Dynamic Protocol-Based SMC for Networked Continuous Stirred Tank Reactor System: Switched Stochastic Semi-Markov Theory

In this paper, the sliding mode control (SMC) problem is investigated for continuous stirred tank reactor (CSTR) via dynamic self-triggered protocol subject to external disturbance. By introducing the switched stochastic system with semi-Markov parameter, the fluctuations in product concentration and the variations in reaction temperature within the CSTR are modeled. Without the sojourn-time constraint, novel strategy about asymptotic mean-square stability is adopted to design the SMC scheme based on the Lyapunov function and the stationary distribution of embedded Markov chain. Furthermore, to enhance the transmission efficiency and the dynamic performance, novel self-triggered protocol is developed in combination with SMC technology, predicting the subsequent triggered moment under the current sampling data and providing the lower bound of internal execution time. Under the dynamic self-triggered protocol, an appropriate SMC law is proposed to ensure the finite-time reachability of the specified sliding surface. Sufficient conditions are established for asymptotic mean-square stability of the associated switched stochastic systems. Finally, the proposed method is verified the simulation. Note to Practitioners—The continuous stirred tank reactor (CSTR) system is widely used in the industrial processes, in which the performance and control are critical to efficiency and quality. Under the key parameters of temperature and concentration, it is necessary to strictly control the temperature and monitor the concentration in real-time. Modern manufacturing and industrial processes have become increasingly complex, and single system can no longer accurately describe the dynamic characteristics. As a special hybrid system with continuous evolution, instantaneous change, and stochastic effect, switched stochastic semi-Markov system can describe the concentration fluctuations and reaction temperature changes in the CSTR, showing significant potential for applications. In recent years, networked control system has attracted attention due to their advantages in remote task execution. The self-triggered protocols conserve bandwidth and reduce dependence on external devices by predicting the next triggered time. In this work, switched stochastic system with semi-Markov parameter is adopted to investigate the self-triggered sliding mode control (SMC) problem for the CSTR. This research provides a novel perspective of SMC strategy based on switched stochastic semi-Markov system and self-triggered algorithm in the CSTR.