PID Control System Design and Automatic Tuning using MATLAB/Simulink. Liuping Wang

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Название PID Control System Design and Automatic Tuning using MATLAB/Simulink
Автор произведения Liuping Wang
Жанр Отраслевые издания
Серия
Издательство Отраслевые издания
Год выпуска 0
isbn 9781119469407



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take the derivative of the feedback error signal into the control signal calculation, this leads to

      where images is the derivative control gain.

equation Block diagram depicting Proportional plus derivative feedback control system.
).

      This is what we called a proportional plus derivative (PD) controller.

      (1.9)equation

      (1.10)equation

      The closed-loop poles are determined by the solutions of the characteristic polynomial equation as

equation

      which are

equation

      Clearly, we can choose the values of images and images to achieve the desired closed-loop performance.

      A commonly used derivative filter is a first order filter and has its time constant linked as a percentage to the actual derivative gain images in the form:

      where images is typically chosen to be 0.1 (10%). images is chosen to be larger if the measurement noise is severe.

      With the derivative filter images, a typical PD controller output is calculated as

      (1.12)equation

Block diagram depicting PD controller structure in implementation.

      (1.13)equation

      If the derivative filter was not considered in the design, there is a certain degree of performance uncertainty due to the introduction of the filter. This may not be ideal for many applications. Designing a PD controller with the filter included will be discussed in Section 3.4.1.

      1.2.3 Proportional Plus Integral Controller

      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 images is the sum of two terms, one from the proportional function and the other from the integral action, having the form,

      (1.14)equation

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

      The Laplace transform of the controller output is

      (1.15)