Design and Implementation of LMI-Based H2 Control for Vertical Nonlinear Coupled-Tank System

Design and Implementation of LMI-Based H2 Control for Vertical Nonlinear Coupled-Tank System

Jaffar Seyyed Esmaeili, Abdullah Başçi
Copyright: © 2021 |Pages: 16
DOI: 10.4018/IJSDA.20211001.oa14
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Abstract

This paper presents the mathematical design and implementation of a robust H_2 output feedback controller for the vertical nonlinear coupled-tank system. Considering the growth of the complicated chemical processes in industries in the last decades, the necessity for the controllers with high robustness and proficiency is demanded. Therefore, to overcome some deficiencies of classical controllers such as Proportional Integral (PI), the robust H_2 output feedback controller is proposed to control the liquid level of the coupled tank system benchmark. Because of the nonlinearity of the system and the interactions between two tanks, the behavior of the controller in terms of the performance and disturbance rejection is on the main scene. The Linear Matrix Inequalities (LMI) is used to derive the design procedure. The effectiveness of the proposed approach in the setpoint tracking is highlighted in comparison with the PI plus feedforward controller and the acceptable results are achieved.
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Introduction

In the last decades, the complexity of the chemical processes in the industries has undeniable growth and the need for appropriate controllers to control these complicated processes properly is highlighted as the main scenario (Aslani, Akbari, & Tabasi, 2018; Salima, Loubna, & Riad, 2018). The common and well-known controllers such as Proportional Integral (PI) and Linear Quadratic Regulator (LQR) have the main role in the control of chemical processes such as level, flow, or pressure control in the industries because of their low cost of implementation. On the other hand, considering the complexity and the nonlinear characteristics of the processes, the performance of this type of conventional controller decreases. Therefore according to the low performance of the abovementioned control methods as their disadvantage, the need for the robust, fast and high-performance controllers is increased. To study and analyse the behaviour and performance of different control strategies in process systems, the coupled-tank system is designed and implemented as one of the well-known benchmark systems in control of the nonlinear processes. Goutta, Said, Barhoumi, and M’Sahli (2015) propose the Observer-based Backstepping controller for the coupled-tank system in comparison with the PID controller. In this research, a robust controller based on backstepping strategy is designed to obtain the stabilization of the nonlinear system. The simulation and experimental results show a good improvement in the tank level tracking in comparison with the PID controller, but tracking error is considerable and the output signals are not smooth enough. Jaafar, Hussien, Selamat, Aras, and Rashid (2014) introduce a new conventional PID controller. Considering the fact that the parameter tuning of the PID controller is done with traditional methods such as Z-N and auto-tuning based on the try and error, it will be time-consuming to obtain good gains of the controllers. Therefore, the optimization methodology is proposed and used to achieve the optimal parameters of the controller. Saad, Albagul, and Abueejela (2014) introduce a comparison study between the PI and Model Reference Adaptive Control (MRAC) controllers to control the liquid level on the second tank of the coupled-tank system. The simulation results show that the MRAC approach has a better performance than the conventional PI controller in the steady-state and transient regions of the system response. In the other research, a comparison study between the well-known PID and LQR controllers using PSE(Particle Swarm Optimization) is done (Selamat, Daud, Jaafar, & Shamsudin, 2015) and the results show that the LQR controller gives a better performance compared to PID. The coupled-tank liquid level control system is introduced as one of the best benchmarks in designing the chemical process control approaches. Hence, some of the researches use this framework as the base model in the design and test of the controller performance. In the complicated processes with the nonlinear model of the system, the performance of the aforementioned controllers decreases. To improve the performance of these common controllers, other types of control methodologies such as Sliding Mode Control (SMC) and Neuro-Fuzzy Control (NFC) are considered (Ghabi, Rhif, & Vaidyanathan, 2018; Bouzaida & Sakly, 2018). Basci and Derdiyok (2016) present an experimental research study on the coupled tank system using an adaptive fuzzy controller to control the liquid level in the tanks. The results are compared to a PI controller and have better reference tracking. A chattering-free sliding mode control methodology is proposed for liquid level control (Derdiyok & Basci, 2013). The results are compared to a general sliding mode controller and the proposed methodology gives better experimental performance. In the other research study, the SMC controller with the conditional integrators is proposed to control the liquid level in the quadruple tank system (Prusty, Seshagiri, Pati, & Mahapatra, 2016). The simulation results demonstrate a good level of tracking of the system. These approaches have satisfying reference tracking besides large chattering and energy consumption as their disadvantage.

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