System-specific PI control theory for fluid process control and for motion control has been developed to enable simple analytical tuning while yielding robust characteristics. The system-specific control theory is essentially an adaptation of PID control theory. The system-specific theory enables the determination of the coefficients required to implement a proportional-integral (PI) control system analytically from physical (not abstract) system characteristics of the fluid or motion system. Although the formulae for the PI coefficients are simple, they are applicable to complex systems. PI control theory is essentially PID control theory with the derivative (D) coefficient set equal to zero. A derivative coefficient is not essential and may have a detrimental effect on system response characteristics. (A first order system requires one coefficient. A second order system requires two coefficients. Higher order systems may be controlled usiing series control loops.)

The objective of a PI or PID control theory is to relate system performance - error attenuation as a function of time - to the values of the proportional, integral, and differential (PID) coefficients. The theory identifies and defines the relevant system properties required for the determination of the values of the PID coefficients. System-specific PI control theory uses different system properties than conventional PID control theory. Physically significant system properties, not abstract properties, are used in system-specific PI control theory. PI / PID coefficients are functions of the defined system properties and parameters specifying the desired (target) system performance. The identification and definition the relevant system properties for the determination of the PI coefficients is of prime importance to the development of system-specific PI control theory and differentiates it from conventional PID control theory.

The control tuning methods are primarily intended for systems satisfying the following criteria:

• systems with open source (known) control algorithms including, but not limited to, systems that use computers with I/O boards or data loggers - the methods are not intended for systems with 'black box' PID controllers having sealed PID control algorithms (I/O boards are available from component suppliers such as Measurement Computing and Omega.)

• the systems use electric motors and actuators

System-specific PI control theory, and control tuning methods, may also be useful to designers of 'black box' PID controllers who 'think outside the box'.

System-specific PI control theory was specifically formulated for digital control systems whereas conventional PID feedback control theory was originally formulated (in the 1940's) for analog control systems. Therefore, for many systems, system-specific PI control theory may be better suited than conventional PID control theory.

There is a principle in engineering - keep it simple for success. System-specific PI control theory and control tuning methods adhere to this principle. Simplicity does not camouflage the physical significance of the parameters involved. Increasing simplicity, (decreasing complexity) decreases the likelihood of misinterpretations and errors, reduces the implementation time (and costs), etc. System-specific PI control theory and control tuning methods are relatively simple compared to conventional PID control theory and control tuning methods. The relative simplicity of system-specific PI control theory and control tuning methods enable a desired system response characteristic - robust, rapid error attenuation with minimal overshoot, zero steady-state off-set - to be easily attained.

Feedback control is used ‘intuitively’ for many everyday tasks, for example, driving a car, riding a bicycle, etc. When one learns to drive a car or ride a bicycle, one learns feedback control without it being identified as feedback control. Feedback control is used when a car, or a bicycle, is decelerated to a stop at a stop sign. Feedback control is used when a car - without cruise control - is kept a constant speed when traveling over hilly terrain. Feedback control is used by many people of all ages, including children, who never heard the terms feedback control, PID control, or PI control. Therefore, feedback control - including PI control - need not be complex.

The second edition contains an extension to the theory that simplifies the use of variable PI coefficients and also simplifies implementation. Variable PI coefficient may yield superior control (relative to constant PI coefficients) of non-linear systems (modulated capacity versus control signal). Non-linear systems are common.

A critical review of PID control theory, including PI control theory, is warranted by the fact that there are numerous web sites on the topic 'PID control theory' - a topic studied in undergraduate engineering courses. The validity of a theory is determined solely by the accuracy of the predicted system performance, nothing else. The usefulness of any PI / PID control theory is determined by the ease with which it enables a system to be tuned to a specified system performance - error attenuation as a function of time. Theories are not scientific laws, theories are not laws of nature, theories are not sacred, and theories are subject to change.