An $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller design and realization for inverted decoupled Two Input Two Output-Liquid Level System

Abstract

In this paper, An $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is proposed for the level control problem in Two Input Two Output-Liquid Level System (TITO-LLS). The proposed $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is designed based on phase margin ( $${{\phi }_{m}}$$ ), gain crossover frequency ( $${{\omega }_{gc}}$$ ) and velocity error constant ( $${{K}_{v}}$$ ) specifications. Oustaloup Recursive Approximation (ORA) method is used to realize the velocity error constant. A mathematical procedure is proposed to identify the linear dynamics of TITO-LLS from the real-time response. An inverted decoupler is used to decouple the TITO-LLS into two separate Single Input Single Output (SISO) systems. The effectiveness of the proposed controller is compared with reported works both in simulation and in real-time. It is observed that the proposed controller gives better results than the existing reported works.