Volume 7 • Issue 1 • 1000266 J Chem Eng Process Technol ISSN: 2157-7048 JCEPT, an open access journal Soumya Ranjan et al., J Chem Eng Process Technol 2016, 7:1 http://dx.doi.org/10.4172/2157-7048.1000266 Research Article Open Access Chemical Engineering & Process Technology J o u r n a l o f C h e m i c a l E n g i n e e ri n g & P r o c e s s T e c h n o l o g y ISSN: 2157-7048 PI Controller Design for a Coupled Tank System Using LMI Approach: An Experimental Study Soumya Ranjan M*, Bidyadhar S and Subhojit G Department of Electrical Engineering, National Institute of Technology Rourkela, Odisha, India *Corresponding author: Soumya Ranjan M, Department of Electrical Engineering, National Institute of Technology Rourkela, Odisha-769 008, India, Tel: 9775194621; E-mail: Mahapatro.soumya@gmail.com Received December 15, 2015; Accepted December 25, 2015; Published January 09, 2016 Citation: Soumya Ranjan M, Bidyadhar S, Subhojit G (2016) PI Controller Design for a Coupled Tank System Using LMI Approach: An Experimental Study. J Chem Eng Process Technol 7: 266. doi:10.4172/2157-7048.1000266 Copyright: © 2016 Soumya Ranjan M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abstract This paper presents a Linear Matrix Inequality (LMI) tuned PI controller for real-time control of a coupled-tank liquid level system. The proposed approach is based on the transformation of the PI controller design problem to a state feedback controller design problem, which is further solved using convex optimization approach. The model of the coupled tank system has been developed based on system identiication technique that employs least square error method (LS) for parameter estimation. The proposed controller algorithm has been applied on the identiied model. The performance of the proposed control algorithm has been compared with that of a Ziegler-Nichols tuned PI controller. From both the simulation as well as the experimental results, it is observed that the performance of the proposed PI control is more eficient than the widely used Ziegler-Nichols approach. Keywords: System identiication; Least square estimation; Linear matrix inequality (LMI); Coupled tank system Introduction Controlling liquid level and low in tanks of a coupled tank system is considered as an important benchmark control platform due to their wide spread applications in the process control industries [1]. he control objective of the coupled tank system is to maintain the liquid level at the desired level. he coupled tank system dynamics has interaction characteristics as it is a MIMO system [2]. his dynamics is nonlinear due to valve characteristics and also exhibits non-minimum phase behaviour [3]. he nonlinearity and the non-minimum phase behaviour makes the associated control problem very challenging. A number of PI controllers have been extensively used in process control industries. hese PI controllers exploit several tuning methods for obtaining appropriate control parameters. Among the several methods reported, Ziegler-Nichols based tuning method is widely used because of its simple structure [4-6]. However, this Ziegler-Nichols based tuning method fails to provide appropriate system response. To overcome this diiculty, various control techniques have been proposed in literature, these includes an auto adjustable PI controller using MRAC technique [7], a standard two DOF PID with decoupling [8], PI controller tuning by CRA technique (characteristics ratio assignment) [9], an inverting decoupling technique [10]. he existing techniques are inadequate to provide robust responses, in the presence of disturbance in the plant dynamics. To eliminate the drawbacks of above-reported controllers, this paper presents a design methodology for tuning of a PI controller by using LMI (an optimization approach) in order to provide appropriate response considering disturbances. In recent times, LMI has emerged as a powerful design tool for solving many convex problems [11,12]. he basic idea behind LMI the problem is that to translate a given control problem to a standard semideinite problem (SDP) [11-15]. In general, the systems are modelled by the common approach i.e., state space or a system matrix form [16]. In most of the applications, the system matrix is used with a low order transfer function that leads to the loss of some accuracy in the modelling. Hence, modelling of nonlinear systems such as NARMAX [17], and ANFIS model [18] have been suggested for better accuracy. It is, in general, diicult to treat various nonlinearities under a uniied framework. Also in some practical situations, due to limited knowledge about certain nonlinear physical phenomena, it is diicult to describe the nonlinearities precisely. Due to this complexity, the nonlinear controllers are very rarely used in industries. In this paper, modelling is accomplished by linear system identiication technique [19,20]. Here the performances are compared with conventional PI Controller in terms of time domain speciications and also diferent performance index criteria such as Integral Square Error (ISE) and Integral Average Error (IAE). he rest of the paper is organized as follows. Section 2 provides development of a simpliied mathematical model of coupled tank system (CTS). Section 3 presents the control algorithm. Section 4 presents both the simulation and experimental results. Finally, conclusions are made in section 5. Coupled tank process modelling Figure 1 gives a sketch of the experimental set-up of the coupled tank system used in the present work. It is a challenging benchmark control device that is commonly used in many process control industries. he control objective of the coupled tank system is to maintain the level of the tanks at the desired level, during inlow and outlow of water. It consists four translucent tanks, and each tank is itted with an outlet pipe to transmit the over low water to the reservoir. In this process, the ith tank is used for water storage purposes i.e., as a reservoir. A level sensor is also attached at the base of each tank to measure the water level of the corresponding tank. he output of the level sensor is converted to 0-5 volt DC by the help of a signal conditioning circuit. here are two pumps installed in the reservoir to drive the water from bottom to top of the tank. A scale is attached in front of all individual tanks for the purpose of monitoring the water level. It works under two basic modes of operations i.e., local mode and remote mode. In local mode, two tanks are controlled by two separate potentiometers that are applied to two tanks to drive water to respective tanks (Figures 4-6). In the present work, the system is used in the remote mode of