Page 251 - Electric Drives and Electromechanical Systems

248 Electric Drives and Electromechanical Systems

of the steady-state error is repeated for a ramp input, it can be shown to be dependent on
the ramp constant and on the load disturbance. If this analysis is conducted on a
multijointed robot, where a large proportion of the disturbance is from adjacent joints, it
will rapidly become apparent that the full analysis is complex and that it requires the use
of control-simulation packages.

10.1.1 Digital controllers

There has been an almost complete shift towards the use of digital systems rather than
analogue systems within the commercial drive market, this results in systems with a
number of significant benefits. When a microprocessor or digital signal processor (DSP)
is used within a servo controller, the data will be processed at specific intervals, leading
to sequential, and discrete, data acquisition and processing activities. Before considering
the implementation of digital-control systems, the advantages of these microprocessor-
based systems should be highlighted:

The use of low-cost microprocessors or digital signal processes reduce the parts
count within the controller; therefore, the system reliability will increase without a
comparable increase in cost.
Digital control provides a highly flexible system which allows the implementation
of a wide range of functions, including those which are non-linear.
Due to the digital nature of the controller there will be no component variations as
a function of temperature and time (in contrast to analogue systems), hence the
gain and the bandwidth will not be subject to drift.
The ability of a digital control loop to accept the control values over a network al-
lows easy modification of the stability terms in real time. However, networking a
drive controller does introduces cyber security concerns.
Once the control parameters have been determined they can be used in an
identical controller, for example, following the replacement of a drive, with the
assurance that the system’s response will be not be affected.
In the analysis of a sampled-data system, the data can be transformed from the
continuous s-domain to the discrete z-domain by the application of the relationship
sT
z ¼ e , where T is the sampling period. The transfer functions in the z-domain have
similar properties to those in the Laplace s-domain. A block diagram of a digital position
or speed loop is shown in Fig. 10.5, it should be noted that the complete system will
contain analogue elements, particularly the motor-drive and the driven elements. The
servo loop stability terms will be implemented as a digital filter in the microprocessor or
Digital Signal Processor. The feedback that is required is provided by an encoder or a
resolver fitted to the load or to the motor, depending on the application. The operation
of the system can be summarised as follows. At a predetermined, but constant time
interval, the output of the digital-to-analogue converter is updated leading to the motor
changing position. It should be recognised that the time interval between updates is very
small, hence can be considered to continuous. At the same time, the motor’s position is
determined from the encoder; this is compared with the demand, to determine the error