# Fuzzy Sliding Mode Control Method for AUV Buoyancy Regulation System

Authors: Wende Zhao; Decheng Wang; Zhenzhong Chu; Mingjun Zhang
Journal: Complexity
 (2021)

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## Abstract

This paper investigates the control problem of the buoyancy regulation system for autonomous underwater vehicle (AUV). There are some problems to be considered in the oil-water conversion-based buoyancy regulation system, including the external seawater pressure, the pressure fluctuations, and the slow switching speed of the ball valve. The control accuracy of the buoyancy regulation under the traditional PID controller cannot meet the requirements of the project. In this paper, a fuzzy sliding mode control scheme is developed for the buoyancy regulation system to solve the abovementioned problems. At first, a mathematical model of the buoyancy regulation system is established, and the stability of the system is analyzed. Then, the sliding mode control algorithm is combined with the fuzzy system to improve the control accuracy. Finally, the pool-experiment results on a prototype show that the developed control scheme can meet the requirements of the control accuracy for the buoyancy regulation system.


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## Body

## 1. Introduction

With the high-speed development of marine resources, autonomous underwater vehicle (AUV) is playing an increasingly important role [1–5]. For the large-depth heave motion of the AUV, it will consume a large amount of energy if the propeller-based drive is selected, while the buoyancy regulation system will provide positive/negative buoyancy by discharging/charging water to achieve unpowered heave [6–9]. Thus, the buoyancy regulation system will effectively reduce energy consumption [10]. Therefore, it is of great significance and practical value to investigate the AUV buoyancy regulation problem with the motion requirement in large range of depth.The buoyancy regulation system for AUV mainly has two ways, including variable volume and variable weight [11–14]. At present, the variable weight-based buoyancy regulation system is most widely used in the underwater vehicle [15, 16], which realizes buoyancy regulation by discharging and charging seawater. “Shin kai 6500” manned submersible in [17] and “Jiao long” manned submersible in [16] both adopt a variable weight-based buoyancy regulation system. In general, the volume of a manned submariner is relatively large, and the accuracy requirement of buoyancy regulation is relatively low. In this paper, the buoyancy regulation system is studied for a small AUV. The features of the developed buoyancy regulation system include small flow rate and high accuracy of buoyancy regulation.In order to realize charging and discharging of seawater under ocean environment with high external pressure, the seawater pump with high pressure is mostly used in the buoyancy regulation system of manned submariners. There are no existing products to simultaneously meet the requirements of high pressure and seawater pump with small flow for the buoyancy regulation system used in a small AUV. Therefore, the authors developed a buoyancy regulation system based on oil-water conversion in [18]. A low-pressure oil pump was used to drive the seawater booster pump to avoid the seawater pump with high pressure and small flow. Based on our previous work in [18], this paper investigates the control method for the buoyancy regulation system based on oil-water conversion so as to satisfy the control requirements of buoyancy regulation.At present, there are some existing research studies about control of the buoyancy regulation system. In [19], an observer-based control scheme was developed for the variable ballast system to achieve the hovering control of the underwater vehicle. In [20], a new type water hydraulic variable ballast system was designed for underwater vehicles and a generalized predictive controller was proposed for this system. In [21], flow rate control was introduced into the water hydraulic variable ballast system to improve the hovering performance of the underwater vehicle. It has been found in our previous experiments that the buoyancy regulation system itself has pressure fluctuations and the switching speed of the ball valve is slow. All of these factors directly affect the response speed and control accuracy of buoyancy regulation. In addition, it is difficult to obtain the accurate dynamic model of the buoyancy regulation system. The Takagi–Sugeno (T-S) fuzzy model is always used to tackle the control of nonlinear systems. For example, the Markov switching system is described by the T-S fuzzy model in [22, 23].Based on the abovementioned consideration, fuzzy technique is applied to sliding mode control in this paper to avoid the use of the dynamic model and reject the external disturbance during the valve-based buoyancy regulation. The main contributions of this paper are presented as follows:(1)
buoyancy regulation system is designed based on oil-water conversion(2)
To address the pressure fluctuations and slow switching speed, a fuzzy logic-based sliding mode control is proposed for the buoyancy regulation system(3)
Simulation and experimental results are provided to show the effectiveness of the developed methodThe remainder of this paper is as follows. Section2 briefly introduces the buoyancy regulation system based on oil-water conversion for a small AUV. Then, the mathematical model of the buoyancy control system considering the external seawater pressure is established in Section 3, including the stability analysis of the system. In Section 4, the traditional PID controller is applied on the buoyancy regulation system. The fuzzy sliding mode control scheme is developed and the simulation results and pool-experiment results are given in Section 5. Finally, conclusions and future research are drawn in Section 6.


## 2. Buoyancy Regulation System Based on Oil-Water Conversion

The charging and discharging process schematic diagram of the buoyancy regulation system based on oil-water conversion developed in this paper is shown in Figures1(a) and 1(b), respectively [18].Figure 1
Schematic diagram of the buoyancy regulation system: (a) seawater charging process; (b) seawater discharging process.
(a)(b)In Figure1, the low-pressure gear pump in the oil circuit drives the seawater booster pump. Two tanks shall be mounted on the fore and aft of the AUV, respectively. The buoyancy regulation is achieved by charging/discharging seawater into the tanks.The process of seawater charging is shown in Figure1(a). Seawater passes through filter ⟶ switching valve ⟶ booster pump ⟶ balance valve ⟶ one-way valve ⟶ on-off valve ⟶ ballast tanks. The process of seawater discharging is shown in Figure 1(b). Seawater is discharged through the ballast tanks ⟶ on-off valve ⟶ switching valve ⟶ booster pump ⟶ balance valve ⟶ one-way valve ⟶ filter ⟶ seawater.The main technical indexes of the buoyancy regulation system include that the average flow is larger than 3 L/min and the overshoot of seawater is within the range between −0.2 L and 0.2 L.


## 3. Modeling and Stability Analysis of Buoyancy Regulation Control System

In [6], the effect of the external seawater pressure on the motor speed and hydraulic power source is not considered during the modeling process. Thus, the model established in [18] cannot reflect the real working environment of AUV. Furthermore, the control accuracy of the buoyancy regulation system in the ocean environment is not satisfactory. Therefore, this section will establish the mathematical model of the buoyancy control system under the external seawater pressure.


### 3.1. Mathematical Model of the Buoyancy Regulation System

According to the principle of the buoyancy regulation system given in Figure1, the motor, gear pump, booster pump, level meter, single valve, and tanks are identified. And then, the block diagram of the buoyancy regulation system is shown as Figure 2.Figure 2
Block diagram of the buoyancy regulation system.In Figure2, Qf represents the desired water volume; Qm represents the actual water volume in the tank; Ku is the proportional coefficient of the controller; Kω is the feedback coefficient of the brushless DC motor; KQ is the flow gain coefficient; and Kq represents the flow line loss coefficient.In this paper, the superposition principle is adopted to obtain the transfer relationship between the desired water volumeQf and the real one Qm. At first, when there is no external seawater pressure, the transfer function is obtained according to the control block diagram of the system [24]:(1)QmsQfs=KuKqWsDs1+KωDS+KQKuKqWsDs.According to equation (1), the influence of external seawater pressure load is superimposed, and the output flow at this time can be obtained as follows:(2)Qms=0.4KTKuqctQfsLaJs2+raJ+LaBVs+raBV+keKT−0.4ra+LaspRpSpqct1.9sLaJs2+raJ+LaBVs+raBV+keKT−0.4k1+1.9k2p1.9s.Relevant parameters in equation (2) are briefly described as follows [24]. Motor torque coefficient KT is 0.477 N·m/A. The displacement of the gear pump qct is 0.008 L/rev. The equivalent inductance La is about 1 × 10−3 H. Winding wire resistance ra is 0.8 Ω. The moment of inertia J is 0.231 × 10−3 kg m2. The viscosity friction coefficient BV is 7.33 × 10−5 N m s. Line back EMF coefficient ke is 0.416. The equivalent area of the gear pump Sp is 1.05 × 10−4 m2. The equivalent radius of the gear pump Rp is 25 × 10−3 m; p is the pressure of the seawater. The flow loss coefficient of the gear pump k1 is 0.04. The flow loss coefficient of the booster pump k2 is 0.024.


### 3.2. System Stability Analysis

According to the overall transfer function and the relevant parameters given in the previous subsection, the Simulink model of the system was established through MATLAB and the simulation was carried out, and the open-loop characteristics of the system are shown in Figure3.Figure 3
Open-loop bode diagram of the system.As can be seen from Figure3, the gain margin of the open-loop system is infinite and the phase margin is 65.5°. In addition, the open-loop traversal frequency is 1.13 × 103 rad/s. Therefore, it can be seen that the response speed of the system is high. The gain margin of the system is far greater than zero, and the phase margin is greater than the common engineering value (40°∼60°). According to the Nyquist stability criterion, it can be judged that the system can meet the stability requirements in the closed-loop state.


## 3.1. Mathematical Model of the Buoyancy Regulation System

According to the principle of the buoyancy regulation system given in Figure1, the motor, gear pump, booster pump, level meter, single valve, and tanks are identified. And then, the block diagram of the buoyancy regulation system is shown as Figure 2.Figure 2
Block diagram of the buoyancy regulation system.In Figure2, Qf represents the desired water volume; Qm represents the actual water volume in the tank; Ku is the proportional coefficient of the controller; Kω is the feedback coefficient of the brushless DC motor; KQ is the flow gain coefficient; and Kq represents the flow line loss coefficient.In this paper, the superposition principle is adopted to obtain the transfer relationship between the desired water volumeQf and the real one Qm. At first, when there is no external seawater pressure, the transfer function is obtained according to the control block diagram of the system [24]:(1)QmsQfs=KuKqWsDs1+KωDS+KQKuKqWsDs.According to equation (1), the influence of external seawater pressure load is superimposed, and the output flow at this time can be obtained as follows:(2)Qms=0.4KTKuqctQfsLaJs2+raJ+LaBVs+raBV+keKT−0.4ra+LaspRpSpqct1.9sLaJs2+raJ+LaBVs+raBV+keKT−0.4k1+1.9k2p1.9s.Relevant parameters in equation (2) are briefly described as follows [24]. Motor torque coefficient KT is 0.477 N·m/A. The displacement of the gear pump qct is 0.008 L/rev. The equivalent inductance La is about 1 × 10−3 H. Winding wire resistance ra is 0.8 Ω. The moment of inertia J is 0.231 × 10−3 kg m2. The viscosity friction coefficient BV is 7.33 × 10−5 N m s. Line back EMF coefficient ke is 0.416. The equivalent area of the gear pump Sp is 1.05 × 10−4 m2. The equivalent radius of the gear pump Rp is 25 × 10−3 m; p is the pressure of the seawater. The flow loss coefficient of the gear pump k1 is 0.04. The flow loss coefficient of the booster pump k2 is 0.024.


## 3.2. System Stability Analysis

According to the overall transfer function and the relevant parameters given in the previous subsection, the Simulink model of the system was established through MATLAB and the simulation was carried out, and the open-loop characteristics of the system are shown in Figure3.Figure 3
Open-loop bode diagram of the system.As can be seen from Figure3, the gain margin of the open-loop system is infinite and the phase margin is 65.5°. In addition, the open-loop traversal frequency is 1.13 × 103 rad/s. Therefore, it can be seen that the response speed of the system is high. The gain margin of the system is far greater than zero, and the phase margin is greater than the common engineering value (40°∼60°). According to the Nyquist stability criterion, it can be judged that the system can meet the stability requirements in the closed-loop state.


## 4. Problems Existing in the Traditional PID Controller

It is found that there are pressure fluctuations in the load and outlet of the hydraulic valve when the hydraulic power source is working in the buoyancy regulation system. Under this scenario, the authors use the traditional PID control method to perform simulation-based analysis.According to the transfer function and performance requirements of the project, the desired water volume is set as 5 L/min and the regulation accuracy is set as ±0.2 L. Under the scenario, PID parameters are optimized in MATLAB, and then the detail parameters are set asKp = 1.75, Ki = 0.001, and Kd = 0.018.For the case without pressure fluctuation, the simulation results for the zero load and 10 MPa are shown in Figure4, respectively.Figure 4
PID control system response curve without disturbances.As can be seen from Figure4, the overshoot is about 0.2 L and the adjustment time is about 69 s when there is no load. For 10 MPa pressure load, the overshoot is about 0.17 L and the adjustment time is about 74 s.In order to verify the anti-interference ability of the PID controller, random disturbance with the amplitude of 1 MPa is added. The corresponding simulation results are shown in Figure5.Figure 5
PID control system response curve with disturbance.As can be seen from Figure6, when there exists pressure fluctuation in the buoyancy regulation system, the overshoot of the PID control method is about 0.25 L, which does not meet the requirement of being less than 0.2 L. For this reason, this paper studies the new control method.Figure 6
Response curve based on the fuzzy sliding mode controller.


## 5. Buoyancy Regulation Based on Fuzzy Sliding Mode Method

This section studies the fuzzy sliding mode control method. And then, the effectiveness of the developed control scheme is verified by simulation results and experiment result, respectively.


### 5.1. Fuzzy Sliding Mode Control Method

The fuzzy sliding mode control method has been widely used in other nonlinear systems [25–27]. In the control system, the sliding mode controller is used as the local controller, and the Sugeno fuzzy controller is used to link and combine the local controllers.The structure diagram of the fuzzy sliding mode control for the buoyancy regulation system designed is shown in Figure7.Figure 7
Block diagram of the fuzzy sliding mode controller.Suppose that when the water quantity error ise>1.5 L, the motor control voltage u is the maximum value; when the water quantity error is e<0, the control voltage u is 0, as shown in the following equation:(3)u=5Ve>1.5L,0e<0.Assuming that the water quantity error is −1.5 L≤e≤ 1.5 L, the fuzzy sliding mode controller is used to regulate the water quantity in the tanks. The distribution of water quantity deviation membership function is shown in Figure 8.Figure 8
Membership function of water quantity deviation.The sliding mode surface is defined ass=e.+λie with positive constant λi. The sliding mode controller corresponding to the controller is distributed in different fuzzy regions, shown as follows:(4)ifeisAi,thenui=−ksgnss≤−π2ω,−ksinωis−π2ω<s≤0,0s>0,where λi is the slope of the sliding line of the ith rule, ωi is the boundary layer thickness of rule i, and ui is the output of rule i of the sliding mode fuzzy controller. Since the range of the control voltage u is [0 V, 5 V], k in equation (3) is set as 5. Ai belong to the set (NB, NM, NS, ZE, PS, PM, PB), shown in Figure 8.Then, the total control effort is given by(5)u=∑i=1mbiui,where bi=μAie/∑j=1mμAje and μAie is the membership function of e in the precomponent of the ith rule.The buoyancy regulation control system developed in this paper can only achieve one-way regulation. Here, the parameter adjustment method of sliding mode controller in [13] is adopted, and the specific control rules are shown in Table 1.Table 1
Rules of the fuzzy sliding mode controller.
Water quantity deviationeBoundary layer thicknessωiSlope of slide lineλiPB0.20.02PM0.30.04PS0.350.05ZE0.50.08NS——NM——NB——


### 5.2. Simulation Verification

When there is no pressure fluctuation, the fuzzy sliding mode controller is applied to the buoyancy regulation system under the conditions of no pressure load and 10 MPa pressure load, respectively, and the response curve of the system is shown in Figure6.To verify the anti-interference ability of the fuzzy sliding mode control algorithm, random disturbance with the amplitude of 1 MPa is added for the case with 10 MPa. The simulation results obtained are shown in Figure9.Figure 9
Response curve of the fuzzy sliding mode controller under disturbance.For the convenience of comparison and analysis, the simulation results of the PID controller and the fuzzy sliding mode controller are summarized in Table2.Table 2
Comparison of simulation results under different controllers.
The control methodNo random interferenceRandom interference (amplitude is 1 MPa)The average flow rate (L/min)Overshoot (L)The average flow rate (L/min)Overshoot amount (L)No load10 MPa loadNo load10 MPa load10 MPa load10 MPa loadPID control4.344.050.20.173.950.25Fuzzy sliding mode control4.484.100.120.104.000.19As can be seen from Table2, the buoyancy regulation system under the fuzzy sliding mode controller meets the requirements of the project, including the adjusting speed, control precision, and anti-interference ability.


### 5.3. Experimental Verification

#### 5.3.1. Experimental Set-Up

The maximum voltage of the motor in the buoyancy regulation system is 5 V. And the sampling frequency of the liquid level sensor is 0.1 s. In this experiment, the desired water quantity is 10 L. In addition, two cases are considered. Specifically, the first case is without any load, while the second case is with 10 MPa load. The protype of the buoyancy regulation system is presented in Figure10.Figure 10
Prototype of the buoyancy regulation system.


#### 5.3.2. Experimental Results

The comparison experiments of the PID controller and the fuzzy sliding mode controller are carried out for the case without load and the case with 10 MPa, respectively. The response curves of water quantity control are shown in Figures11 and 12.Figure 11
Experimental results of different control methods under no load.Figure 12
Experimental results of different control methods under 10 MPa load.For the convenience of comparative analysis, the above experimental data are converted into a table, as shown in Table3.Table 3
Experimental results of different controllers.
No load10 MPa loadAdjustment time (s)Overshoot amount (L)Adjustment time (s)Overshoot amount (L)PID controlAbout 1300.22About 1450.3Sliding mode fuzzy controlAbout 1240.17About 1420.2As can be seen from Table3, for the case with no load, the adjustment time of the fuzzy sliding mode controller is 124 s, which is 4.0% faster than that of the PID controller. The overshoot of the fuzzy sliding mode control method is 0.17 L, which is 22.7% higher than that of the PID method. The adjustment time of the fuzzy sliding mode control method is 142 s for the case with 10 MPa load, which is about 1.9% faster than that of the PID controller. The overshoot of the sliding mode fuzzy control method is 0.20 L, while the corresponding result is 0.3 L under the PID controller. The flow rate of the sliding mode fuzzy control method is higher than 4 L/min through the calculation of the liquid level sensor information of the water storage cylinder. It can be seen from the experimental results that the fuzzy sliding mode control can meet the requirements of the average flow being larger than 3 L/min and the overshoot being within the range of ±0.2 L under the different conditions.


## 5.1. Fuzzy Sliding Mode Control Method

The fuzzy sliding mode control method has been widely used in other nonlinear systems [25–27]. In the control system, the sliding mode controller is used as the local controller, and the Sugeno fuzzy controller is used to link and combine the local controllers.The structure diagram of the fuzzy sliding mode control for the buoyancy regulation system designed is shown in Figure7.Figure 7
Block diagram of the fuzzy sliding mode controller.Suppose that when the water quantity error ise>1.5 L, the motor control voltage u is the maximum value; when the water quantity error is e<0, the control voltage u is 0, as shown in the following equation:(3)u=5Ve>1.5L,0e<0.Assuming that the water quantity error is −1.5 L≤e≤ 1.5 L, the fuzzy sliding mode controller is used to regulate the water quantity in the tanks. The distribution of water quantity deviation membership function is shown in Figure 8.Figure 8
Membership function of water quantity deviation.The sliding mode surface is defined ass=e.+λie with positive constant λi. The sliding mode controller corresponding to the controller is distributed in different fuzzy regions, shown as follows:(4)ifeisAi,thenui=−ksgnss≤−π2ω,−ksinωis−π2ω<s≤0,0s>0,where λi is the slope of the sliding line of the ith rule, ωi is the boundary layer thickness of rule i, and ui is the output of rule i of the sliding mode fuzzy controller. Since the range of the control voltage u is [0 V, 5 V], k in equation (3) is set as 5. Ai belong to the set (NB, NM, NS, ZE, PS, PM, PB), shown in Figure 8.Then, the total control effort is given by(5)u=∑i=1mbiui,where bi=μAie/∑j=1mμAje and μAie is the membership function of e in the precomponent of the ith rule.The buoyancy regulation control system developed in this paper can only achieve one-way regulation. Here, the parameter adjustment method of sliding mode controller in [13] is adopted, and the specific control rules are shown in Table 1.Table 1
Rules of the fuzzy sliding mode controller.
Water quantity deviationeBoundary layer thicknessωiSlope of slide lineλiPB0.20.02PM0.30.04PS0.350.05ZE0.50.08NS——NM——NB——


## 5.2. Simulation Verification

When there is no pressure fluctuation, the fuzzy sliding mode controller is applied to the buoyancy regulation system under the conditions of no pressure load and 10 MPa pressure load, respectively, and the response curve of the system is shown in Figure6.To verify the anti-interference ability of the fuzzy sliding mode control algorithm, random disturbance with the amplitude of 1 MPa is added for the case with 10 MPa. The simulation results obtained are shown in Figure9.Figure 9
Response curve of the fuzzy sliding mode controller under disturbance.For the convenience of comparison and analysis, the simulation results of the PID controller and the fuzzy sliding mode controller are summarized in Table2.Table 2
Comparison of simulation results under different controllers.
The control methodNo random interferenceRandom interference (amplitude is 1 MPa)The average flow rate (L/min)Overshoot (L)The average flow rate (L/min)Overshoot amount (L)No load10 MPa loadNo load10 MPa load10 MPa load10 MPa loadPID control4.344.050.20.173.950.25Fuzzy sliding mode control4.484.100.120.104.000.19As can be seen from Table2, the buoyancy regulation system under the fuzzy sliding mode controller meets the requirements of the project, including the adjusting speed, control precision, and anti-interference ability.


## 5.3. Experimental Verification

### 5.3.1. Experimental Set-Up

The maximum voltage of the motor in the buoyancy regulation system is 5 V. And the sampling frequency of the liquid level sensor is 0.1 s. In this experiment, the desired water quantity is 10 L. In addition, two cases are considered. Specifically, the first case is without any load, while the second case is with 10 MPa load. The protype of the buoyancy regulation system is presented in Figure10.Figure 10
Prototype of the buoyancy regulation system.


### 5.3.2. Experimental Results

The comparison experiments of the PID controller and the fuzzy sliding mode controller are carried out for the case without load and the case with 10 MPa, respectively. The response curves of water quantity control are shown in Figures11 and 12.Figure 11
Experimental results of different control methods under no load.Figure 12
Experimental results of different control methods under 10 MPa load.For the convenience of comparative analysis, the above experimental data are converted into a table, as shown in Table3.Table 3
Experimental results of different controllers.
No load10 MPa loadAdjustment time (s)Overshoot amount (L)Adjustment time (s)Overshoot amount (L)PID controlAbout 1300.22About 1450.3Sliding mode fuzzy controlAbout 1240.17About 1420.2As can be seen from Table3, for the case with no load, the adjustment time of the fuzzy sliding mode controller is 124 s, which is 4.0% faster than that of the PID controller. The overshoot of the fuzzy sliding mode control method is 0.17 L, which is 22.7% higher than that of the PID method. The adjustment time of the fuzzy sliding mode control method is 142 s for the case with 10 MPa load, which is about 1.9% faster than that of the PID controller. The overshoot of the sliding mode fuzzy control method is 0.20 L, while the corresponding result is 0.3 L under the PID controller. The flow rate of the sliding mode fuzzy control method is higher than 4 L/min through the calculation of the liquid level sensor information of the water storage cylinder. It can be seen from the experimental results that the fuzzy sliding mode control can meet the requirements of the average flow being larger than 3 L/min and the overshoot being within the range of ±0.2 L under the different conditions.


## 5.3.1. Experimental Set-Up

The maximum voltage of the motor in the buoyancy regulation system is 5 V. And the sampling frequency of the liquid level sensor is 0.1 s. In this experiment, the desired water quantity is 10 L. In addition, two cases are considered. Specifically, the first case is without any load, while the second case is with 10 MPa load. The protype of the buoyancy regulation system is presented in Figure10.Figure 10
Prototype of the buoyancy regulation system.


## 5.3.2. Experimental Results

The comparison experiments of the PID controller and the fuzzy sliding mode controller are carried out for the case without load and the case with 10 MPa, respectively. The response curves of water quantity control are shown in Figures11 and 12.Figure 11
Experimental results of different control methods under no load.Figure 12
Experimental results of different control methods under 10 MPa load.For the convenience of comparative analysis, the above experimental data are converted into a table, as shown in Table3.Table 3
Experimental results of different controllers.
No load10 MPa loadAdjustment time (s)Overshoot amount (L)Adjustment time (s)Overshoot amount (L)PID controlAbout 1300.22About 1450.3Sliding mode fuzzy controlAbout 1240.17About 1420.2As can be seen from Table3, for the case with no load, the adjustment time of the fuzzy sliding mode controller is 124 s, which is 4.0% faster than that of the PID controller. The overshoot of the fuzzy sliding mode control method is 0.17 L, which is 22.7% higher than that of the PID method. The adjustment time of the fuzzy sliding mode control method is 142 s for the case with 10 MPa load, which is about 1.9% faster than that of the PID controller. The overshoot of the sliding mode fuzzy control method is 0.20 L, while the corresponding result is 0.3 L under the PID controller. The flow rate of the sliding mode fuzzy control method is higher than 4 L/min through the calculation of the liquid level sensor information of the water storage cylinder. It can be seen from the experimental results that the fuzzy sliding mode control can meet the requirements of the average flow being larger than 3 L/min and the overshoot being within the range of ±0.2 L under the different conditions.


## 6. Conclusion

This paper investigates the control problem for the buoyancy regulation system. And a fuzzy sliding mode control scheme is applied to the buoyancy regulation system. According to the experiment results, it is shown that the flow rate is higher than 4 L/min under the developed control scheme, and the overshoots are 0.17 L and 0.20 L for the case without load and with 10 MPa load, respectively. The experiment results satisfy the performance requirements, i.e., the average flow being larger than 3 L/min and the overshoot is within the range of ±0.2 L. The developed controller requires the complete information of the system. In future research, we need to investigate control scheme for the buoyancy regulation system with uncomplete information.



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