Low energy consumption depth control method of self-sustaining intelligent buoy

ZHENG Di，XU Jiayi,LI Xingfei,LI Hongyu

(1. State Key Laboratory of Precision Measurement Technology and Instruments，Tianjin University，Tianjin 300072，China；2. Qingdao Institute for Ocean Technology of Tianjin University，Qingdao 266235，China；3. College of Ocean Science and Engineering，Shandong University of Science and Technology，Qingdao 266590，China)

Abstract：Aiming at the contradiction between the depth control accuracy and the energy consumption of the self-sustaining intelligent buoy,a low energy consumption depth control method based on historical array for real-time geostrophic oceanography (Argo) data is proposed.As known from the buoy kinematic model,the volume of the external oil sac only depends on the density and temperature of seawater at hovering depth.Hence,we use historical Argo data to extract the fitting curves of density and temperature,and obtain the relationship between the hovering depth and the volume of the external oil sac.Genetic algorithm is used to carry out the optimal energy consumption motion planning for the depth control process,and the specific motion strategy of depth control process is obtained.Compared with dual closed-loop fuzzy PID control method and radial basis function(RBF)-PID method,the proposed method reduces energy consumption to 1/50 with the same accuracy.Finally,a hardware-in-the-loop simulation system was used to verify this method.When the error caused by fitting curves is not considered,the average error is 2.62 m,the energy consumption is 3.214×104 J,and the error of energy consumption is only 0.65%.It shows the effectiveness and reliability of the method as well as the advantages of comprehensively considering the accuracy and energy consumption.

Key words：self-sustaining intelligent buoy;low energy consumption;depth control;Argo data;genetic algorithm;hardware-in-the-loop simulation system

0 Introduction

Self-sustaining intelligent as buoys are important instruments for observing and measuring ocean data in the ocean observation such as array real-time geostrophic oceanography(Argo) project[1-3].Its depth control process,including diving to the hovering depth and hovering for a period of time at that depth[4],is an important process to realize the measurement of ocean current at a specific depth.Therefore,the accuracy of depth control will affect the accuracy of the measured data[5].

At present,there are many depth control methods used on underwater equipment[6-9]such as proportional-integral-differential (PID) control,fuzzy control,auto disturbance rejection control (ADRC),etc.Most of the buoy depth control methods are developed from these control methods.Yang et al.[10]built a kinematic model of buoy based on the model of autonomous underwater vehicle(AUV) and designed a fuzzy PID controller.Compared with two single control methods,it has advantages in dynamic characteristics.Mu et al.[11]proposed improved double proportional-differential (PD) controller for single PD controllers with large overshoot and long stability time at large hovering depths.To overcome the change and non-linearity of model parameters and combine the advantages of fuzzy control and double loop,a dual closed-loop fuzzy PID controller was designed to improve the system fault tolerance and reduce the system overshoot and stability time[12].Fang et al.[13]perfected the nonlinear model of buoys based on Ref.[12].According to the complexity of the model and the motion environment,radial basis function (RBF)-PID depth control method with automatic adjustment and optimization of PID parameters through RBF neural network was proposed.The method improved the accuracy and anti-interference ability of controller.Qiu et al.[14-15]proposed the finite-time boundedness (FTB) method and the ADRC method to optimize the performance when the system is disturbed,but they were used to adjust a small depth range.

The above-mentioned methods are all negative feedback control methods.To hover stably at a certain depth,the buoyancy adjustment system needs to work all the time.The hovering depth of the buoy is above 1 000 m.When it works at this depth,the power of motor is large.Since the hovering control process takes a long time,the above-mentioned methods consume a lot of energy.Self-sustaining intelligent buoys rely on their own batteries for energy supply after launching,and cannot supplement energy[16].Therefore,reducing the energy consumption of the buoy in each movement cycle and improving the working life are of great significance to the study of buoys[17].Current depth control methods ignore the energy consumption of the buoys and are also difficult to be applied in practice,therefore we consider accuracy of depth control and energy consumption and then propose a low energy consumption depth control method based on ocean observation data.By analyzing the kinematic model of the buoy and extracting and fitting ocean data,the relationship between the hovering depth and the volume of the external oil sac is obtained,and the error of this method is also calculated.The genetic algorithm is used to carry out optimal motion planning for the depth control process.The proposed method is compared with the double closed-loop fuzzy PID control method in Ref.[12] and the RBF-PID method in Ref.[13] about accuracy and energy consumption.Finally,an experiment was carried out on hardware-in-the-loop simulation system to verify the effectiveness and feasibility of the method.

1 Principle of low energy consumption depth control method

Before designing the depth control method,it is necessary to understand the movement mechanism and force of the buoy.The ascent and descent of the self-sustaining intelligent buoy in the sea water is realized by the buoyancy adjustment system,and the structure of the buoyancy regulating system is shown in Fig.1.When the buoy dives,the steering gear is turned on.Because the internal pressure of the buoy is relatively small,the hydraulic oil is pressed back to the internal oil tank by the pressure of seawater.After the oil is returned to the internal oil tank,the volume of the external oil sac decreases,which leads to a decrease in buoyancy,so the buoy dives.When floating,the pressure of the seawater is greater than that inside the buoy,which requires the motor to always work to discharge the oil from the internal oil tank to the external oil sac.After draining the oil,the buoyancy of the buoy increases and begins to float.

Fig.1 Structure of buoyancy adjustment system

According to the buoy kinematic model established in Ref.[13] and verified by the sea trial,in seawater the buoy is mainly affected by its own gravityG,the buoyancyFfand resistance of seawaterFRon it.The descriptions of the kinematic modelparameters are shown in Table 1.

Table 1 Model parameters (Unvalued part is variable)

According to Newton’s second law,the kinematic equation of buoyiis

ma=G-Ff-FR.

(1)

Substituting the formula of each force in Eq.(1),we obtain

C0(25-Th)]-kρhv|v|.

(2)

The buoy is stationary when hovering,and the speed and acceleration are 0.After this condition is substituted into Eq.(2),the following equation needs to be satisfied when the buoy hovers,that is

(3)

It can be seen from Eq.(3) that at hovering depthh,the volume of the external oil sac is only related to the density and temperature of the seawater at that depth.Therefore,as long as the density and the temperature as a function of depth is obtained,the volume of the external oil sac at a specific hovering depth can be calculated,and then the motion strategy with the least energy consumption can be proposed.

When the buoy reachesVsur,the speed and acceleration of the buoy gradually become 0,and the buoy hovers at the target depth.After stopping at the target depth,the buoy does not drain and return oil and is in a standby state when it floats.Because the hovering depth is generally 1 000 m and above,it is less disturbed by the direction vertical to the sea level,thus it can keep drifting near the hovering depth.Even if it deviates,it will return to the hovering depth where the force is balanced after the disturbance is over.

2 Data extraction based on Argo observation

Through the above analysis,to realize the proposed depth control method,it is necessary to clarify the relationship between sea water density,temperature and depth.The accuracy of this relationship determines the accuracy of the depth control method.In this paper,Global Argo Observational Data Set (V3.0)[18]was used to extract the ocean data of the target sea area and obtain the fitting curves of the density and the temperature.

2.1 Extraction of fitting curve of density and temperature

The data in Global Argo Observational Data Set (V3.0) covers the global sea area,with a time span from 1997 to the present.Therefore,the amount of data is very large.We selected 2.076×105data from 621 profiles in 2016-2018 within the target sea area (longitude is in [-12°,3°] and latitude is in [-28°,-16°].

Using the extracted depth,temperature,and salinity data,the corresponding density data could be calculated according to the International Equation of State of Seawater,1980[19].Then,the discrete data was piecewise fitted and the fitting curve expressions of density-depth and temperature-depth are

(4)

(5)

The fitting curves are shown in Fig.2.

(a) Density (b) Temperature

According to fitting curves expressions of the target sea area and Eq.(3),the relationship between the volume of the external oil sac and the hovering depth was calculated,as shown in Fig.3.

Fig.3 Relationship between external oil sac volume and depth during hovering

2.2 Depth control error by fitting curve

Because the difference between the fitting curves and the actual data (see Fig.2) will bring errors to the actual depthcontrol process,we analyze and obtain the error caused by using the fitting curve to obtain the relationship between the volume of the external oil sac and the hovering depth.

When the target hovering depth ish0,the actual values and fitting values of density and temperature at this depth areρh0,Th0,ρfh0andTf,h0,respectively.According to Eq.(3),when hovering,the relationship between the volume of the external oil sacVsurandh0satisfies

(6)

However,the actual hovering depth of this volume is

(7)

Therefore,the absolute error is

(8)

According to the actual values and the fitting values of density and temperature at a certain target depth,the depth control error at that depth can be solved.

There were 35 027 data from 158 profiles in the target sea area in 2019 selected as the actual values of density and temperature,and the depth control error brought by the fitting curves was calculated.At different target depths,the range of the absolute error is shown in Fig.4,and the center point is the mean value of the error.The maximum error shows a downward trend when the hovering depth increases,and the average error fluctuates,which is related to the different deviations of different depths when fitting a large number of data.

Fig.4 Depth control error caused by fitting curves

3 Low energy consumption motion planning for depth control process

According to the principle of low energy consumption depth control method proposed,the buoy is in a standby floating state after reaching the hovering depth.Therefore,the low energy consumption motion planning of depth control process is mainly the motion planning of diving down to the hovering depth.

3.1 Energy consumption model of dive process before hovering

The dive process before hovering is divided into four stages:oil return,transition,oil discharge,and stop.The buoys in the transition and stop phases naturally dive,and no oil return or oil discharge operations is performed.t1,t2,t3andt4are the ends of the four phases,respectively.And its motion planning is shown in Fig.5.

Fig.5 Motion planning of dive process before hovering

Taking the energy consumption of the dive process before hovering as objective function,it is expressed as

(9)

wherePsis the static power,PM(h) is the motor power,andQseis the energy consumption of the steering gear.In addition to the energy consumption of turning on the steering gear briefly before returning oil and the energy consumption of the motor during the oil discharge phase,there is also static energy consumption in the hovering control process.

Constraint conditions are as follows:

1) At oil return stage,the oil volume is greater than 0,which is expressed as

(10)

whereV0is the initial oil volume andQ(h) is the speed of oil return.

2) At oil discharge stage,the oil volume isVsur,which is expressed as

(11)

whereqis the oil discharge speed of the motor.

3) At stop stage,the speed of the buoy is 0,which is expressed as

(12)

whereacan be calculated by Eq.(2).

4) The sequence of four stages is

t1≤t2≤t3≤t4.

(13)

3.2 Solution of energy consumption model

The genetic algorithm was proposed by Holland et al.It is a simulated evolutionary algorithm developed from the biological evolution mechanism to solve complex optimization problems.It has been widely used for solving many optimization problems.Genetic algorithms are generally divided into simple/standard genetic algorithm (SGA),adaptive genetic algorithm (AGA)and optimum maintaining simple genetic algorithm (OMSGA).Unlike SGA with selection,crossover,and mutation that is hard to converge to the global optimal solution[20],OMSGA has good global convergence[21].

The specific flow of OMSGA for the optimization problem is shown in Fig.6.The parameter settings are shown in Table 2.In the two variables of the optimization problem,the range oft1is small,while the range oft2is large.Whent1is a fixed value andt2changes by 1 s,the change inWis very small.Therefore,we set the resolution oft2at 10 s.

Fig.6 Flow chart of genetic algorithm

Table 2 Parameters of genetic algorithm

After setting the parameters,we set target hovering depth at 1 000 m,2 000 m,and 3 000 m,respectively,and then perform the solution.The optimization process and results are shown in Fig.7.In the iterative process of genetic algorithm,the minimum energy consumption is continuously optimized with the increase of generation.Table 3 shows the motion planning with the lowest energy consumption at different target depths.

(a) Hovering depth=1 000 m

Table 3 Optimal solution at different hovering depths

3.3 Comparison with dual closed-loop fuzzy control method and RBF-PID method

After completing the design of the low-power hovering control method,we compared it with the dual closed-loop fuzzy control method in Ref.[12] and the RBF-PID control method in Ref.[13] in terms of error and energy consumption.The hovering depth of the buoy changed from 1 000 m to 4 000 m,and the hovering time of the buoy after reaching target depth was six days.

The error of the proposed method was brought by the difference between the fitting curves and the actual data.When calculating the depth control error and the energy consumption of the dual closed-loop fuzzy control method and the RBF-PID control method,the ocean data were changed to the same as those of this article.

The comparison of these three methods on the error and the energy consumption are shown in Fig.8 and Fig.9,respectively.

(a) Average depth control error

Fig.9 Semi-logarithmic graph of total energy consumption of three control methods

The maximum and minimum energy consumption of the RBF-PID method and the low energy consumption depth control method at different hovering depths are also marked in Fig.8 (the energy consumption of the dual closed-loop fuzzy PID control is similar to that of RBF-PID method).

It can be seen from Fig.8 that the proposed method has a smaller maximum and average error when the hovering depth is less than 1800 m or between 3 200 m and 3 700 m,and the other two methods are opposite.However,the error range of the proposed method is close to those of the others,that is,average error is within 25 m.

The error of the proposed method is nonlinear because the error of the proposed method mainly comes from the deviation between the fitting curves and the actual data,and the fitting is based on the principle of least squares.However,in practice,the size of the error is more concerned than the linearity.

In terms of energy consumption,according to Fig.8,the RBF-PID method is equivalent to the double closed-loop fuzzy control method,which is more than 50 times that of proposed method.Comprehensively,the errors of the three methods are equivalent,and the proposed method greatly saves the energy consumption of the buoy depth control process and increases the working life of the buoy.

4 Experiment on hardware-in-the-loop simulation system

Due to high cost and long experiment period of sea trials,a hardware-in-loop simulation system is used for the experiments.The system can simulate the change of seawater pressure with depth in real time when the buoy is in operation and verify the effectiveness and stability of the depth control method.Therefore,it can provide a reliable reference for sea trials.

4.1 Structure and principle of hardware-in-the-loop simulation system

The hardware-in-loop simulation system mainly includes hydraulic device,simulation control software,digital multimeter and buoy.The structural relationship of these four parts is shown in Fig.10.

Fig.10 Structural relationship of hardware-in-the-loop simulation system

The main controller of the buoy controls the buoyancy adjustment system to move and simutaneously sends the volume of the external oil sac to the simulation control software.The simulation control software combines the current depth of the buoy with the temperature and density data of the seawater to calculate the acceleration,speed and depth at the next moment and then sends the calculated motion state to the buoy as a reference for its actions.At the same time,the simulation control software controls the hydraulic device to generate the pressure required for the current depth of the buoy and provide the same pressure environment as the ocean,which makes the working process of the buoyancy adjustment system consistent with the actual marine situation.Finally,the digital multimeter measures the energy consumption of the buoy.

4.2 Experimental results and analysis

The target hovering depth of the experiment was 2 000 m.For the convenience of the experiment,the hovering time was 12 h.And the ocean data were used for the fitting curves.The depth variation of the buoy is shown in Fig.11.

Fig.11 Depth variation of buoy in experiment

Line 1 is the depth corresponding to the pressure tracked by the hydraulic system,and line 2 is the actual depth.Except for little fluctuations when the motor was turned on,the hydraulic device could track the target pressure in real time and effectively simulate the pressure environment of the ocean.For the target hovering depth of 2 000 m,the depth control error was very small.

As shown in Table 4,when the ocean data was accurate,that is,the error caused by the fitting curves was not considered,the depth control error of the proposed method was very small.There are two main reasons for this error.First,when the motor returns oil,there was an error of about 1 mL between the target value and the actual value.Secondly,the wire displacement sensor also had a little deviation when measuring the volume of the external oil sac.

Table 4 Results of simulation experiments

As for the total energy consumption in the depth control process,the error between the experimentally measured value and the theoretical value was less than 0.65%.The energy consumption error was mainly due to the fact that the actual oil discharge and return volume of the buoy cannot reach the theoretical accuracy.For every 1 mL of the error,there would be an error about 67 J in energy consumption when returning oil.

The marine data of this experiment is based on the selected target sea area.In different sea areas,the relationship between density,temperature and depth will change slightly,and the motion planning for different hovering depths is also different.Therefore,the accuracy of depth control and the energy consumption will be different,but it can be seen that the difference from the theoretical value will be small.

In conclusion,the experiment on the hardware-in-loop simulation system confirms that the depth control method based on the relationship between the volume of the external oil sac and the hovering depth as well as the motion planning based on genetic algorithm can be effectively applied in practice,and the accuracy and the energy consumption are close to the theoretical values.It also shows that the hovering error of this method will mainly come from the difference between the fitting curves and the actual value.

5 Conclusions

In this paper,a low energyconsumption depth control method was proposed based on the kinematic model of the buoy.According to the density and temperature of the hovering depth and the balance of the force,the volume of the external oil sac when the buoy is hovering at this depth can be calculated.Then the optimal motion strategy for energy consumption could be solved based on this volume.In order to realize this method,Argo data was extracted,and the expressions of density and temperature in the target sea area were obtained by piecewise fitting.At the same time,the depth control error caused by the difference between the fitted curve and the true value was analyzed and calculated.Then the energy consumption model of depth control process was established to find the optimal energy consumption control method by genetic algorithm.Comprehensively comparing the proposed depth control method with dual closed-loop fuzzy control method and RBF-PID method,the hovering accuracy values of the three methods are equivalent,but the energy consumption of the former is much less than those of the others.Finally,an experiment on hardware-in-the-loop simulation system was conducted to verify the effectiveness of the method.In the future,sea trials will be conducted to further verify this method.