Tutorial pid

CONTROL SYSTEMS, ROBOTICS, AND AUTOMATION – Vol. II - PID Control - Araki M.

PID CONTROL
Araki M. Kyoto University, Japan Keywords: feedback control, proportional, integral, derivative, reaction curve, process with self-regulation, integrating process, process model, steady-state error, overshoot, decay ratio, rise time, settling time, gain margin, phase margin, action mode, ultimatesensitivity test, step response test, Ziegler–Nichols’ tuning methods, Chien–Hrones– Reswick’s tuning method, modulus-optimum tuning method, symmetrical-optimum tuning method, anti-windup, two-degrees-of-freedom controller Contents 1. Introduction 2. Process Models 3. Performance Evaluation of PID Control Systems 4. Action Modes of PID Controllers 5. Design of PID Control Systems 6. Advanced TopicsGlossary Bibliography Biographical Sketch

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Summary

1. Introduction

“PID” is an acronym for “proportional, integral, and derivative.” A PID controller is a controller that includes elements with those three functions. In the literature on PID controllers, acronyms are also used at the element level: the proportional element is referred to as the “P element,” the integralelement as the “I element,” and the derivative element as the “D element.” The PID controller was first placed on the market in 1939 and has remained the most widely used controller in process control until today. An investigation performed in 1989 in Japan indicated that more than 90% of the controllers used in process industries are PID controllers and advanced versions of the PID controller.Encyclopedia of Life Support Systems (EOLSS)

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The PID controller, which consists of proportional, integral and derivative elements, is widely used in feedback control of industrial processes. In applying PID controllers, engineers must design the control system: that is, they must first decide which action mode to choose and then adjust the parameters of the controller so thattheir control problems are solved appropriately. To that end, they need to know the characteristics of the process. As the basis for the design procedure, they must have certain criteria to evaluate the performance of the control system. The basic knowledge about those topics is summarized in this article.

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CONTROL SYSTEMS, ROBOTICS, AND AUTOMATION –Vol. II - PID Control - Araki M.

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Figure 1. Conventional feedback control system

Early PID control systems had exactly the structure of Figure 1, where the PID controller is used as the compensator C(s). When used in this way, the three elements of the PID controller produce outputs with the following nature:

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Thus, the PID controller can beunderstood as a controller that takes the present, the past, and the future of the error into consideration. After digital implementation was introduced, a certain change of the structure of the control system was proposed and has been adopted in many applications. But that change does not influence the essential part of the analysis and design of PID controllers. So we will proceed based on the structureof Figure 1 up to Section 6, where the new structure is introduced.

Encyclopedia of Life Support Systems (EOLSS)

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P element: proportional to the error at the instant t, which is the “present” error. I element: proportional to the integral of the error up to the instant t, which can be interpreted as the accumulation of the “past” error. D element: proportional to the derivativeof the error at the instant t, which can be interpreted as the prediction of the “future” error.

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“PID control” is the method of feedback control that uses the PID controller as the main tool. The basic structure of conventional feedback control systems is shown in Figure 1, using a block diagram representation. In this figure, the process is the object to be...