Controller tuning of a third-order process under proportional-integral control

Abstract

The control of a third-order process under proportional-integral feedback control was studied. A previous paper of Weber has been extended to include processes that are inherently underdamped. Stability criteria are developed, and it is shown that the commonly used continuous cycling method (COM) of Ziegler and Nichols sometimes leads to unstable behavior for proportional-integral control. The region of instability is defined in terms of the reciprocal of the maximum gain and critical frequency under proportional control. The paper by Weber Is further extended to explore how the unstable region varies when the "standard" COM parameters (0.45 for gain and 1.2 for reset time) are changed. A procedure Is then suggested for determining satisfactory controller settings through the use of a gain margin. The method is illustrated for an actual process.

Use of relay‐feedback test for automatic tuning of multivariable systems

“…The stability problem may arise when one tries t o tune underdamped system with Z-N method. Tan and Weber (1985) explore stability problems associated with Z-N tuning for third-order systems. As pointed out earlier, the sequential design may produce an underdamped system since the poles of h, are also the poles of g,,,CL(i#j), and typical process transfer function is given in Eq.…”