PID Controller for Servo Motor explained: How does it work?

A Proportional Integral Derivative Controller also known as PID controller op amp circuit is designed as Speed-Locked Loop for a Servomotor with two operational amplifiers and two capacitors realizing a closed loop PID controller to set the speed of the motor at the desired value and to keep the rotator speed error minimized. For more op amp circuit design and analysis examples and tutorials please see    • Electrical Engineering, Analog, Digital De...  
In this PID servomotor tutorial and walkthrough example, the first op amp in this circuit is wired as difference amplifier to effectively implements a speed error detector similar phase error detector in a Phase-Locked Loop or PLL circuit. The second operational amplifier then receives this measured error at its input and then generates an output voltage comprised of three voltage terms in the form of Proportional Integral Derivative of the error. This PID voltage is then fed to the input of a power amplifier that is capable of generating large currents at proper voltage level (power level) to drive a PWM or Pulse Width Modulator that then adjusts the speed of the servo motor. A Tachometer or RPM-meter then mechanically or optically measures the speed of the motor (e.g. optical counters or encoders) and generates a voltage Vrpm that ideally should match the Vref that is the setpoint voltage at the input of the circuit that defines the target speed for the motor. A combination of Kirchhoff circuit laws KCL and KVL and op amp virtual short and inverting and noninverting amplifier gains are applied to quickly analyze this PID circuit and to find the transfer function.