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6. Classical PID Control


In this chapter we review a particular control structure that has become almost universally used in industrial control. It is based on a particular fixed structure controller family, the so-called, PID controller family. They have proven to be robust in the control of many important applications.

The simplicity of these controllers is also their weakness, since it limits the range of plants that they can control satisfactorily. Indeed, there exists a set of unstable plants which cannot even be stabilized with any member of the PID family. Nevertheless, the surprising versatility of PID control (really, PID control simply means: control with an up to second-order controller) ensures continued relevance and popularity for this controller. It is also important to view this second-order setting as a special case of modern design methods, as presented, for example, in Chapters 7 and 15. This chapter covers the classical approaches to PID design. This is done due to the historical and practical significance of the methods and their continued use in industry.


  • PI and PID controllers are widely used in industrial control.
  • It has been empirically found that the PID structure often has sufficient flexibility to yield excellent results in many applications.
  • The basic term is the proportional term, ${\bf P}$, which cause a corrective control actuation proportional to the error.
  • The integral term, ${\bf I}$, gives a correction proportional to the integral of the error. This has the positive feature of ultimately ensuring that sufficient control effort is applied to reduce the tracking error to zero. However, integral action tends to have a destabilizing effect due to the increased phase shift.
  • The derivative term, ${\bf D}$, gives a predictive capability yielding a control action proportional to the rate of change of the error. This tends to have a stabilizing effect but often leads to large control movements due to the amplification of noise by the derivative action.
  • Various empirical tuning methods can be used to determine the PID parameters for a given application. They should be considered as a first guess in a search procedure. Attention should also be paid to the PID structure. Systematic model-based procedures are covered in later chapters.