The requirements of an ideal control system are
Speed
The control system's response should be swift.  This is necessary to ensure that the process variables do not stray away from the set point which can affect the process.
Damping
The number of oscillations should be as low as possible.  Oscillations can cause disturbances in the system.  The damping of the system should be optimum.
Accuracy
Accuracy refers to the ability of the system to detect even the smallest deviation and initiate a corrective response.   The sensors and the error sensing algorithms should have a high resolution.
Noise
Noise refers to undesirable interferences in the signal of the transducer.  There are many reasons for noise.  Electromagnetic Interference (EMI) is one of the reasons.  A good Control system should be able to filter the noise and process only the principal signal.
Stability
Any control system should be stable about the set point.  It should maintain the process variable at the set point.  It should not react to changes in the surroundings, temperature or any other external parameter.  It should react only to the principal input signal.
Bandwidth
Bandwidth is dependent on the frequency of operation.  The Bandwidth should be as large as possible for a good frequency response of the system
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