Decentralized Disturbance Rejection Control of Triangularly Coupled Loop Thermosyphon System

Abstract

In this paper, we investigate the stability of a triangularly coupled triple loop thermosyphon system with momentum and heat exchange at the coupling point as well as the existence of disturbances. The controller consists of a single, local state feedback. From the stability analysis, we obtain explicit bounds on the feedback gains, which depend on the Rayleigh numbers and the momentum coupling parameter, but independent of the thermal coupling parameter. The existence of the stability bounds allows us to design decentralized adaptive controllers to automatically search for the feasible gains when the system parameters are unknown. In the case of existing disturbances in the system, we approximate the disturbances via an extended state observer for the purpose of disturbance rejection. Numerical results are given to demonstrate the performance of the proposed decentralized disturbance rejection controller design.

Figures (7)

• Figure 1: Triangularly coupled loop thermosyphon system.
• Figure 2: Tracking error of the $y_2$-state with respect to a sinusoid reference signal
• Figure 3: (a) Stabilized fluid flow in each loop with controller activated at $t=30s;$ (b) dynamic gain search with a learning rate at $0.8$.
• Figure 4: (a) Stabilized fluid flow in each loop with controller activated at $t=30s;$ (b) dynamic gain search with a learning rate at $2.5$.
• Figure 5: (a) Stabilized $y$- temperature state in each loop (b) Stabilized $z$- temperature state in each loop

Theorems & Definitions (13)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Lemma 5
• proof