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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target="_blank" rel="nofollow" href="#ulink_338aafe2-8c73-5509-9712-cae1c916abac">(1.44)equation

      where images is the steady-state gain of the system, images is the time delay, and images is the time constant. This is mainly because the primary applications of tuning rules are for process control where typically the process is stable with time delay. There are many methods available for obtaining a first order plus delay model. Among them is an incredibly simple procedure that is called fitting a reaction curve. This reaction curve is the so-called step response test.

      (1.45)equation

Image described by caption and surrounding text.

      The time delay images is shown in the figure, which is the delayed time when the output responds to the change in the input signal. The parameter time delay images reflects the situation that the output response remains unchanged despite the step input signal being injected. Thus, it is estimated using the time difference between when the step reference change occurred (images for this figure) and when the output response moved away from its steady-state value (see the time interval in Figure 1.14(b) marked with the first set of arrows). A line with maximum slope is drawn on Figure 1.14(b), which is intersected with the line corresponding to the indicator of images. The intersecting point shown in Figure 1.14(b) determines the value of images that is a measurement of the dynamic response time.

      Alternatively, because the step response of a first order system (images) to a unit step input signal can be expressed as

equation

      and when the variable time images,

equation

      thus, we can determine the time constant images using 63.2% of the rising time in the step response. This estimation of time constant gives a different value from the case when using the maximum slope approach. For the majority of the applications, this will result in a smaller time constant images, and from the empirical tuning rules stated in the later part of the section, a smaller proportional gain images will follow. One can evaluate this approach as an exercise using Problem 1.2.


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