Page 61 - Instrumentation and Measurement

EXAMPLE 4.4
A derivative controller has a derivative constant Kd of 0.4 s. What will be the controller output when
the error (a) changes at 2%/s, (b) is constant at 4%?
Answer:
a. Using the equation given above, i.e. controller output5Kd3rate of change of error, then we have

controller output = 0.4 x 2 = 0.8%
This is a constant output.
b. With a constant error, there is no change of error with time and thus the controller output is zero.

EXAMPLE 4.5
What will the controller output be for a proportional plus derivative controller (a) initially and (b) 2
s after the error begins to change from the zero error at the rate of 2%/s (Figure 4.15). The controller
has Kp = 4 and Td = 0.4 s.

FIGURE 4.15 Example.
Answer:
a. Initially the error is zero and so there is no controller output due to proportional action. There will,

however, be an output due to derivative action since the error is changing at 2%/s. Since the output
of the controller, even when giving a response due to derivative action alone, is multiplied by the
proportional gain, we have

controller output = Td x rate of change of error = 4 x 0.4 x 2% = 3.2%
b. Because the rate of change is constant, after 2 s the error will have become 4%. Hence, then the

controller output due to the proportional mode will be given by
controller output = Kp x error

and so that part of the output is

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