II. TWO DEGREE-OF-FREEDOM (2 DOF) CONTROL
Consider a single-input-single-output (SISO), linear timeinvariant (LTI) plant defined by a rational transfer function (1).
( ) ( ) ( ) ⁄ ( ) ( ) ⁄ (1)
The transfer function is strictly proper, and is both controllable
and observable. The nominal plant polynomials ( ) and ( )
are coprime with ( ) ( ).
The basic controller design objectives are as follows:
1. To ensure an acceptable response to some standard
inputs (model matching problem). To achieve this,
it is obviously necessary that the poles of the
compensated system must be in the in left half
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plane (LHP). This is known as stabilization
problem. It would, however, be better if the poles
could be placed at desired locations (poleplacement problem).
2. To ensure that the system remains stable not only
for the nominal plant but also in the face of plant
uncertainties (robustness problem).
3. To reject external disturbances/noise (disturbance
rejection/ noise attenuation problem).
To achieve these, the most commonly used controller is the
conventional error-driven controller (also known as the servo
controller) which is as shown in Fig. 1.