A magnitude optimum multiple integration tuning method for filtered PID controller

Magnitude Optimum Techniques for PID Controllers

“…On the other hand, the moments can also be obtained directly from the process transfer function (1), as follows (Vrančić et al, 1999;Vrančić et al, 2001a): …”

“…By solving the first three equations in (9), the following PID controller parameters are obtained (Vrančić et al, 2001a):…”

“…Since a filter is usually not needed in a PI controller (T F =0), the original moments (A i ) are applied in the calculation. Repeating the same procedure as before and solving the first two equations in (9), the following PI controller parameters are obtained (Vrančić et al, 2001a):…”

PID control of FOPDT plants with dominant dead time based on the modulus optimum criterion

“…The design based on the well-known modulus optimum (MO) criterion [9], [1], [10], [14] is one of the approaches that allow working even with long τ with respect to T . This design criterion requires that the closed loop frequency response modulus is as flat as possible in the range of low frequencies, i.e.…”

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.…”