Optimal PI/PID design for inverse response systems

PID type controllers are still extensively being used in industrial applications despite improvements in modern control in recent years. For a control system to result in satisfactory closed loop responses, tuning parameters of controllers must be determined appropriately. There are many methods in the literature to calculate setting parameters of the controller. Integral performance criterion is one of the well-known methods and has been accepted widely to determine tuning parameters of PI/PID controllers. Integral performance criteria have been used to find setting of a PID controller to control different type of processes. However, it has been used very little in the control of inverse response processes. In this study, analytical expressions have been derived to calculate optimum tuning parameters of a PI and/or PID controller to control stable processes with inverse response plus dead time and integrating processes with inverse response plus dead time. For this purpose, low order processes transfer functions have been assumed. Later, normalized process and controller transfer functions have been used in the error function of the closed loop system and repeated optimizations, in the sense of ISTE, IST2E and IST3E criterion, have carried out to find tuning parameters that minimize the error function. So, plots that give the relation between the parameters of the process and the controller and normalized dead time and normalized zero have been obtained. By applying curve fitting approach to those plots, analytic expressions which lead to determine optimum tuning parameters of a PI/PID controller have been derived. In order to show the use of obtained expressions in the control of stable processes with inverse response plus dead time and integrating processes with inverse response plus dead time, simulation results have been supplied. In addition, comparisons with design methods existing in the literature and suggested for the control of inverse response processes have been given. If appropriate models for stable processes with inverse response plus dead time and integrating processes with inverse response plus dead time can be obtained, it has been shown that the design methods proposed in this thesis can result in better closed loop performances than design methods given in the literature.