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

Authors: Wael Chakchouk; Chiheb Ben Regaya; Abderrahmen Zaafouri; Anis Sellami
Journal: Mathematical Problems in Engineering
 (2017)

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## 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.


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## Body

## 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 Section2, 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:(1)x1k+1=f1Tx1+g1x1x2,x2k+1=f2Tx1,x2+g2x1,x2uk,where x1x2T represents the discrete state space vector and u is the input of system. The output y is chosen equal to x1 and the reference signal yr 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,(2)Rp1:yP1k=1.0853yp1k-1-0.1744yp1k-2+0.0570u1k-1+0.0318u1k-2,Rp2:yP2k=1.0851yp2k-1-0.1743yp2k-2+0.0565u2k-1+0.0320u2k-2,Rp3:yP3k=1.0852yp3k-1-0.1750yp3k-2+0.0560u3k-1+0.0315u3k-2.(ii)
For the flow subsystems,(3)RQ1:yQ1k=1.0853yQ1k-1-0.1744yQ1k-2+1.4118u1k-1-1.31u1k-2,RQ2:yQ2k=1.0851yQ2k-1-0.1743yQ2k-2+1.4116u2k-1-1.33u2k-2,RQ3:yQ3k=1.0852yQ3k-1-0.1750yQ3k-2+1.4120u3k-1-1.31u3k-2.For the total system identification, the rule for each subsystem (flow and pressure) can be calculated by the following equation [19, 21]:(4)yk+1=∑i=1cμik·xk·yik+1∑i=1cμik·xk;using (2), (3), and (4) the global rules are given by (5) and (6).(i)
For the pressure output,(5)RPG:yPGk=1.0851ypk-1-0.1745ypk-2+0.0563uk-1+0.0317uk-2.(ii)
For the flow output,(6)RQG:yQGk=1.0851yQk-1-0.1745yQk-2+1.4116uk-1-1.32uk-2.Thus, the open loop transfer functions are(7)HBOP=0.05632z+0.0317z2-1.0851z+0.1745,HBOQ=1.4116z-1.32z2-1.0851z+0.1745.The discrete state representation is given by [19, 21](8)Pk+1Qk+1=1.085-0.174510PkQk+10uk,yk=0.05630.03171.412-1.32PkQk+00uk,A=1.085-0.174510,B=10,C=0.05630.03171.412-1.32.Based on Shannon theory, the sampling period Ts 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 Figure1 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 Kp=0.5Ti=1 m:(9)Usεs=Kp1+1Tis.The form of discrete PI controller is given by(10)Uzεz=Kp1+T/Ti-Kpz-11-z-1=r0+r1z-11-z-1=r0z+r1z-1.Simulation results of PI controller are shown in Section 3.5.Figure 1
Block scheme of the pumping station controlled by PI regulator.


### 3.2. Fuzzy-PD Control Design

The pumping station controlled by the fuzzy logic shown in Figure2 [21] must be programmed through the tool “FUZZY” of MATLAB. Entries “and” are chosen of Gaussian form (bell) and the universe of speech for each one is divided into three sets: Z,  P, and N. Thus, by using all the possible combinations, nine fuzzy rules were generated for five singletons on the level of the consequence part as shown in Table 1.Table 1
Inference matrix of the fuzzy controller.
N
Z
P
N
PB
PS
NS
Z
PS
Z
NS
P
PS
NS
NBFigure 2
Block scheme of the controlled pumping station based on fuzzy logic.In the proposed method each input variable of the fuzzy logic controller has three Gaussian membership functions. The fuzzy sets used in the proposed method are as follows: N: Negative, P: Positive, and Z: Zero. Output variables have five membership functions as follows: NB: Negative Big, NS: Negative Small, Z: Zero, PB: Positive Big, and PS: Positive Small. The variation law of fuzzy controller is shown. The rules can be written in Table1.(11)fεisAandε˙isBthenUcf=Siε,ε˙.The discourse universe of output Ucf is decomposed in five fields. The method min-max is used for inferences system and the gravity centre method for the defuzzification step. Then the fuzzy controller can be written as follows:(12)Siε,ε˙=min⁡μAiε,μBiε˙,UcfG=max⁡Siε,ε˙.Simulation results of fuzzy controller are shown in Section3.5.


### 3.3. Fuzzy-PID Control Design

The additive combination of proportional, integral, and derivative actions is called proportional-integral-derivative action [29, 30]. These types of controllers have been widely used for industrial processes owing to their heuristic nature associated with simplicity and effectiveness for both linear and nonlinear systems. A parallel structure of Fuzzy-PID control systems is proposed in [29, 30] based on the parallel combination of Fuzzy-PI and PD controllers which shows its simplicity in determining the control rules and controller parameters. It is associated with a tuning method which is based on gain margin and phase margin specifications. The block diagram of a Fuzzy-PID control is shown in Figure 3. The input linguistic variables to the Fuzzy-PID controller are as follows: error (e(k)) and change in error (e(k)). Error and change in error are defined on the universe of discourse of −5 to 5. The fuzzy sets have the same structure as the Fuzzy-PD in Section 3.2.Figure 3
Fuzzy-PID controller block.The simulation results are illustrated in Figures4 and 5 which present the pressure and the flow outputs of the proposed system based on switching technique, respectively.Figure 4
Pressure evolution of pumping station with Fuzzy-PID controller.Figure 5
Pressure evolution of pumping station with Fuzzy-PID controller.The evolution of the pressure tracking error with Fuzzy-PID controller is given by Figure4. From the output tracking errors, the proposed Fuzzy-PID method shows that the tracking error is smaller than 1%, which proves the tracking accuracy. The proposed design based on combination of Fuzzy-PI and PD controllers technique shows a better tracking performance and high efficiency.


### 3.4. Switching Control Synthesis

The solution presented in this paper consists in using simultaneously controllers1 and 2 as illustrated in Figure 6. This solution has the advantage of combined performances of both controllers based on an appropriate switching algorithm described in Figure 7.Figure 6
Bloc scheme using the switching controller technique.Figure 7
Switching control algorithm.


#### 3.4.1. Fuzzy Supervisor

To ensure the more robustness of the closed loop system and a fast dynamic response with the best performance, a combination of the two previously defined controllers is made. This combination multiplexes the fuzzy logic control during the transient state and the PI control in steady state. The first command ensures a fast convergence of the system to steady state with insensitivity to external disturbances, while the second takes over steady state to ensure a more smooth and a minimal static error. To avoid a sudden transition from one controller to another, a gradual switching is used [31–34] which has the following form:(13)UHC=αUFLC+1-αUPIC,where α is a weighting factor generated by a fuzzy supervisor. The rule base of the latter is constructed such that the output moves “to zero” when the system is far from the desired value, and “value 1” when the tracking error and its derivatives converge to zero [31, 32]. The main objective of fuzzy supervisor is to determine the weighting factor α, which gives the participation rate of each control signal.The state space is partitioned in several regions using a Sugeno fuzzy system. Also, the product inference, the algebraic sum, and the singleton for the consequent-part are used to design fuzzy supervisor as shown in Figure8. Hence, the fuzzy system output can be written as follows:(14)α=∑j=1mαj∏i=1n-1μHijei∑j=1m∏i=1n-1μHijei,where Hij is a fuzzy set, μHij is the membership degree of e(i) to Hij, αj is a singleton, and m is the number of used fuzzy rules.Figure 8
Supervisory fuzzy inference machine.


#### 3.4.2. Simulation Results

The first test proposes a switching controller based on the combination between two conventional controllers: PI and Fuzzy-PD. In fact, the evolution of the pressure and the flow outputs are presented in Figures9 and 10, respectively.Figure 9
Pressure output with PI-Fuzzy-PD switching controller.Figure 10
Flow output with PI-Fuzzy-PD switching controller.The second test presents a switching controller based on the combination between two controllers: conventional PI and Fuzzy-PID. The pressure and the flow outputs with PI/Fuzzy-PID controllers are given by Figures11 and 12.Figure 11
Pressure output with PI-Fuzzy-PID switching controller.Figure 12
Flow output with PI-Fuzzy-PID switching controller.


### 3.5. Comparative Study

In this section, a comparative study of all control laws applied for the pumping station is made.The choice of the reference signal is rich on a vast time range, in which we find at the beginning a dead zone and then a ramp and a series of steps signals with different amplitude. This choice allows highlighting the effect of the control law in all operation points and studying the system robustness against the sudden changes of needed water level into sprinklers.The obtained results ensure the pressure regulation because the response follows the given reference as illustrated in Figures13 and 14. The response time and the static error related to the pressure output are summarized in Table 2. Table 3 presents the response time and the overshoot related to the flow output. The major drawback of this method of regulation resides primarily at the adaptation problem of the controller face to the external variations such as the extension of drain network, disturbance, and the slowness outputs response.Table 2
Response time and static error of all controllers for the pressure output.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
Response time at ±5%
12.6 s
6.6 s
7 s
6.37 s
6.14 s
Static error of position (in Bar)
0.68
0.1
0.01
0.06
0.02Table 3
Response time and overshoot of all controllers for the flow output.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
Response time at ±5%
13.4 s
11.6 s
8 s
9 s
6 s
Overshoot in %
25.44%
58%
28.94%
30.56%
27.21%Figure 13
Performance results of different control laws for pressure output.Figure 14
Flow performance results of different control laws for pressure output.Note that a saturation was added in the control loop in order to limit the overshoot of flow which is motioned in the constructor document that does not exceed 8 m3/h.Apart from stability, the transient behaviour is another focus of attention for control systems design. There are several properties that can be used to evaluate the transient behaviour of a closed loop control system, for example, steady state accuracy, settling time, and overshoot [35].Beyond these properties, more widely used criteria for quality of control (QoC) relate to the control error, which is defined as the difference between the setpointP∗k and the system outputs Pk and Qk. Some of these performance indices are given below in both continuous-time and discrete-time forms, where k0 and kf are the initial and final discrete-times of the evaluation period [35]. The quality of control criteria are given as follows.(i)
Integral of Absolute Error (lAE):(15)IAE≈∑k=k0kfek≈∑k=k0kfP∗k-Pk.(ii)
Integral of Time-weighted Absolute Error (ITAE):(16)ITAE≈∑k=k0kfkek≈∑k=k0kfkP∗k-Pk.(iii)
Integral of Square Error (ISE):(17)ISE≈∑k=k0kfek2≈∑k=k0kfP∗k-Pk2.(iv)
Integral of Time-weighted Square Error (ITSE):(18)ITSE≈∑k=k0kfkek2≈∑k=k0kfkP∗k-Pk2.According to Figures13 and 14 the ratio speed/power for both outputs (pressure and flow) of the studied system with switching control is higher than other controllers (PI, Fuzzy-PD, and Fuzzy-PID).For pressure output, we notice that fuzzy supervisor approach takes the speed performance of Fuzzy-PD or Fuzzy-PID controllers and the smooth evolution of PI controller, so the switching controller eliminates the small oscillation in transient state for mixing PI/Fuzzy-PD controller.The obtained results by switching controller show that this control strategy is able to limit the oscillation in transient state, without need of the saturation in flow output of pumping station with fuzzy controller (Fuzzy-PD or Fuzzy-PID).Figure14 shows the stable value of steady state (e.g., 4.83 m3/h between t=60 and t=100), which ensured the saving of water use and the economy of electrical energy absorbed by the pumps to reach the pressure set point (5 bar) in the pipelines of the pumping station even in the sprinklers.The quantitative comparison as shown in Tables2, 3, and 4 reflects the switching of PI-Fuzzy-PD and PI-Fuzzy-PID which are better than single controllers as PI, Fuzzy-PD, and Fuzzy-PID.Table 4
Quality of control criteria of all controllers.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
IAE
0.943
0.2256
0.115
0.11
0.108
ITAE
188.6
45.11
13.109
11.87
9.73
ISE
0.8893
0.05088
2.416
e
-
3
9.27
e
-
4
7.415
e
-
4
ITSE
177.9
10.18
4.832
3.774
3.027


## 3.1. PI Control Design

The block scheme of the pumping station controlled by a PI regulator as shown in Figure1 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 Kp=0.5Ti=1 m:(9)Usεs=Kp1+1Tis.The form of discrete PI controller is given by(10)Uzεz=Kp1+T/Ti-Kpz-11-z-1=r0+r1z-11-z-1=r0z+r1z-1.Simulation results of PI controller are shown in Section 3.5.Figure 1
Block scheme of the pumping station controlled by PI regulator.


## 3.2. Fuzzy-PD Control Design

The pumping station controlled by the fuzzy logic shown in Figure2 [21] must be programmed through the tool “FUZZY” of MATLAB. Entries “and” are chosen of Gaussian form (bell) and the universe of speech for each one is divided into three sets: Z,  P, and N. Thus, by using all the possible combinations, nine fuzzy rules were generated for five singletons on the level of the consequence part as shown in Table 1.Table 1
Inference matrix of the fuzzy controller.
N
Z
P
N
PB
PS
NS
Z
PS
Z
NS
P
PS
NS
NBFigure 2
Block scheme of the controlled pumping station based on fuzzy logic.In the proposed method each input variable of the fuzzy logic controller has three Gaussian membership functions. The fuzzy sets used in the proposed method are as follows: N: Negative, P: Positive, and Z: Zero. Output variables have five membership functions as follows: NB: Negative Big, NS: Negative Small, Z: Zero, PB: Positive Big, and PS: Positive Small. The variation law of fuzzy controller is shown. The rules can be written in Table1.(11)fεisAandε˙isBthenUcf=Siε,ε˙.The discourse universe of output Ucf is decomposed in five fields. The method min-max is used for inferences system and the gravity centre method for the defuzzification step. Then the fuzzy controller can be written as follows:(12)Siε,ε˙=min⁡μAiε,μBiε˙,UcfG=max⁡Siε,ε˙.Simulation results of fuzzy controller are shown in Section3.5.


## 3.3. Fuzzy-PID Control Design

The additive combination of proportional, integral, and derivative actions is called proportional-integral-derivative action [29, 30]. These types of controllers have been widely used for industrial processes owing to their heuristic nature associated with simplicity and effectiveness for both linear and nonlinear systems. A parallel structure of Fuzzy-PID control systems is proposed in [29, 30] based on the parallel combination of Fuzzy-PI and PD controllers which shows its simplicity in determining the control rules and controller parameters. It is associated with a tuning method which is based on gain margin and phase margin specifications. The block diagram of a Fuzzy-PID control is shown in Figure 3. The input linguistic variables to the Fuzzy-PID controller are as follows: error (e(k)) and change in error (e(k)). Error and change in error are defined on the universe of discourse of −5 to 5. The fuzzy sets have the same structure as the Fuzzy-PD in Section 3.2.Figure 3
Fuzzy-PID controller block.The simulation results are illustrated in Figures4 and 5 which present the pressure and the flow outputs of the proposed system based on switching technique, respectively.Figure 4
Pressure evolution of pumping station with Fuzzy-PID controller.Figure 5
Pressure evolution of pumping station with Fuzzy-PID controller.The evolution of the pressure tracking error with Fuzzy-PID controller is given by Figure4. From the output tracking errors, the proposed Fuzzy-PID method shows that the tracking error is smaller than 1%, which proves the tracking accuracy. The proposed design based on combination of Fuzzy-PI and PD controllers technique shows a better tracking performance and high efficiency.


## 3.4. Switching Control Synthesis

The solution presented in this paper consists in using simultaneously controllers1 and 2 as illustrated in Figure 6. This solution has the advantage of combined performances of both controllers based on an appropriate switching algorithm described in Figure 7.Figure 6
Bloc scheme using the switching controller technique.Figure 7
Switching control algorithm.


### 3.4.1. Fuzzy Supervisor

To ensure the more robustness of the closed loop system and a fast dynamic response with the best performance, a combination of the two previously defined controllers is made. This combination multiplexes the fuzzy logic control during the transient state and the PI control in steady state. The first command ensures a fast convergence of the system to steady state with insensitivity to external disturbances, while the second takes over steady state to ensure a more smooth and a minimal static error. To avoid a sudden transition from one controller to another, a gradual switching is used [31–34] which has the following form:(13)UHC=αUFLC+1-αUPIC,where α is a weighting factor generated by a fuzzy supervisor. The rule base of the latter is constructed such that the output moves “to zero” when the system is far from the desired value, and “value 1” when the tracking error and its derivatives converge to zero [31, 32]. The main objective of fuzzy supervisor is to determine the weighting factor α, which gives the participation rate of each control signal.The state space is partitioned in several regions using a Sugeno fuzzy system. Also, the product inference, the algebraic sum, and the singleton for the consequent-part are used to design fuzzy supervisor as shown in Figure8. Hence, the fuzzy system output can be written as follows:(14)α=∑j=1mαj∏i=1n-1μHijei∑j=1m∏i=1n-1μHijei,where Hij is a fuzzy set, μHij is the membership degree of e(i) to Hij, αj is a singleton, and m is the number of used fuzzy rules.Figure 8
Supervisory fuzzy inference machine.


### 3.4.2. Simulation Results

The first test proposes a switching controller based on the combination between two conventional controllers: PI and Fuzzy-PD. In fact, the evolution of the pressure and the flow outputs are presented in Figures9 and 10, respectively.Figure 9
Pressure output with PI-Fuzzy-PD switching controller.Figure 10
Flow output with PI-Fuzzy-PD switching controller.The second test presents a switching controller based on the combination between two controllers: conventional PI and Fuzzy-PID. The pressure and the flow outputs with PI/Fuzzy-PID controllers are given by Figures11 and 12.Figure 11
Pressure output with PI-Fuzzy-PID switching controller.Figure 12
Flow output with PI-Fuzzy-PID switching controller.


## 3.4.1. Fuzzy Supervisor

To ensure the more robustness of the closed loop system and a fast dynamic response with the best performance, a combination of the two previously defined controllers is made. This combination multiplexes the fuzzy logic control during the transient state and the PI control in steady state. The first command ensures a fast convergence of the system to steady state with insensitivity to external disturbances, while the second takes over steady state to ensure a more smooth and a minimal static error. To avoid a sudden transition from one controller to another, a gradual switching is used [31–34] which has the following form:(13)UHC=αUFLC+1-αUPIC,where α is a weighting factor generated by a fuzzy supervisor. The rule base of the latter is constructed such that the output moves “to zero” when the system is far from the desired value, and “value 1” when the tracking error and its derivatives converge to zero [31, 32]. The main objective of fuzzy supervisor is to determine the weighting factor α, which gives the participation rate of each control signal.The state space is partitioned in several regions using a Sugeno fuzzy system. Also, the product inference, the algebraic sum, and the singleton for the consequent-part are used to design fuzzy supervisor as shown in Figure8. Hence, the fuzzy system output can be written as follows:(14)α=∑j=1mαj∏i=1n-1μHijei∑j=1m∏i=1n-1μHijei,where Hij is a fuzzy set, μHij is the membership degree of e(i) to Hij, αj is a singleton, and m is the number of used fuzzy rules.Figure 8
Supervisory fuzzy inference machine.


## 3.4.2. Simulation Results

The first test proposes a switching controller based on the combination between two conventional controllers: PI and Fuzzy-PD. In fact, the evolution of the pressure and the flow outputs are presented in Figures9 and 10, respectively.Figure 9
Pressure output with PI-Fuzzy-PD switching controller.Figure 10
Flow output with PI-Fuzzy-PD switching controller.The second test presents a switching controller based on the combination between two controllers: conventional PI and Fuzzy-PID. The pressure and the flow outputs with PI/Fuzzy-PID controllers are given by Figures11 and 12.Figure 11
Pressure output with PI-Fuzzy-PID switching controller.Figure 12
Flow output with PI-Fuzzy-PID switching controller.


## 3.5. Comparative Study

In this section, a comparative study of all control laws applied for the pumping station is made.The choice of the reference signal is rich on a vast time range, in which we find at the beginning a dead zone and then a ramp and a series of steps signals with different amplitude. This choice allows highlighting the effect of the control law in all operation points and studying the system robustness against the sudden changes of needed water level into sprinklers.The obtained results ensure the pressure regulation because the response follows the given reference as illustrated in Figures13 and 14. The response time and the static error related to the pressure output are summarized in Table 2. Table 3 presents the response time and the overshoot related to the flow output. The major drawback of this method of regulation resides primarily at the adaptation problem of the controller face to the external variations such as the extension of drain network, disturbance, and the slowness outputs response.Table 2
Response time and static error of all controllers for the pressure output.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
Response time at ±5%
12.6 s
6.6 s
7 s
6.37 s
6.14 s
Static error of position (in Bar)
0.68
0.1
0.01
0.06
0.02Table 3
Response time and overshoot of all controllers for the flow output.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
Response time at ±5%
13.4 s
11.6 s
8 s
9 s
6 s
Overshoot in %
25.44%
58%
28.94%
30.56%
27.21%Figure 13
Performance results of different control laws for pressure output.Figure 14
Flow performance results of different control laws for pressure output.Note that a saturation was added in the control loop in order to limit the overshoot of flow which is motioned in the constructor document that does not exceed 8 m3/h.Apart from stability, the transient behaviour is another focus of attention for control systems design. There are several properties that can be used to evaluate the transient behaviour of a closed loop control system, for example, steady state accuracy, settling time, and overshoot [35].Beyond these properties, more widely used criteria for quality of control (QoC) relate to the control error, which is defined as the difference between the setpointP∗k and the system outputs Pk and Qk. Some of these performance indices are given below in both continuous-time and discrete-time forms, where k0 and kf are the initial and final discrete-times of the evaluation period [35]. The quality of control criteria are given as follows.(i)
Integral of Absolute Error (lAE):(15)IAE≈∑k=k0kfek≈∑k=k0kfP∗k-Pk.(ii)
Integral of Time-weighted Absolute Error (ITAE):(16)ITAE≈∑k=k0kfkek≈∑k=k0kfkP∗k-Pk.(iii)
Integral of Square Error (ISE):(17)ISE≈∑k=k0kfek2≈∑k=k0kfP∗k-Pk2.(iv)
Integral of Time-weighted Square Error (ITSE):(18)ITSE≈∑k=k0kfkek2≈∑k=k0kfkP∗k-Pk2.According to Figures13 and 14 the ratio speed/power for both outputs (pressure and flow) of the studied system with switching control is higher than other controllers (PI, Fuzzy-PD, and Fuzzy-PID).For pressure output, we notice that fuzzy supervisor approach takes the speed performance of Fuzzy-PD or Fuzzy-PID controllers and the smooth evolution of PI controller, so the switching controller eliminates the small oscillation in transient state for mixing PI/Fuzzy-PD controller.The obtained results by switching controller show that this control strategy is able to limit the oscillation in transient state, without need of the saturation in flow output of pumping station with fuzzy controller (Fuzzy-PD or Fuzzy-PID).Figure14 shows the stable value of steady state (e.g., 4.83 m3/h between t=60 and t=100), which ensured the saving of water use and the economy of electrical energy absorbed by the pumps to reach the pressure set point (5 bar) in the pipelines of the pumping station even in the sprinklers.The quantitative comparison as shown in Tables2, 3, and 4 reflects the switching of PI-Fuzzy-PD and PI-Fuzzy-PID which are better than single controllers as PI, Fuzzy-PD, and Fuzzy-PID.Table 4
Quality of control criteria of all controllers.
PI
Fuzzy-PD
Switch PI-Fuzzy-PD
Fuzzy-PID
Switch PI-Fuzzy-PID
IAE
0.943
0.2256
0.115
0.11
0.108
ITAE
188.6
45.11
13.109
11.87
9.73
ISE
0.8893
0.05088
2.416
e
-
3
9.27
e
-
4
7.415
e
-
4
ITSE
177.9
10.18
4.832
3.774
3.027


## 4. Control Algorithm Validation

### 4.1. Experimental Bench Configuration

To check the performances of the proposed DABs controller, simulations and experimental tests were carried out based only on the estimation model. Operational algorithm of pumps and system regulation are shown in Figure7. The scheme used for the experimental setup is shown in Figure 15.Figure 15
View of the experimental test system.The experimentation has been carried out using MATLAB-Simulink and dSpaceDS1104 real-time controller board. This board contains a Motorola Power PC 603e model that operates at the speed of 250 MHz and a DSP (TMS320F240–20MHz).The developed experimental test bench of the electrical control cabinet is shown in Figure16. In the cabinet configuration, A3, A4, and A5 blocks represent, respectively, flow sensor and two pressure sensors. The electrical regulator pressure card is described by A2 block. The A1 block represents the speed variator. In addition, the cabinet configuration contains two motor-pumps: fixed speed motor-pump of 1.1 kW rated power and variable speed motor-pump of 1.5 kW rated power. Table 5 summarizes the characteristics of the two motor-pumps.Table 5
Pumps parameters.
Variable speed pump
Fixed speed pump
Coupling star 400 V/50 Hz
Coupling star 400 V–50 Hz
N
n
v
=
2870 tr/min
N
n
f
=
2835 tr/min
cosv⁡(φ)=0,81
cos
f
⁡
(
φ
)
=
0
,
84
I
n
v
=
3
,
3 A
I
n
f
=
2
,
5 A
Power: 1,5 kW
Power: 1,1 kW
H
max
⁡ = 80 m
H
max
⁡ = 58 m
N
n represents rated speed, cos⁡(φ) is the power factor, In is the rated current, and Hmax⁡ represents the maximum height of pumps.Figure 16
Experimental testing configuration.The practical process is controlled as follows:(1)
Measure the pressure (Bar) from A5 block of the station.(2)
Send this information to the controller board of the dSpace through ADC, 16-bit input.(3)
In another side, we load the parameters of the BS controller in real-time simulation using MATLAB-Simulink software, with the presence of the dSpace cardDS1104 plugged in a personal computer.A PCI bus cable makes the connection between theDS1104 cards and the controller board. The new control set point is calculated in dSpace (closed loop system with PI controller). The DS1104 sends the order to the pumping station by one of the connectors, DAC, in the controller board. The practical dynamics of IS outputs are extracted from the control Desk software which are given in Figures 17 and 18.Figure 17
First test: experimental result of pressure with trapezoidal reference.Figure 18
First test: experimental result of flow.


### 4.2. Experimental Results

The first test proposes an experimental validation result of switching controller based on the combination between two conventional controllers: PI and Fuzzy-PD. In fact, the real evolution of the pressure and the flow outputs are presented in Figures17 and 18, respectively.In Figure17, it is can be noted that the pressure evolution curve (in red color) can converge towards the reference pressure. Figure 18 shows that the practical evolution of flow output is similar to the simulation results, which converge to 4.8 m3/h.The flow response has a relation with the absorbed energy by the pumps units. It can be noted that the proposed switching control strategy can guarantee at the same time the saving of water use, and the economy of electrical energy absorbed by the pumps to reach the reference pressure in the pipelines of the pumping station even in the sprinklers.The second test presents an experimental validation of switching controller based on the combination between two controllers: conventional PI and Fuzzy-PID. The pressure and the flow outputs with PI/Fuzzy-PID controllers are given by Figures19 and 20.Figure 19
Second test: experimental result of pressure with trapezoidal reference.Figure 20
Second test: experimental result of flow.The digital simulation and experimental results show clearly the improvement in performance of the proposed switching controller algorithm. Similarly, in Figure19, the tracking error between the reference and the real pressure output reached the objective of the experimental validation and confirmed the simulation results.According to the obtained results, the switching controller PI-Fuzzy-PID has a good performance in pressure output while the switching controller PI-Fuzzy-PD presents a good performance in flow output. The switching PI-Fuzzy-PD controller has a benefit in terms of experimental implementation as convergence time and implementation simplicity compared to switching PI-Fuzzy-PID controller.


## 4.1. Experimental Bench Configuration

To check the performances of the proposed DABs controller, simulations and experimental tests were carried out based only on the estimation model. Operational algorithm of pumps and system regulation are shown in Figure7. The scheme used for the experimental setup is shown in Figure 15.Figure 15
View of the experimental test system.The experimentation has been carried out using MATLAB-Simulink and dSpaceDS1104 real-time controller board. This board contains a Motorola Power PC 603e model that operates at the speed of 250 MHz and a DSP (TMS320F240–20MHz).The developed experimental test bench of the electrical control cabinet is shown in Figure16. In the cabinet configuration, A3, A4, and A5 blocks represent, respectively, flow sensor and two pressure sensors. The electrical regulator pressure card is described by A2 block. The A1 block represents the speed variator. In addition, the cabinet configuration contains two motor-pumps: fixed speed motor-pump of 1.1 kW rated power and variable speed motor-pump of 1.5 kW rated power. Table 5 summarizes the characteristics of the two motor-pumps.Table 5
Pumps parameters.
Variable speed pump
Fixed speed pump
Coupling star 400 V/50 Hz
Coupling star 400 V–50 Hz
N
n
v
=
2870 tr/min
N
n
f
=
2835 tr/min
cosv⁡(φ)=0,81
cos
f
⁡
(
φ
)
=
0
,
84
I
n
v
=
3
,
3 A
I
n
f
=
2
,
5 A
Power: 1,5 kW
Power: 1,1 kW
H
max
⁡ = 80 m
H
max
⁡ = 58 m
N
n represents rated speed, cos⁡(φ) is the power factor, In is the rated current, and Hmax⁡ represents the maximum height of pumps.Figure 16
Experimental testing configuration.The practical process is controlled as follows:(1)
Measure the pressure (Bar) from A5 block of the station.(2)
Send this information to the controller board of the dSpace through ADC, 16-bit input.(3)
In another side, we load the parameters of the BS controller in real-time simulation using MATLAB-Simulink software, with the presence of the dSpace cardDS1104 plugged in a personal computer.A PCI bus cable makes the connection between theDS1104 cards and the controller board. The new control set point is calculated in dSpace (closed loop system with PI controller). The DS1104 sends the order to the pumping station by one of the connectors, DAC, in the controller board. The practical dynamics of IS outputs are extracted from the control Desk software which are given in Figures 17 and 18.Figure 17
First test: experimental result of pressure with trapezoidal reference.Figure 18
First test: experimental result of flow.


## 4.2. Experimental Results

The first test proposes an experimental validation result of switching controller based on the combination between two conventional controllers: PI and Fuzzy-PD. In fact, the real evolution of the pressure and the flow outputs are presented in Figures17 and 18, respectively.In Figure17, it is can be noted that the pressure evolution curve (in red color) can converge towards the reference pressure. Figure 18 shows that the practical evolution of flow output is similar to the simulation results, which converge to 4.8 m3/h.The flow response has a relation with the absorbed energy by the pumps units. It can be noted that the proposed switching control strategy can guarantee at the same time the saving of water use, and the economy of electrical energy absorbed by the pumps to reach the reference pressure in the pipelines of the pumping station even in the sprinklers.The second test presents an experimental validation of switching controller based on the combination between two controllers: conventional PI and Fuzzy-PID. The pressure and the flow outputs with PI/Fuzzy-PID controllers are given by Figures19 and 20.Figure 19
Second test: experimental result of pressure with trapezoidal reference.Figure 20
Second test: experimental result of flow.The digital simulation and experimental results show clearly the improvement in performance of the proposed switching controller algorithm. Similarly, in Figure19, the tracking error between the reference and the real pressure output reached the objective of the experimental validation and confirmed the simulation results.According to the obtained results, the switching controller PI-Fuzzy-PID has a good performance in pressure output while the switching controller PI-Fuzzy-PD presents a good performance in flow output. The switching PI-Fuzzy-PD controller has a benefit in terms of experimental implementation as convergence time and implementation simplicity compared to switching PI-Fuzzy-PID controller.


## 5. Conclusion

Performances of a developed method for high-performance pumps pressure control based on switching technique that achieves global asymptotic pressure tracking outputs of a pumping station are presented. The elaborated switching control proves a good effectiveness and a simplicity compared to other controllers. After having developed the technical aspects of the switching controller using fuzzy supervisor, the complete control scheme of the pumping station incorporating the proposed controller experimentally was implemented using a digital signal processor boardDS1104. The proposed switching controller gave satisfactory results in terms of pressure reference tracking and minimization of the response time of pressure and flow, which show the effectiveness of control for this kind of controller of pumping station. Based on the obtained results, it can be concluded that the research into the switching technique has been very successful and can be implemented in any pumping station, which can increase the performance of pumping stations and will be the objective of other research.



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*Source: 3597346-2017-11-23.xml*