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in SMPS when there is a difference between actual output signal and desired output an error signal is being generated. this error signal vanishes as soon as actual output reaches to desired output. so have doubt that how only proportional controller works in this scenario.

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    \$\begingroup\$ So when the error is zero, the error signal is zero. Why would this be a problem? \$\endgroup\$ – CL. Dec 22 '16 at 8:01
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    \$\begingroup\$ A proportional controller will typically allow some error to remain, but if that error is small enough there is no problem, right? \$\endgroup\$ – Spehro Pefhany Dec 22 '16 at 9:20
  • \$\begingroup\$ @CL bz when only proportional controller is used a finite error must be there corresponds to specific demand (disturbance) in order to keep desired switch ON time (duty cycle). what i thing that if error becomes zero system will start oscillates. \$\endgroup\$ – user133896 Dec 23 '16 at 5:32
  • \$\begingroup\$ @spehro but in smps error cant have single value it should have range if only proportional controller is used. the range will be decided by the maximum demand variation. in smps duty cycle is changed to meet the demand variation. if error is fixed duty cycle will also fixed then how SMPS will responds to load variation? \$\endgroup\$ – user133896 Dec 23 '16 at 6:04
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Study this .gif picture below: -

enter image description here

There are three phases in this little movie. Phase one just uses proprotional control to get the blue trace to align with the red dotted line. The red dotted line is the demand and the blue is the response to that demand changing at t = 0.

You should be able to see that with just proportional control, there is a finite error and a fair bit of overshoot. If more gain were used to "close the gap", it's likely that the overshoot would be sustained and you get an oscillator (undesirable).

Adding integral control gets the error down to zero but there is still a fair amount of overshoot. Addding differential control reduces the overshoot.

The above public domain picture taken from here.

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