PID Controller Design based on Generalized Stability Boundary Locus to Control Unstable Processes with Dead Time

This paper proposes a method so that all PID controller tuning parameters, which are satisfying stability of any unstable time delay processes, can be calculated by forming the stability boundary loci. Processes having a higher order transfer function must first be modeled by an unstable first order plus dead time (UFOPDT) transfer function in order to apply the method. Later, UFOPDT process transfer function and the controller transfer function are converted into normalized forms to obtain the stability boundary locus in (KKc,KKc(T/T-i)), (KKc,KKc(T-d/T)) and (KKc(T/T-i),KKc(T-d/T)) planes for PID controller design. PID controller parameter values achieving stability of the control system can be determined by the obtained stability boundary loci. The advantage of the method given in this study compared with previous studies in this subject is to remove the need of re-plotting the stability boundary locus as the process transfer function changes. That is, the approach results in somehow generalized stability boundary loci for unstable plus time delay processes under a PID controller. Application of the method has been clarified with examples.