Module 4 : Feedback controller

Lecture 3 : Transmission Lines

Where

(IV.14)

(IV.15)

and are the closed loop transfer functions (CLTF) of the process. maps the effect of change of setpoint on the process output whereas maps the effect of change of load (disturbance) on the process output.

Two types of control problems are encountered with the feedback control systems, viz . servo and regulatory.

When setpoint of a process undergoes a change while the disturbance affecting the process remains constant, i.e. , the objective of the control system would be to steer the output as close as the setpoint trajectory. In such situation,

(IV.16)

However, when the setpoint remains constant, i.e. , while the disturbance forces the process output to move out of the track of the setpoint, the objective of the control system would be to reject the effect of disturbance as soon as possible and steer the output back to the setpoint trajectory. In such situation,

(IV.17)

Note that the CLTFs depend not only on the process transfer functions, but also on the transfer functions of measuring element, controller and final control element.

To expedite the construction of overall closed loop transfer function of any feedback loop, following rules may be applied:

1.  The denominator of the overall transfer function is “the product of all transfer functions in the feedback loop PLUS one” i.e .,

2.  The numerator of the overall transfer function is “the product of all transfer functions in the forward path between setpoint and the controlled output (for servo problem) or the load and the controlled output (for regulatory problem)” i.e ., or