensating networks” are given in Figure 12.9.
For the controlling element, when design in the frequency domain is used, a lead
lag or a lag
/
/
12.3 Motivation and Overview of Human Manual
Control Models
12.3.1 Motivation
The motivation for obtaining mathematical models of human control behavior has evolved from the
need to explain the behavior of human-vehicle control systems to understanding human behavior in
general. The analytical descriptions desired are in control-theoretical terms. The main purposes of the
engineering models are:
1. To summarize behavioral data
2. To provide a basis for rationalization and understanding of human control behavior
3. To be used in conjunction with vehicle dynamics in forming predictions or in explaining the
behavior of combined closed loop human-machine systems
Modeling humans using systems theory has proved to be a tremendous challenge. Humans are complex
control and information processing-systems: they are time-varying, adaptive, nonlinear, and their beha-
vior is essentially stochastic in nature (McRuer and Jex, 1967). Such systems are difficult to be charac-
terized in mathematical
terms because most of
the mathematical
tools are applied strictly to
stationary, linear, and nonadaptive systems.
12.3.2 Quasi-Linear Function Theory
Research in the two decades after Word War II resulted in the successful application of quasi-linear
describing function theory to the problem of modeling human control behavior in the single-axis com-
pensatory tracking task (Krendel and McRuer, 1960). In the compensatory tracking task the human
operator is controlling a dynamic system and responding to a displayed error signal in such a way
that the output of that system approximates the value of a reference signal. This is essentially the
same task as introduced earlier, Figure 12.7.
In the early days the model structure and model parameters obtained experimentally using the
quasi-linear describing function models had predictive significance only in applications that were
similar to the experimental conditions. No attempts were conducted to relate the model structure or
model parameters to the context in which the task was conducted, the so-called task variables. This
changed with the publication of McRuer et al. (1965). This landmark report provided an overview of
earlier experiments, putting them in a general framework, and reported the results of new experiments
that were especially conducted to show the relation between human control behavior and the task
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