Indirect optimal tuning rules for fractional order proportional integral derivative controller

• Published in: International journal of numerical modelling Vol. 34; no. 2
• Main Authors: Trivedi, Rishika, Verma, Bharat, Padhy, Prabin K.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Inc 01.03.2021; Wiley Subscription Services, Inc
• Subjects: canonical tank system; Controllers; fractional order PID controller; Mathematical analysis; optimal control; Proportional integral derivative; robust control; Robustness (mathematics); Sensitivity; time delay system; Time lag; Tuning
• ISSN: 0894-3370; 1099-1204
• DOI: 10.1002/jnm.2838

In this article, the tuning rules of fractional order PID controller are derived using Indirect Design Approach‐1. In Indirect Design Approach‐1, the plant is shifted in the frequency domain using the shifting parameter ψ. The tuning rules of stochastically optimized fractional order PID controllers exist in literature for the fixed values of maximum sensitivity. Maximum Sensitivity or robustness of the process is application dependent. Due to complex fractional order mathematics, the design of fractional order PID controller is complex. Therefore, in this article, new optimal tuning rules for FOPID controller are proposed using the shifted version of the plant. The adjustable robustness is achieved by varying tuning variable ψ which has a linear relation with the Maximum Sensitivity, Gain margin and Phase Margin. The range of ψ within which it can be varied is also proposed for both stable and unstable processes. Simulation is carried out in the MALTAB environment for validating the proposed methodology. A stable and an unstable first order process with time delay is considered for simulation. For the practical viability and novelty, a real‐time experiment on the level control of Canonical Tank using the proposed methodology is shown.