Engineering Rock Mechanics

Soft, stiff and servo-controlled testing machines 93

Error signal

adjusted

Electronic

Experiment

of Recording required indicating

experimental desired value

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Figure 6.9 (a) Principle of closed-loop control. (b) Schematic of fast-response,
closed-loop servo-controlled testing machine (courtesy MTS Systems Corp.).
The basic principle of closed-loop control is shown in Fig. 6.9(a) and the
specific application for obtaining the complete stress-strain curve is shown
in Fig. 6.9(b). The principle of closed-loop control is ubiquitous in
mechanical, electrical and biological control systems. In our context, and
with reference to Fig. 6.9(a), an experiment is being conducted in the top
left-hand box. From this experiment, a choice of feedback signal is made,
representing the value of a particular parameter at a specific time. In the
top right-hand box, the feedback signal,f, is compared with a programmed
signal, p, being generated in the lower right-hand box. If there is any
difference between the feedback signal and the programmed signal, the
hydraulic pressure in the experiment is adjusted to bring the feedback
signal to the correct value. Thus there is continuous and automatic closed-
loop control by the continual comparison of the signals. The correction
signal, c, can be expressed as
where k is the gain, p is the programmed signal, and f is the feedback
signal.
From the closed-loop control equation, several aspects of machine control
are immediately evident:
the programmed and feedback signals must be of the same polarity in
order to enable the system to be brought to equilibrium (i.e. p -f = 0)
through application of a control signal of correct sense;
alteration of the gain, k, will alter the magnitude with which the
correction is applied;
if c < cmin (where cmin is a given small difference in the control signal),
we can make c = 0 in order to avoid ‘dithering’ (i.e. rapid, small
oscillations about an equilibrium position); and conversely
if c > c,,, (where c,,, represents, say, a control signal that can only
be induced by a system malfunction), the system can be shut down to
avoid damage.