SMC for Stirred Tank Reactor Model: Hybrid Systems With Bi-Boundary Sojourn Time

Area of Science:

• Chemical Engineering
• Control Theory
• Systems Science

Background:

• Stirred tank reactors (STRs) are critical in chemical processes but exhibit complex dynamics.
• Semi-Markov switching systems with bi-boundary sojourn times offer a more realistic model than traditional hybrid systems.
• Existing control strategies for such systems are limited, especially concerning sliding mode control (SMC).

Purpose of the Study:

• To develop a novel sliding mode control (SMC) law for stirred tank reactors (STRs) operating under semi-Markov switching with bi-boundary sojourn time (ST).
• To address the challenge of partly known semi-Markov kernel (SMK) information within a control framework.
• To guarantee the reachability of the quasi-sliding mode (QSM) and ensure system stability despite parameter uncertainties.

Main Methods:

• Development of a new SMC law tailored for discrete hybrid systems with semi-Markov switching and bi-boundary ST.
• Utilization of a linear matrix inequality (LMI)-based framework to incorporate partly known SMK information.
• Design of control strategies that consider both upper and lower bounds of sojourn times for enhanced system characterization.

Main Results:

• The proposed SMC law successfully drives the system states to a prespecified sliding region.
• The control method effectively compensates for parameter uncertainties within the STR.
• Numerical simulations confirm the efficacy and robustness of the developed control strategy.

Conclusions:

• The developed SMC law provides a robust and effective solution for controlling STRs with complex semi-Markov switching dynamics.
• The LMI-based framework offers a viable approach for handling systems with partly known statistical properties.
• This research advances the field of control for hybrid systems with advanced switching characteristics.