Title Optimal Fractional Order Proportional And Integral Controller For Processes With Random Time Delays

Varsha Bhambhani, Utah State University

This work made publicly available electronically on July 7, 2011.


This work made publicly available electronically on July 7, 2011.This thesis developed a new practical tuning method for fractional order proportional and integral controllers (FO-PI / PI®) for varying time-delay systems like networked con- trol systems (NCS), sensor networks, etc. Based on previously proposed FO-PI controller tuning rules using fractional Ms constrained integral gain optimization (F-MIGO), simulta- neous maximization of the jitter margin and integrated time weighted absolute error (ITAE) performance for a set of hundred gain delay time-constant (KLT) systems having di®erent time-constants and time-delay values are achieved. A multi-objective optimization algo- rithm is used to simultaneously maximize the ITAE factor and jitter margin of the plants at initial F-MIGO gain parameters. The new values of controller gain parameters are gen- eralized to give a new set of optimal fractional order proportional integral (OFOPI) tuning rules such that the jitter margin and system performance of closed-loop KLT systems are maximized and yet the closed-loop feedback system is stable. This is further tested and veri¯ed by simulation techniques. Comparisons are made with other existing proportional integral derivative (PID) and fractional order proportional integral (PI) tuning rules to prove the e±ciency of the new technique. It is further shown that OFOPI tuning rules per- form better than traditional tuning methods for lag-dominated FOPDT systems, because it can take the varying time-delay better into account. The tuning method is modi¯ed to work with discrete-time controllers in the context of NCSs. Furthermore, experimental results in a NCS platform, Stand-alone Smart Wheel (omnidirectional networked control robot wheel), are reported using the tuning rules developed in this thesis. The optimization tuning method performed almost equally well in practice as in simulations. The thesis also shows that the tuning rule development procedure for OFOPI is not only valid for FOPDT systems but is also applicable for other general classes of plants which could be reduced to ¯rst order plant systems. Temperature control in heat °ow apparatus and water-level control in a coupled tank system using FO-PI tuning rules are other major contributions of this thesis work.