Mathematical Problems in Engineering

Volume 2017, Article ID 3597346, 12 pages

https://doi.org/10.1155/2017/3597346

## Fuzzy Supervisor Approach Design Based-Switching Controller for Pumping Station: Experimental Validation

Higher National Engineering School of Tunis (ENSIT), Laboratory of Industrial Systems Engineering and Renewable Energy (LISIER), University of Tunis, Taha Hussein Street, BP 56, Bab Menara, 1008 Tunis, Tunisia

Correspondence should be addressed to Wael Chakchouk; nt.unr.tisne@kuohckahc.leaw

Received 16 June 2017; Revised 7 September 2017; Accepted 1 November 2017; Published 23 November 2017

Academic Editor: Stefan Balint

Copyright © 2017 Wael Chakchouk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a discrete-time switching controller strategy for a hydraulic process pumping station. The proposed solution leads to improving control system performances with two tests: combination of Fuzzy-PD and PI controllers and Fuzzy-PID and PI controllers. The proposed design methodology is based on accurate model for pumping station (PS), which is developed in previous works using Fuzzy-C Means (FCM) algorithm. The control law design is based on switching control; a fuzzy supervisor manages the switching from one to another and regulates the rate of participation of each order, in order to satisfy various objectives of a stable pumping station like the asymptotic stability of the tracking error. To validate the proposed solution, experimental tests are made and analyzed. Compared to the conventional PI and fuzzy logic (FL) approaches, the results show that the switching controller allows exhibiting excellent transient response over a wide range of operating conditions and especially is easier to be implemented in practice.

#### 1. Introduction

Nonlinear system modeling has been a subject of some interest in the field of control theory for many years. In this review, the material is presented which provides the relevant perspective of the subject area with regard to signal processing applications. Therefore, the biggest challenge to researchers is to find solutions to problems encountered in real applications; in our case it is the pumping station. It is a complex nonlinear and interconnected system; then to build a precise mathematical model of this system is difficult task because the mathematical solutions for this system are very complex and require enormous amounts of computation. Moreover, it contains many variables which are too vague to model. In order to build an accurate model for the pumping station system, several algorithms based on Takagi-Sugeno (T-S) fuzzy model [1–7] have been carried out recently to identify the parameters for “black-box” systems using input-output data sets, among them the Fuzzy-C Means (FCM) algorithm [8–16]. The latter is particularly the most effective technique that can be used in nonlinear systems identification.

It is applied in many fields such as image segmentation [17] and sensor networks [18]. For this, we have used FCM algorithm to find a mathematical model for pumping station.

Many control laws have been developed in literature for pumping station using different techniques. The authors of [19, 20] have used a proportional integral (PI) controller to drive the pumping station system. In [20, 21] the authors have applied a fuzzy logic control (FLC) to the same system. More recently, a hybrid controller based on PI and FLC controllers has been developed in [22]. However, those aforementioned works have the major drawbacks. In [19–23], the problems are higher steady state error, higher overshoot, and having unstable tracking performance.

To overcome those problems, in this paper a new methodology based on switching approach is proposed for Single-Input Multiple-Output (SIMO) discrete-time system.

The control scheme developed consists of a fuzzy supervisor managing the combination between two controllers in two tests: the first one is the combination of Fuzzy-PD and PI controllers [21], and the second deals with the combination of Fuzzy-PID and PI controllers.

In literature, combination of different techniques to obtain the best performances is widely used today. Wong et al. [24] proposed a combination of three methods: SMC, fuzzy logic control (FLC), and PI control. The resulting controller eliminates the chattering and the steady error introduced by the FLC. Lin and Chen [25] used genetic algorithms to optimize the mixing of SMC and FLC and hence to reduce chattering in the system. Barrero et al. [26] developed a FLC-based hybrid controller to manage the switching between a SMC and a Fuzzy-PI controller. Reference [27] developed a hybrid controller to manage the switching between fuzzy logic and PI controllers. Nevertheless, the above-mentioned works use a fixed combination or restrictive assumptions for the rapidity and the stability of the pumping station.

Based on the aforementioned works, the main contribution of this paper is to develop a discrete-time switching (hybrid) control applied for a water pumping station (Irrigation Station (IS)). It should be noticed that the mathematical model of IS is discrete-time linearized system described in [19]. The aim of this paper is to propose a fuzzy supervisor for switching combination between two controllers to overcome their disadvantages and to ensure the robustness and the stability of the closed loop system. The discrete-time switching control is based on the combination of the Fuzzy-PD or Fuzzy-PID with PI controllers. The developed method has the advantage of combining the performance of both controllers. A fuzzy supervisor manages the switching from one to another controller in order to resolve the tracking problem of pressure in pipe line and sprinklers. Then, the proposed switching control applied to the water pumping station is validated experimentally through MATLAB-Simulink (R2011b“7.13.0.564”) environment and the dSpace DS1104 card based on real-time data acquisition control system.

This study is organized as follows: In Section 2, the mathematical model of pumping station is presented. In the next section, there exists presentation of different control laws (PI, Fuzzy-PD, and Fuzzy-PID). The switching control structure is designed and expressed in a suitable form. To demonstrate the various features of the proposed switching controller scheme, formulating switching controller problems, fuzzy logic supervisor, and the proposed approach, simulation results are given and compared to classical PI, Fuzzy-PD, and Fuzzy-PID controllers. The experimental validation of the switching control implemented to pumps is detailed in Section 4. Finally, Section 5 presents some concluding remarks.

#### 2. Pumping Station Model

The pumping station model is developed in previous research. The authors [22, 28] used the hydraulic description model, which is based on the fluid mechanics laws, Navier-Stokes equations, and their simplification. However, in [19] they used the Takagi-Sugeno fuzzy model.

In this case, the above system may have the following form:where represents the discrete state space vector and is the input of system. The output is chosen equal to and the reference signal is assumed to be known and uniformly bounded. The linear numerical model is described by (1) using the fuzzy Takagi-Sugeno technique which is obtained by the following three steps [19]: (1)Determination of premises parameters using the Fuzzy-C Means (FCM) algorithm(2)Estimating consequential parameters using the Recursive Least Square (RLS)(3)Model validation using the Root Mean Square Error (RMSE) and Variance Accounting For (VAF).

The IS is made up of two nonlinear systems which has the same inputs and different outputs, one of pressure and the other of flow, where each one is partitioned in three subsystems. The pressure and flow subsystems are described in previous works [19, 21] which are given by the following equations.(i)For the pressure subsystems,(ii)For the flow subsystems,For the total system identification, the rule for each subsystem (flow and pressure) can be calculated by the following equation [19, 21]:using (2), (3), and (4) the global rules are given by (5) and (6).(i)For the pressure output,(ii)For the flow output,Thus, the open loop transfer functions areThe discrete state representation is given by [19, 21]Based on Shannon theory, the sampling period is chosen as 0.04 s.

#### 3. Controls Used on the Pumping Station

This section defines the different controllers such as PI, Fuzzy-PD, Fuzzy-PID, and the switching between PI/Fuzzy-PD and PI/Fuzzy-PID.

##### 3.1. PI Control Design

The block scheme of the pumping station controlled by a PI regulator as shown in Figure 1 is provided by LEROY-SOMMER. This controller ensures specific control for the pumps. The originators in the LEROY-SOMMER company choose the parameters of following adjustments m:The form of discrete PI controller is given bySimulation results of PI controller are shown in Section 3.5.