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 order PIλDµ controller was introduced as the generalization of classical PID controller with the help of non-integer order (fractional order) calculus. The fractional calculus uses integration and differentiation with a fractional order or complex order. The major advantage of fractional derivative is the ability 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 the plant model is obtained as fractional model, it is converted into integer order model by approximating the fractional terms using different approximations proposed in the literature. With all the above mentioned advantages, several fractional order PIλ/PIλDµ tuning rules are proposed in the literature for integer order systems and researchers are still proposing the new rules. The main aim of this paper is to compare fractional order PI/PID tuning methods based on Integral of Absolute Error (IAE), Total Variation (TV) and Maximum Sensitivity (Ms). The main reason for choosing fractional order PIλ/PIλDµ controllers is their additional degrees of freedom that result in better control performance. These tuning rules were 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 the simulation results the optimal tuning method is recommended based on the control objective of the process and the process dead time (L) to time constant (T) ratio. It is observed that the performance of tuning methods vary with the nature of the process like lag dominant, balanced and delay significant processes. The FOPTD processes were checked for robustness with increasing L/T ratio with respect to IAE, TV and Ms.