Explicit Representation of a SISO system
Figure 23.2: Representating of SISO system
The Closed loop Transfer Function (TF) of the system:
Displacement output of the plant is sensed through a sensor of transfer function H(s). The output of H(s) is fed-back to a loop where the error E(s) between the desired signal and actual output is compared and sent to a controller or compensator Kc(s) which in turn generates the control effort. The control effort is usually amplified by power amplifier and applied to the vibrating system.
The entire process continues with an objective to match the output C(s) with the reference signal R(s).
What will be the structure of Kc(s)?
For a generalized PID Controller
for a simplified PD Controller
 , 
For a simplified PI Controller
 , 
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