What are the functions of proportional control, integral control, and derivative control respectively?

PID is an abbreviation for the English terms Proportion, Integral, and Differential coefficient. PID control is actually composed of three control methods: proportional, integral, and derivative. Proportional control: It responds proportionally to the deviation of the system; as soon as a deviation occurs, proportional control takes action to reduce that deviation. A large proportional gain enables faster adjustment and reduces errors, but an excessive proportionate gain reduces the stability of the system, and may even lead to its instability. Integral control: It enables the system to eliminate steady-state error and improve accuracy. Due to errors, integral regulation is carried out until no error remains, at which point it stops; the output of integral regulation becomes a constant value. The strength of the integration effect depends on the integration time constant Ti; the smaller Ti is, the stronger the integration effect. Conversely, a larger Ti value results in a weaker integral effect; the addition of integral control can reduce system stability and slow down the dynamic response. Integral action is often combined with the other two control laws to form a PI controller or a PID controller. Differential control: The differential action reflects the rate of change of the system’s error signal; it has predictive capabilities, allowing it to anticipate the trend in error changes. As a result, it enables preemptive control, eliminating the error before it even arises. Therefore, the dynamic performance of the system can be improved. By selecting an appropriate differential time, overshoot can be reduced, as well as the settling time. Differential action amplifies noise interference; therefore, excessive differential adjustment is detrimental to the system’s resistance to interference. Furthermore, a differential reaction is the rate of change, and when there is no change in the input, the differential output is zero. Differential action cannot be used alone; it needs to be combined with the other two control mechanisms to form PD or PID controllers.

In simple terms, proportional control involves making adjustments based on the magnitude of the deviation; the greater the deviation, the stronger the adjustment； Integral regulation adjusts based on the timing of the deviation; as long as there is a deviation, an output is generated, thereby eliminating the residual error ； Differential regulation adjusts based on the rate of change of the deviation; the faster the rate of change, the greater the output. When there is no change in the deviation, no output is generated, thereby serving a lead-regulation function.