A new PID controller tuning method based on multiple integrations

Magnitude Optimum Techniques for PID Controllers

“…Accordingly, the accuracy of the estimated process parameters in practice remains questionable. Note that the actual expressions (12)- (14) remain exactly the same when the process with pure time-delay is developed into a Taylor (10) or Padé (11) series (Vrančić et al, 1999).…”

“…The closed-loop parameters e i and f i can be obtained by comparing expressions (8) and (5). The PID controller parameters are then obtained by solving the first three equations (n=1, 2 and 3) in expression (9) (Vrančić et al, 1999):…”

“…Fortunately, the moments A i can also be obtained by calculating repetitive (multiple) integrals of the process input (u) and output (y) signals during the change of the process steady-state (Strejc, 1960;Vrančić et al, 1999;Vrančić, 2008): …”

“…One such method is a magnitude optimum method (MO) (Whiteley, 1946). The MO method results in a very good closed-loop response for a large class of process models frequently encountered in the process and chemical industries (Vrančić, 1995;Vrančić et al, 1999). However, the method is very demanding since it requires a reliable estimation of quite a large number of process parameters, even for relatively simple controller structures (like a PID controller).…”

PID compensation of time delayed processes 1998-2002: a survey

“…Such tuning rules, to compensate delayed processes by either minimising a performance criterion, or achieving a specified gain and/or phase margin, are discussed when the SISO process is modelled in IPD form (Kookos et al 1999), or stable or unstable SOSPD form ( Luyben 2000). Alternatively, ultimate cycle tuning rules, and modifications of the rules in which the proportional gain is set up to give a closed loop transient response decay ratio of 0.25, or a phase lag of 0 135 , may compensate general, possibly delayed, stable or unstable processes (Hay 1998;Tan et al 1999;Yu 1999;Prashanti and Chidambaram 2000;Tan et al 2001;Robbins, 2002a), sometimes to achieve either a specified gain and/or phase margin ( Prashanti and Chidambaram 2000;Tan et al 2001) or a specified closed loop response (Vrancic et al 1999(Vrancic et al , 2001). The controller settings are easily calculated; however, the system must generally be destabilised under proportional control, the empirical nature of the method means that uniform performance is not achieved in general, several trials must typically be made to determine the ultimate gain, the resulting process upsets may be detrimental to product quality, there is a danger of misinterpreting a limit cycle as representing the stability limit and the amplitude of the process variable signal may be so great that the experiment may not be carried out for cost or safety considerations.…”