Practical Tuning of Fractional Order Proportional and Integral Controller (i): Tuning Rule Development

This paper presents a new practical tuning method for fractional order proportional and integral controller (FO-PI). The plant to be controlled is mainly FOPDT (first order plus delay time). The tuning is optimum in the sense that the load disturbance rejection is optimized yet with a constraint on the maximum or peak sensitivity. We generalized MIGO (Ms constrained integral gain optimization) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order α. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only applies the relative dead time, τ of the FOPDT model to determine the best fractional order α and at the same time to determine the best FO-PI gains. Extensive simulation results are included to illustrate the simple yet practical nature of the developed new tuning rules. In Part (II) of this companion paper, interesting experimental results in two experimental platforms are reported using the tuning rule of this paper. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants as illustrated. ∗FOR SUBMISSION TO SPECIAL SESSION ON “FRACTIONAL ORDER CONTROL” ORGANIZED BY PROFS. BLAS M. VINAGRE AND VICENTE FELIU, THE THIRD SYMPOSIUM ON FRACTIONAL DERIVATIVES AND THEIR APPLICATIONS (ASME FDTA2007) AT THE 6TH ASME INTERNATIONAL CONFERENCE ON MULTIBODY SYSTEMS, NONLINEAR DYNAMICS AND CONTROL AT THE ASME 2007 INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES, LAS VEGAS, NEVADA, USA, SEPTEMBER 4-7, 2007. HTTP://WWW.ASMECONFERENCES.ORG/IDETC07 †Jan. 2007. Corresponding author. Center for Self-Organizing and Intelligent Systems (CSOIS), UMC 4160, College of Engineering, Utah State University, Logan, Utah 84322-4160, USA. Tel. 1(435)797-0148; Fax: 1(435)797-3054. URL: http://www.csois.usu.edu/