Electrical Engineering Dictionary - part 58

dynamic load line

graphical plot showing

the instantaneous relationship between volt-
age across and current through a transistor
when driven by an input AC signal.

dynamic matching

See

variational

similarity

dynamic memory allocation

the run-

time assignment of small units of memory to
an active program. Used typically to support
growing structures such as lists.

dynamic path reconnect

used in IBM’s

high-end computer systems to allow a “sub-
channel” to change its channel path each time
it cycles through a disconnect/reconnect with
a given device. This enables it to be assigned
to another available path, rather than just wait
for the currently allocated path to become
free.

dynamic programming

introduced by

Bellman, one of the best known methods for
solving the optimal control problems. A re-
cursive method to compute the optimal con-
trol as a function of the state, dynamic pro-
gramming is used in multistage systems by
working backward from the final stage.

Dynamic programming is based on The

Optimality Principle. The Principle says that
optimal control strategy has the feature that
regardless of initial state and initial decision,
decision in the next step must form an opti-
mal control strategy with respect to the final
state of the previous decisions. This principle
allows us to find an optimal strategy in a nu-
merical way. The principle serves to limit the
number of potentially optimal control strate-
gies that must be investigated. It also implies
that optimal control strategies must be deter-
mined by working backward from the final
stage.

dynamic random access memory (DRAM)

a semiconductor memory using one capac-

itor and one access transistor per cell (bit).
The information is stored dynamically on a
small charge on the cell capacitance, and can

be read or written through the “access tran-
sistor” in the cell.

Since the charge will

slowly leak away (through semiconductor
junctions), the cells need to be “refreshed”
once every few milliseconds. This is typi-
cally done using on-chip circuitry. DRAMs
have very high storage density, but are slower
than SRAMs (static RAMs). See also

burst

refresh

distributed refresh

dynamic range

refers to the range of input

signal amplitudes over which an electronic
device will operate within a set of specified
parameters. Usually expressed in decibels.
In a communications receiver, the upper end
of the dynamic range is determined by the
largest tolerable input signal, while the lower
end is set by the receiver’s sensitivity. The
sensitivity is the minimum discernible signal
for a specific signal-to-noise ratio (SNR). See
also

signal-to-noise ratio

dynamic reconfiguration

changes of op-

tical paths from sources to detectors which
are instantly controllable. Paths of optical
signals are controlled and changed by an op-
tical crossbar switch that is usually a spatial
light modulator.

dynamic scattering

procedure to study

the change of state of atoms and molecules by
analyzing the frequency shift and fluctuations
of scattered light.

dynamic scheduling

(1) creating the ex-

ecution schedule of instructions at run-time
by the hardware, which provides a different
schedule than strict program order (i.e., a pro-
cessor issues instructions to functional units
out of program order). The processor can dy-
namically issue an instruction as soon as all
its operands are available and the required ex-
ecution unit is not busy. Thus, an instruction
is not delayed by a stalled previous instruc-
tion unless it needs the results of that previous
instruction.

(2) changing the software program sched-

ule dynamically depending on data or oper-
ating conditions.

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(3) automatic adjustment of the multipro-

cessing program at run time that reflects the
actual number of CPUs available presently.
For instance, a DO loop with 100 itera-
tions is automatically scheduled as 2 blocks
with 50 iterations on a two-processor sys-
tem, as 10 blocks with 10 iterations on a
ten-processor system, and as one block on a
single-processor machine. This enables one
to run multiprocessor programs on single-
processor computers.

dynamic simulation

See

direct dynamics

dynamic stability

a measure of a power

system to return to a pre-disturbance steady-
state condition following a disturbance.

dynamic system

See

static system

dynamic time division multiple access
(D-TDMA)

time division multiple access

scheme in which the channels are assigned
dynamically. See also

time division multiple

access

dynamic time warping

in problems of

temporal pattern recognition, each exemplar
can be regarded as a sequence of vectors.
The process of pattern matching requires to
carry out an optimal alignment of the vectors
composing the sequences so as to minimize
a proper distance. For example, in automatic
speech recognition, the problem of isolated
word recognition requires producing an op-
timal alignment between the incoming word
to be classified and a reference template. Let

= [a

, . . . , a

]

= [b

, . . . , b

]

be two sequences of vectors

, b

∈ R

)

that must be aligned optimally. Formally, de-
termining the optimal alignment consists of
finding a warping function

C = c

, . . . , c

where

c(k) = [i

, j

], such that the distance

d(A, B) = .=

k=1

i(k)

− b

j(k)

)

is minimum.

The optimization must take

place under the following conditions:
1. monotonic condition
i(k) ≥ i(k − 1) and j (k) ≥ j (k − 1)
2. boundary conditions

i(1) = k(1) = 1

i(K) = M

j (K) = N

3. non-skip condition

i(k)−i(k −1) ≤ 1 and

j (k) − j (k − 1) ≤ 1
4. efficiency condition
|i(k) − j (k)| < Q

The solution of this problem can be ob-

tained by Belmann’s dynamic programming.
The algorithm that produces the optimal tem-
plate alignment is referred to as dynamical
time warping (DTW).

dynamic time warping (DTW)

a recog-

nition technique based on nonlinear time
alignment of unknown utterances with ref-
erence templates.

dynamical

linear

nonstationary

continuous-time finite-dimensional sys-
tem

a system described by the linear

ordinary differential state-equation

(t) = A(t)x(t) + B(t)u(t)

and the linear algebraic output equation

y(t) = C(t)x(t) + D(t)u(t)

where

x(t) ∈ R

is the state vector,

u(t) ∈ R

is the input vector,

y(t) ∈ R

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is the output vector.

u ∈ L

loc

([t

, ∞), R

)

is an admissible control,

A(t) is n×n dimen-

sional matrix, with piecewise-continuous el-
ements,

B(t) is n × m dimensional matrix,

with piecewise-continuous elements,

C(t) is

q × n dimensional matrix with piecewise-
continuous elements,

D(t) is q × m dimen-

sional matrix with piecewise-continuous ele-
ments. The solution of the state equation has
the form

x(t, x(t

), u) = F (t, t

)x(t

)

F (t, s)B(s)u(s)ds

where

F (t, s) is n×n dimensional transition

matrix for a dynamical system.

dynamical linear nonstationary discrete-
time finite-dimensional system

a system

described by the linear difference state equa-
tion

x(k + 1) = A(k)x(k) + B(k)u(k) (1)

and the linear algebraic output equation

y(k) = C(k)x(k) + D(k)u(k)

where

x(k) ∈ R

is the state vector,

u(k) ∈

is a control vector,

y(k) ∈ R

is an out-

put vector, and

A(k), B(k), C(k), and D(k)

are matrices of appropriate dimensions with
variable coefficients. Solution of the differ-
ence state equation (1) has the form

x(k, x(k

), u) = F (k, k

)x(k

)

j=k−1

j=k

F (k, j + 1)B(j)u(j)

where

F (k, j) is n×n dimensional transition

matrix defined for all

k ≥ j

in the following manner:

F (k, k) = I

nxn

for

k ∈ Z

F (k, j) = F (k, j + 1)A(j)

= A(k − 1)A(k − 2) . . . A(j + 1)A(j)

for

k > j.

dynamical linear stationary continuous-
time finite-dimensional system

a sys-

tem described by the linear differential state-
equation

(t) = Ax(t) + Bu(t)

(1)

and the linear algebraic output equation

y(t) = Cx(t) + Du(t)

where

x(t) ∈ R

is the state vector,

u(t) ∈ R

is the input vector,

y(t) ∈ R

is the output vector,

A, B, C, and D are

constant matrices of appropriate dimensions.
The transition matrix of (1) has the form
F (t, s) = e

A(t−s)

dynamical linear stationary discrete-time
finite-dimensional system

a system de-

scribed by the linear difference state equation

x(k + 1) = Ax(k) + Bu(k) (1)

and the linear algebraic output equation

y(k) = Cx(k) + Du(k)

where

x(k) ∈ R

is a state vector,

u(k) ∈ R

is a control vector,

y(k) ∈ R

is an output

vector, and

A, B, C, and D are constant ma-

trices of appropriate dimensions. The tran-
sition matrix of (1) has the form

F (k, j) =

k−j

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dynamical systems with delays

a system

described by the linear state equation

(t) = A

x(t) + A

x(t − h) + Bu(t) (1)

where

x(t) is n-dimensional vector, u(t) is

m-dimensional control vector, and A

and

B are constant matrices of appropriate di-

mensions and

h > 0 is a constant delay. For

a given admissible control and initial data,
the above differential equation (1) with devi-
ating argument has a unique solution derived
by the method of steps.

The state space for dynamical sys-

tem (1),

X = W

(2)

([−h, 0], R

), is infinite-

dimensional Sobolev space of absolutely
continuous functions defined on

[−h, 0] with

values in

and with square integrable

derivatives.

Linear unbounded operator connected

with the dynamical system (1) generates the
solution in the state space

X and has in-

finite number of eigenvalues each of finite
multiplicity. The corresponding eigenfunc-
tions may form the basis in the infinite-
dimensional state space

It should be stressed that it is possible

to consider another type of linear dynamical
systems with delays, namely systems with
multiple delays, systems with delays in the
control or neutral dynamical systems with de-
layed derivative.

dynamo

a term used to describe any of

a variety of rotating machines that convert
mechanical to electrical energy, or less com-
monly, electrical to mechanical energy. Dy-
namos typically consist of a stationary struc-
ture, called the stator, supporting a rotating
element called the rotor. Energy conversion
occurs via Faraday induction. A field wind-
ing (or in some smaller machines, permanent
magnets) is mounted on one of the mechan-
ical structures and produces a magnetic flux.
An armature winding is mounted on the other
structure, and rotation of the rotor produces
relative motion between the field flux and
the coils of an armature winding, inducing
a Faraday voltage in the armature coil. This
Faraday induced voltage is the source of elec-
trical energy at the dynamo output.

dynamometer

a rotating device used to

measure the steady-state torque and power
output of rotating machines. Dynamometers
generally provide precise control of the load
torque applied to a test machine, and power
output is determined through precise speed
measurements.

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