Читать книгу PID Control System Design and Automatic Tuning using MATLAB/Simulink - Liuping Wang - Страница 19

A proportional plus integral (PI) controller is the most widely used controller among PID controllers. With the integral action, the steady-state error that had existed with the proportional controller alone (see Example 1.1) is completely eliminated. The output of the controller is the sum of two terms, one from the proportional function and the other from the integral action, having the form,

(1.14)

where is the error signal between the reference signal and the output , is the proportional gain, and is the integral time constant. The parameter is always positive, and its value is inversely proportional to the effect of the integral action taken by the PI controller. A smaller will result in a stronger effect of the integral action.

The Laplace transform of the controller output is

(1.15)

with being the Laplace transform of the error signal . With this, the Laplace transfer function of the PI controller is expressed as

(1.16)

Figure 1.5 shows a block diagram of the PI control system.

The example below is used to illustrate closed-loop control with a PI controller. For comparison purpose, we use the same plant as that used in Example 1.1.

Figure 1.5 PI control system.