PI and pID controller design based on generalized stability boundary locus

In this study, a generalized controller design method has been presented for closed loop stability of time delay processes that form a large part of industrial applications. Through this method, it is possible to determine all Proportional Integral (PI) and Proportional Integral Derivative (PID) controller parameter values which provide closed loop stability of the processes including open loop stable, unstable and integrator transfer functions. In the proposed method, it is acknowledged that open loop stable plus time delay processes can be modeled by first order plus dead time (FOPDT) model transfer function. Similarly, plus time delay processes with integrator can be modeled by plus first order plus dead time (IFOPDT) with integrator model transfer function and open loop unstable plus time delay processes can be modeled by unstable first order plus dead time (UFOPDT) model transfer function. Normalized forms of the controller and the process transfer function model are used to compose the generalized stability boundary locuses for calculating all PI and PID controller setting parameters that make the closed loop process stable. The necessity of re-forming the stability boundary locus by changing the process transfer function has been abolished with the suggested method. All PI and PID controller parameter values that make the closed loop system stable for processes including open loop stable, unstable and integrator transfer functions can be determined through the formed generalized stability boundary locus. In the event that there is an exact match between the actual system and the model transfer functions, the proposed method does not contain any approximations. On the other hand, if the actual system transfer function occurs at high level, the proposed method may contain some approximations. Some suggestions have been presented to overcome this situation. In addition, some examples have been given to display the usage of the proposed method.