A comparative study of fractional order PIλ/PIλDμ tuning rules for stable first order plus time delay processes

Abstract

Conventional PID tuning methods may not be sufficient to deal with complex processes of modern industry. For better control, fractional orderPIλDμ controller was introduced as the generalization of classical PID controller with the help of non-integer order (fractional order) calculus. Thefractional calculus uses integration and differentiation with a fractional order or complex order. The major advantage of fractional derivative is theability to inherit the nature of the processes. In general, the control loop includes both fractional order process model and fractional order controller.However, the processes to be controlled are usually modeled as integer order models and controlled using fractional order controllers. But if theplant model is obtained as fractional model, it is converted into integer order model by approximating the fractional terms using differentapproximations proposed in the literature. With all the above mentioned advantages, several fractional order PIλ/PIλDμ tuning rules are proposedin the literature for integer order systems and researchers are still proposing the new rules. The main aim of this paper is to compare fractional orderPI/PID tuning methods based on Integral of Absolute Error (IAE), Total Variation (TV) and Maximum Sensitivity (Ms). The main reason forchoosing fractional order PIλ/PIλDμ controllers is their additional degrees of freedom that result in better control performance. These tuning ruleswere applied on several first order plus time delay processes subjected to step change in setpoint and disturbance.Six recent tuning methods, three for fractional order PIλ and the remaining for fractional order PIλDμ, were considered. Finally, from thesimulation results the optimal tuning method is recommended based on the control objective of the process and the process dead time (L) to timeconstant (T) ratio. It is observed that the performance of tuning methods vary with the nature of the process like lag dominant, balanced and delaysignificant processes. The FOPTD processes were checked for robustness with increasing L/T ratio with respect to IAE, TV and Ms.