Auto-Tuning of Pid Controllers for Mimo Processes by Relay Feedback

Tuning of Multivariable Decentralized Controllers Through the Ultimate-Point Method

“…In multivariable processes like (1), the ultimate quantities can be defined similarly to the SISO case [14].…”

“…The set of all the ultimate gains is a curve in the parameter space. In the more general case, these gains will form a surface of dimension ; this surface will be called the ultimate surface [14].…”

“…5, and different ultimate points are identified with different relay amplitudes [13], [14]. In DRF, only one experiment is performed, with all control loops in relay feedback, i.e.,…”

“…Of course, the equations become more complex. Consider again the case in which all characteristic loci are dislocated to the same desired point ; for a TITO process, the controllers are obtained through (14) and (15). For a process of order , the equations used to obtain the controllers are given by (25) where are the th-order principal minors of the matrix , and each sum is taken over all principal minors of the order .…”

“…Moreover, MIMO processes have infinitely many ultimate points, and the resulting closed-loop performance is strongly related to the particular ultimate point used. Hence, a better understanding of the MIMO control problem and how to use the ultimate quantities to design MIMO controllers is in order [13], [14].…”