Analytical tuning rules for Reduced-order Active Disturbance Rejection Control with FOPDT models through Multi-Objective optimization and multi-criteria decision-making.

Active Disturbance Rejection Control (ADRC) emerged as a promising control solution in various engineering domains. However, increased ADRC order makes it difficult to implement and tune in practice. On the other hand, Reduced-order ADRC (RADRC) structure solves this issue with the appropriate tuning of its parameters to achieve the desired performance. This paper aims to develop analytical tuning rules for RADRC for processes approximated as First-order plus dead-time models (FOPDT). These rules meet the conflicting goals of tracking and disturbance rejection restricted by robustness specification. The tuning rules are derived based on a multi-stage approach. In the first stage, the tuning problem is formulated as a multi-objective optimization problem with appropriate constraints. A Multi-objective Quasi-Oppositional Rao-1 (MOQO-Rao-1) Algorithm solves the optimization problem to produce a collection of Pareto-optimal solutions (alternatives) in the second stage. In the third stage, using the Best-Worst based PROMETHEE method, the best one is chosen among the available options. Finally, using linear regression, analytical tuning rules are developed. Separate tuning rules are proposed for lag-dominated and dead-time dominated cases. Simulation experiments on benchmark industrial processes are performed, and the findings assess the efficacy of the suggested tuning rules relative to the methods recently published. The proposed tuning rules are experimentally validated to assess their applicability in the practical scenario. Besides, the closed-loop system's stability with the suggested tuning rules is confirmed by the small-gain theorem and the dual-locus process.