Absolutely Exponential Stability and Temperature Control for Gas Chromatograph System Under Dwell Time Switching Techniques

Abstract

This paper provides a design strategy for temperature control of the gas chromatograph. Usually gas chromatograph is modeled by a simple first order system with a time-delay, and a proportion integration (PI) controller is widely used to regulate the output of the gas chromatograph to the desired temperature. As the characteristics of the gas chromatograph varies at the different temperature range, the single-model based PI controller cannot work well when output temperature varies from one range to another. Moreover, the presence of various disturbance will further deteriorate the performance. In order to improve the accuracy of the temperature control, multiple models are used at the different temperature ranges. With a PI controller designed for each model accordingly, a delay-dependent switching control scheme using the dwell time technique is proposed to ensure the absolute exponential stability of the closed loop. Experiment results demonstrate the effectiveness of the proposed switching technique.

Event‐triggered H∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

“…If N (t, L) ≤ N 0 + L−t holds for N 0 ≥ 0, > 0, then is called the average dwell time and N 0 is the chatter bound. (14) have an H ∞ performance level (ℜ,Ī) under the event-triggering schemes (15) and the controllers (13) if the following conditions are satisfied.…”

“…As a major complex system with wide engineering background, switched systems are composed of limited number of subsystems and a switching law arranging the working sequence of subsystems . For nonlinear time‐varying switched system, the absolutely exponential stability is guaranteed under a delay‐dependent switching control scheme . For stochastic switching systems, the σ ‐error mean‐square stability of systems is achieved via integrating the weights of all system modes .…”

“…[12][13][14] For nonlinear time-varying switched system, the absolutely exponential stability is guaranteed under a delay-dependent switching control scheme. 15 For stochastic switching systems, the -error mean-square stability of systems is achieved via integrating the weights of all system modes. 16 For asynchronously switched linear systems, a new Lyapunov function is proposed to ensure a finite nonweighted L 2 gain for the systems.…”

A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

“…Remark 1: Delays are very common in industrial processes and chemical processes [38]. For example, the gas chromatograph is modeled by a simple first-order system with some delays in [39]. As a typical chemical process, the thermostatic oven can be modeled as a first-order system with a considerably large delay (see [40], and reference therein).…”

Delay-Hybrid-Dependent Stability for Systems With Large Delays

“…Time-delays are unavoidable in many practical control systems such as, networked control systems (NCSs) [1], temperature control systems [2], multi-agent systems [3], [4], sampled control systems [5], biological systems [6], pneumatic systems [7]. The presence of time-delays often leads to poor performances and even instability [8].…”