PID controller

The integration time T is a parameter that describes the strength of the integrating effect. Integration time T is defined as the time it takes for the controller’s output to increase to the value corresponding to a step input A, when there is such a step input in the control room. The larger the integration time, the longer it takes for the controller output to reach step A, indicating that the integral effect is weaker. When the integration time is infinite, it takes an infinitely long time to reach step A, at which point there is no integral effect. The reciprocal of the integration time is the integration rate, denoted by KT.

Don’t worry about what it means; just know that the greater the effect of the integral, the stronger the control. If the effect of the integral is too strong, the control becomes unstable. In any case, keep testing until stability is achieved

Integral action: The integral action of a controller is designed to eliminate the residual error in an automatic control system. The so-called integration refers to the accumulation over time; that is, when a deviation input e is present, the integral controller must continuously accumulate this deviation over time. The rate of this integral accumulation is proportional to the magnitude of the deviation e and to the integration speed. As long as a deviation e exists, the output of the integral controller must change; in other words, integration is always active, and it only stops when there is no deviation. For a constant deviation, the essence of adjusting the integral action is to change the rate of change of the controller’s output; this rate is measured by the time required for the output from the integral action to equal the output from the proportional action. A small integration time indicates a high integration speed, and thus a stronger integrating effect ； Conversely, the larger the integration time, the weaker the integrating effect. If the integration time is infinite, it means there is no integration effect, and the controller becomes a pure proportional controller. In practice, the integral action is rarely used alone; it is usually combined with the proportional action, thereby giving it both the proportional effect of amplifying (or reducing) the error, and the integral effect of accumulating the error over time, with their effects acting in the same direction. At this point, the output of the controller is: △P = Ke + △Pi, where △P represents the change in the controller’s output value ； Ke is the output caused by proportional action ； △Pi is the output resulting from the integral action.

Integration is used to eliminate residual errors, and the duration should be determined based on the adjustment curve