Analytical tuning rules for second-order reduced ADRC with SOPDT models

Abstract

This paper presents a set of tuning rules for second-order reduced linear active disturbance rejection control for second-Order Plus-Dead-time (SOPDT) models. Rules are developed with a target to achieve a good compromise between tracking and disturbance rejection performances. Subsequently, it is formulated as a multi-objective optimization problem consisting of Integral Absolute tracking and regulatory errors as its objectives with a specified robustness level and a stability condition as constraints. The optimization problem is solved by a Multi-objective Quasi-Oppositional Rao-1 (MOQO-Rao-1) algorithm to generate the required Pareto optimal solutions. A compromised solution is chosen among these Pareto optimal solutions using Grey Relational Analysis (GRA). Finally, the resulting best solutions are used to fit a polynomial model using regression resulting in analytical tuning rules. Separate tuning rules are presented for lag-dominated and delay-dominated SOPDT models. The proposed tuning rules are validated through simulations on standard benchmark systems, power-system load frequency control problems, and experimentally on a temperature control system and DC motor control system. Furthermore, a condition on tuning parameters for closed-loop system stability is presented using the dual-locus method; the same is incorporated as one of the constraints in the proposed tuning framework.

Keywords: Linear active disturbance rejection control; Multi-attribute decision making; Multi-objective optimization; Second-order plus dead-time process.