pid调节器中积分器的作用（Understanding the Role of the Integral Term in PID Controllers）

Understanding the Role of the Integral Term in PID Controllers

When it comes to proportional-integral-derivative (PID) controllers, the integral term plays a significant role in controlling the system response. The proportional term provides an immediate response to any changes in the error, the derivative term dampens any overshoot or oscillation, and the integral term eliminates any steady-state error and helps the system reach its setpoint. In this article, we will delve deeper into the role of the integral term in a PID controller.

What is the Integral Term?

The integral term is the part of a PID controller that sums up the error over time. The error is calculated by subtracting the process variable (PV) from the setpoint (SP). Mathematically, the integral term is calculated by taking the area under the error curve. The larger the error, the more the integral term accumulates. This integral sum is then multiplied by the integral gain (Ki) and added to the controller output.

Eliminating Steady-State Error

One of the primary roles of the integral term is to eliminate any steady-state error that may occur in the system. Steady-state error occurs when the process variable does not reach the setpoint, even though there are no external disturbances. This error can happen due to various reasons, such as friction, deadband, or sensor inaccuracies. The integral term helps to eliminate this error by continuously summing the error and adding it to the control output. This accumulation of error value eventually raises the controller output until it eliminates the steady-state error.

The Impact of Integral Gain on the System

While the integral term is essential for eliminating steady-state error, too much integral gain can also cause problems. Increasing the Ki value can lead to a higher integral sum, causing the control output to keep increasing even when the process variable reaches its setpoint. This overshoot can cause the system to oscillate, leading to instability. Thus, the integral gain should be optimized based on the characteristics of the system, and the various gains should be tuned accordingly to achieve the best possible performance.

Overall, the integral term plays a critical role in PID controllers by eliminating any steady-state error that may occur in the system. However, it is essential to tune the controller's various gains to ensure that the integral term does not lead to instability. By understanding the integral term's working, we can improve the efficiency and performance of PID controllers in various industrial applications.