Fractional Order Sliding Mode Controller for Coupled Tank System | ||||
| Menoufia Journal of Electronic Engineering Research | ||||
| Article 2, Volume 30, Issue 2, July 2021, Page 10-16 PDF (448.5 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/mjeer.2021.192100 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| Esraa Mostafa1; Ahmed M. El-Nagar2; Osama Elshazly3; Mohammad El-Bardini3 | ||||
| 1Department of Industrial Electronics and Control Engineering Faculty of Electronic Engineering, Menoufia University Menouf, 32952,Egypt | ||||
| 2Menoufia University, Faculty of Electronic Engineering | ||||
| 3Department of Industrial Electronics and Control Engineering Faculty of Electronic Engineering, Menoufia University Menouf, 32952, Egypt | ||||
| Abstract | ||||
| In this paper, a fractional order sliding mode controller (FOSMC) is proposed for nonlinear coupled tank system. The proposed controller integrates the advantages of the fractional order control and sliding mode control. Fractional order controller has an extra flexibility to meet the specifications of the controller design and sliding mode control is a robust controller, which is able to respondtoexternal disturbances combined with nonlinear systems.The objective of the controller is to allow the system states to move to the sliding surface and remain on it so as to ensure the asymptotic stability of the closed-loop system. The stability analysis for the proposed controller is studied based on the Lyapunov stability theorem. Simulation results show the ability of the proposed controller to improve the system performance especially when the controlled system is exposed to external disturbances and variation of reference trajectory compared with the conventional proportional-integral-derivative controller (PID) and conventional sliding mode controller (SMC), which is based on integer order derivatives. | ||||
Highlights | ||||
This paper proposeda fractional order sliding mode control for coupled tank system with disturbances, and variation of desired output. The proposed FOSMC makes the output quickly tracking the reference without any affection from the external disturbances. The proposed FOSMC can decrease the tracking error, compared with the SMC. The results show that FOSMC achieves better system performance compared with SMC and PID controller with the shortest rising time and settling time and the least overshoot and verify that the proposed FOSMC could obtain better robustness and more superior adaptability to variable control systems. A comparative study has been carried out and the obtained results are quite acceptable for FOSMC, SMC and PID controller but the FOSMC seems to be more robust. | ||||
| Keywords | ||||
| Fractional control; Sliding mode control; Lyapunov function; Nonlinear systems | ||||
| Full Text | ||||
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I. INTRODUCTION
Fractional calculus (FC) is an ancient branch of mathematical science that deals with derivatives and integrals from non-integer orders [1-3]. Due to the higher degree of freedom that can be provided with the fractional calculus, it has been applied in many areas of engineering and science in recent decades [4]. Several research papers have been published on the topic of fractional order(FO) calculus, which is distinguished by some non-classical phenomena in many applications found in engineering and natural sciences [5-8]. FO calculus provides perfect mathematical models for complex and proportional systematic procedures and events. So, it has much contribution to many fields such as physics, biology, and control theory[9-11].
Theory and application of the FO controllers have attracted the focus of many studies in the past decades especially in science and engineering areas. Fractional order control (FOC) has been introduced in different schemes such as fractional order PID control, which is used for controlling FO plants with dead time [12], fractional order adaptive control, which is applied for non-identical chaotic FO systems [13] and FO optimal control, which is designed for time invariant and time varying problems [14].
Most practical engineering systems are complex with nonlinearity. These systems contain a time-delay, an external disturbance and modeling error. These problems reduce the performance of the systems [15, 16]. It is undesirable to be efficiently controlled these systems by the conventional controllers. One of the robust and effective control approaches that deal with disturbances is the sliding mode control (SMC) [17]. SMC is an effective approach for the control of some nonlinear systems that are not stable using continuous state feedback approaches and it is basically considered as a consequence of discontinuous control. SMC is superior to other control schemes in the sense of design[18]. SMC techniques contain two steps; firstly, the desired system performance in the sliding mode is provided using an arbitrary switching surface. Secondly, a control law is designed based on the sliding mode theory and Lyapunov stability theory to ensure the sliding motion [19]. The asymptotic stability concepts are the main concern using these two steps. Using such control algorithm, the desired performances are maintained, and the system states can reach the equilibrium points. SMC technique has been improved based on different methods and it is proposed based on linear matrix inequality (LMI) [20], Riccati approach [21], adaptive technique [22], and neural network [23]. Integral sliding mode control (I-SMC) designs an integral sliding surface for a class of nonlinear FO systems [24–26]. Furthermore an improved stable sliding surface is given in [27]. However, the best knowledge of the prior works shows that there are many researches in control of nonlinear dynamical systems in which the authors have used the FC for designing the SMC such as [28–30]. The utilization of the FO integrals and derivatives in designing of the SMC can cause robust and finite time stability, reduction the chattering and fast response of the closed loop system in presence of disturbances. A novel fractional order sliding mode control (FOSMC) is designed for output tracking of a broad class of FO systems [31]. Different applications have been proposed for FOSMCs such as heat transfer [32], economic system [33] , speed control of permanent magnet synchronous motor [34], secure communication [35] and antilock braking systems [36] .However, the research about FOSMC for controlling nonlinear systems still exists.
In this paper, a FOSMC is proposed for nonlinear systems. In the proposed algorithm, an appropriate sliding surface is designed and the finite-time stability of this surface is proved. It means that all the state trajectories of the system reach to this surface in a finite time and stay on
it for all future times. Therefore, the proposed control law
is able to overcome disturbances and guarantees the
asymptotic convergence of the system’s output toward the
desired reference signal. Finally, in order to verify the
theoretical results and show the applicability and
performance of the proposed design scheme, it is applied
to two coupled tanks system. Simulation results show the
efficiency of the proposed controller to overcome the
system disturbances and compared to other existing
schemes.
This study has several contributions, which
summarized as follows:
Proposing a FOSMC for nonlinear systems.
The stability analysis of the proposed controller is
derived based on Lyapunov theorem.
The proposed controller is able to improve the system
performance compared with other existing controllers.
The rest of the paper is organized as follows: In Section
2, the basic definitions of FC are introduced. Section 3
presents the proposed FOSMC. Section 4 shows the
simulation results for nonlinear system. Section 5 is
devoted to conclusions.
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