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The following circuit illustrates a PI controller.
The essence of adding a controller is to ensure that the output will follow the input.
The green signal is the input, the blue signal is the output, and the orange signal is the error.
The first op amp (from left to right) is a subtractor. The output is subtracted from the input (-e = input - output ). The second op amp is a proportional gain and an integrator (i.e: -{Kp + Ki/s}). Thus the controller's transfer function becomes U(s)/E(s) = D(s) = Kp + Ki/s.) The third op amp injects disturbance to the output of the controller. The disturbance can be changed to any type of signal you desire (a constant, pulse or sinusoid). Since the controller is of type 1 (1 free integrator), it will follow a constant with no error. Therefore any constant disturbance will be completely rejected. In order to reject other signals, either more free integrators must be added, or the proportional gain can be increased. The gain can be increased by increasing the resistor next to the capacitor. Note as the gain increases, the ouput follows the input more accurately.
Enjoy.
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