Page 119 - Electric Drives and Electromechanical Systems

112 Electric Drives and Electromechanical Systems

FIG. 4.4 The effects of systematic and random errors on measurements where T is the true value of the data. M R
is the measured value if the measurement system is subject to random error and M S is the measured value if the
measurement system is subject to both a systematic and random errors.

then the maximum value of the systematic error, DM, will be,

2
2
DM ¼ dx þ dy þ d z 2 (4.5)
where dx, dy, and dz are the respective errors in x, y, and z. However, this approach can be
considered to be rather pessimistic, because the systematic errors may not all operate in
the same direction, and therefore they can either increase or decrease the reading. It is
useful, therefore, to quote the systematic error in the form,
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
DM ¼ dx þ dy þ dz 2 (4.6)

4.1.3 Digital-system errors
There is an increasing reliance on digital-control techniques in drive systems. Digital
controllers require the transducer’s output to be sampled and digitised. The actual
process of sampling will introduce a number of errors of its own. Consider the controller
shown in Fig. 4.5, where a reference signal, R(kT), a feedback signal, P(kT), and the
resultant computed value, C(kT), are discrete signals, in contrast to the output, p(t),
which is a continuous function of time. If the sampling period, T, is small compared with
the system’s time constant, the system can be considered to be continuous; however,
if the sampling time is close to the system’s time constant, the effects of digital sampling

FIG. 4.5 A block diagram of a digital-control system, showing the location of the analogue to digital (A/D) and
the digital to analogue (D/A) converters.