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Controllers:

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A Controller is a device introduced in the system to modify the error signal and to produce a control signal.
The Controller modifies the transient response of the system.

Types of controllers:

ON-OFF Controllers
Proportional Controllers
Integral Controllers
Proportional plus Integral Controllers
Proportional plus derivative Controllers
Proportional plus Integral plus derivative Controllers

Proportional plus derivative Controllers:

The PD Controller produces an output signal consisting of 2 terms:one proportional to error signal and the other proportional to the derivative of the error signal.

Proportional plus Integral plus derivative Controllers:

The PID Controller produces an output signal consisting of 3 terms:one proportional to error signal,another proportional to the derivative of the error signal and the other proportional to the Integral of the error signal.

Analysis of controllers:

P Controllers increases the loop gain, improves the steady state tracking accuracy,disturbance signal rejection and the relative stability and also makes the system less sensitive to parameter variations,but it may lead to constant steady state error..
I Controllers reduces the steady error,but it may lead to oscillatory response of increasing or decreasing magnitude.
The Derivative controller antipates the error,initiates a early corrective action and increases stability.
In PI controllers: Proportional action increases the loop gain and makes the system less sensitive to parameter variations,integral action reduces steady state error.
In PID ControllersTongueroportional controller stabilises the gain but produces a steady state error, integral controller reduces steady state error and derivative controller reduces rate of change of error.