Page 171 - Electrical Engineering Dictionary

dynamical system satisfies the condition
See also dynamical linear stationary
continuous-time finite-dimensional system.
x (k 1 ,x (k 0 ) ,u) = x 1
controlled process part of the control
controllability in a given time interval scene that can be influenced by the manipu-
a characteristic of some dynamical systems. lated inputs set by the controller and the free
A dynamical continuous system is said to be inputs from the (process) environment; ma-
controllable in a given time interval [t 0 ,t 1 ] if nipulated inputs will be set (adjusted) to real-
for any initial state ize specified control objectives. Control ob-
jectives can be stated in terms of constraints
n
x (t 0 ) ∈ R imposed on specified quantities, in terms of
performance indices to be minimized or max-
and any vector imized, or in other form; free inputs to the
process from its environment do not depend,
n
x 1 ∈ R by definition, on the process behavior.
there exists an admissible control controlled process model model, usu-
ally stated in form of a set of differential or

u ∈ L 2 [t 0 ,t 1 ] ,R m difference equations, describing the behavior
of the controlled process as caused by its in-
such that the corresponding trajectory of the puts; different models of the same controlled
dynamical system x(t, x(t 0 ), u) satisfies the process may be used for various purposes,
following condition: for steady-state control or for model-based
predictive control.
x (t 1 ,x (t 0 ) ,u) = x 1
controlled rectifier a rectifier that uses
switching elements that have forward volt-
controllability of nonstationary systems
age blocking capability to allow a variable
a characteristic of some dynamical systems.
voltage DC output. See also thyristor.
A linear dynamical nonstationary system is
controllable in time interval [t 0 ,t 1 ] if and
controlled source a voltage or current
only if the n × n dimensional controllabil-
source whose intensity is controlled by a cir-
ity matrix
cuit voltage or current elsewhere in the cir-
Z 1 cuit. Also called dependent source.
t
W (t 0 ,t 1 ) = F (t 1 ,t) B(t)
controlled variable (1) the quantity, usu-
t 0
T
T
× B (t)F (t 1 ,t) dt ally the output of a plant or process, that is be-
ing controlled for the purpose of the desired
is nonsingular. See also dynamical linear behavior, for example, transient response or
nonstationary continuous-time finite- steady-state response.
dimensional system.
(2) variable associated with the behavior
of the controlled process and such that one
controllability of stationary systems a
wants this variable either to follow a desired
characteristic of some dynamical systems. A
lineardynamicalstationarysystemiscontrol- trajectory over a given time interval or to be
lable if and only if kept at a prescribed constant value, i.e., at a
specified set-point; introduction of a set of
h i
2 k n−1
rank B|AB|A B| ... |A B| ... |A B = n controlled variables is necessary to define a
two-layer industrial controller with the reg-
c
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