Page 58 - Instrumentation and Measurement

liquid in the tank and reached the sensor. The differential amplifier will then give an error signal and
the power amplifier a signal to the heater which is proportional to the error. The current to the heater
will be proportional to the error, the constant of proportionality being the gain of the amplifier. The
higher the gain the larger will be the current to the heater for a particular error and thus the faster the
system will respond to the temperature change. As indicated in Figure 4.11, the inflow is constantly
at this lower temperature. Thus, when steady state conditions prevail, we always need current passing
through the heater. Thus, there must be a continuing error signal and so the temperature can never
quite be the set value. This error signal which persists under steady state conditions is termed the
steady state error or the proportional offset. The higher the gain of the amplifier the lower will be the
steady state error because the system reacts more quickly.

FIGURE 4.11 Inflow change.

In the above example, we could have obtained the same type of response if, instead of changing the
temperature of the input liquid, we had made a sudden change of the set value to a new constant
value. There would need to be a steady state error or proportional offset from the original value. We
can also obtain steady state errors in the case of a control system which has to, say, give an output of
an output shaft rotating at a constant rate, the error results in a velocity lag.

All proportional control systems have a steady state error. The proportional mode of control tends to
be used in processes where the gain KP can be made large enough to reduce the steady state error to
an acceptable level. However, the larger the gain the greater the chance of the system oscillating. The
oscillations occur because of time lags in the system, the higher the gain the bigger will be the
controlling action for a particular error and so the greater the chance that the system will overshoot
the set value and oscillations occur.

EXAMPLE 4.2

A proportional controller has a gain of 4. What will be the percentage steady state error signal
required to maintain an output from the controller of 20% when the normal set value is 0%?

Answer:

With a proportional controller we have

%controller output = gain x %error = 20 = 4 x %error

Hence the percentage error is 5%.

Page | 58