(a)
Interpretation:
The expression for controller output is to be derived.
Concept Introduction :
The response of the transfer function is derived by taking the inverse Laplace of the function.
The transfer function of a PID controller is as follows:
Here,
P(s) represents the output variable in s domain.
E(s) represents the input variable (error) in s domain.
Kc represents the gain of the controller.
ti represents the integral time constant.
td represents the derivative time constant.
Inverse Laplace of the function used is used in the given controller is given as follows:
(b)
Interpretation:
The expression for controller output excluding the derivative controller is to be derived.
Concept Introduction :
The transfer function of the derivative controller equates to zero and the PID controller becomes the PI controller.
(c)
Interpretation:
The controller output is to be plotted and analyzed qualitatively.
Concept Introduction :
Derivative controller speeds up the response and takes action in an anticipatory manner.
PID controller decreases the time of response while PI delays the response comparatively.
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Process Dynamics and Control, 4e
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