Researching and Development of an Autonomous Underwater Vehicles with Capability of Collecting Solar Energy

Nội dung text: Researching and Development of an Autonomous Underwater Vehicles with Capability of Collecting Solar Energy

1. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 Researching and Development of an Autonomous Underwater Vehicles with Capability of Collecting Solar Energy Nguyen Van Tuan1,2*, Dinh Van Phong1, Nguyen Chi Hung1 1 Hanoi University of Science and Technology, Hanoi, Vietnam 2 Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Viet Nam *Email: tuan.nguyenvan@phenikaa-uni.edu.vn Abstract Autonomous Underwater Vehicles (AUV) is an unmanned underwater device with capability of performing a variety of missions in the water environment such as ocean operation, offshore waters, polluted water investigation including: marine scientific research, maritime monitoring, exploration, marine economics, oil and gas, security and defense, surveillance and measurement and in rescue and salve. In this article, the authors developed a model of AUV with retractable wings and evaluate the efficiency of solar energy collection. The establishment of the controller to adapt the stability requirements, in accordance with the model of equipment S-AUV (Solar - Autonomous Underwater Vehicles) was built. The hydrodynamic equations with the predefined conditions were modeled and solved. The Hierarchical Sliding Mode Controller (HSMC) for the S-AUV were applied in this research. Experimental results showed that the efficiency of the collection of the solar cell has been significantly improved comparing to a diving equipment without retractable energy wings. In addition, the simulation results showed that the developed controller performed much better control quality, adhering to the set value with the error within the permissible limit. Keywords: Autonomous underwater vehicles, energy solar, underactuated system, control AUV, hierarchical sliding mode controller. 1. Introduction* Underwater Vehicles with capability of collecting solar energy namely SAUV I [2]. Autonomous Underwater Vehicles (AUV) have been used in many industrial applications such as Vietnam is a country with a coastline of over oceanography, fisheries, environmental monitoring, 3,000 km and a large territorial sea with many islands. security and defense, rescue and salve, etc. With the Therefore, the study of AUV will have a lot of automatic operation function, AUV is very suitable for potential applications in economic activities, society, missions required for exploring deep water/ocean [1]. security and defense and in scientific research. The AUV is an automatic, programmable device that Moreover, as a subtropical tropical country, Vietnam is self-propelled, or remotely controlled by sending has a huge amount of solar radiation with hours of commands from the monitoring center or semi- sunshine from 1,400 to 2,600 hours/year. The North automatic operation without the need for an operator has an average of 1,400 - 2,100 hours of sunshine per depending on the targeted function. The AUV plays an year, the South from Da Nang City on average from important role such as in marine exploitation, oil and 2,000 to 2,600 hours of sunshine per year. The gas installation and large-scale subsea surveys, observed data shows that the average radiation energy offshore research, etc . across the country per day is from 3.3 to 5.7 kWh/m2 [3]. The potential for energy use in almost every region The ability to store energy on AUV is an of the country is very promising. important factor in the design and operation of the AUV. With the limitations of size, mass and different With the ability to move automatically in the design requirements, the energy storage on the AUV is water environment, AUV is very suitable for missions often limited, so the operation time of the AUV is that explore deep, toxic or need long-term activities. limited. The integration of AUV and energy However, the fixed energy wing increases the motion replenishment systems have been studied for decades resistance on the AUV under the water [5], since the [2]. The IMTP Institute of Technology and the Russian design structure of the diving equipment affects drag Academy of Sciences have evaluated the technologies when moving. The greater the drag force is, the energy required for a solar-powered AUV [2]. One of the loss increases. The relationship between drag force and products of this development program is the the shape, size, and velocity of the AUV diving manufacture and testing of an Autonomous equipment is represented by the following formula: ISSN 2734-9373 Received: February 03, 2021; accepted: August 02, 2021 75
2. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 1 meet specific objectives such as motion trajectory F= ρ uCS2 . . (1) drag 2 d control, dive depth control, direction control, In general, the movement of S-AUV can be represented where Fdrag is the resistance acting on the AUV in the by equations of motion with six degrees of freedom direction of movement, ρ is the density of water, u is (6-DOF) [5]. Parameters such as the direction of the velocity of the AUV, Cd is the form resistance motion, force and torque, speed and position for the coefficient and S is the projected area of the AUV on S-AUV are shown in Table. 1 and Fig. 1. the plane perpendicular to the direction of motion. Table 1. Parameter symbols are represented in The linear controllers have been used for dynamic and fixed coordinate systems controllers for AUV by many researchers [5, 6]. PID Position controller is mainly applied to linear systems, however Forces and DOF Motion and Velocity there are also some PID extending controllers to Euler moments nonlinear systems that can be adopted for AUV [7]. angles The controllers for AUV are Sliding Mode Controls Surge [8], adaptive controllers [9], Fuzzy logic controllers 1 X u x (x-direction) [10], Model Predictive Controller (MPC) [11], Sway controllers based on neural networks [12] and Object- 2 Y v y oriented control method . In this paper, the author (y-direction) Heave focuses on the Sliding Mode Controller for a small S- 3 Z w z AUV with added solar energy. The outstanding (z-direction) advantage of the Hierarchical Sliding Mode Controller Roll is its stability and robustness even in the case of system 4 (Rotation K p φ with noise or when the object's parameters change over about x) time. Pitch 5 (Rotation q θ The authors designed and built a small AUV with M about y) energy supplementation by retractable solar wings. The energy wings remain closing in moving states, and Yaw ψ starting opening when the AUV approaches the surface 6 (Rotation N r of the energy-harvesting water radiated by sunlight in about z) the day time. Optimizing the energy collected by the Velocity vector v, reference vector η can be wings to reduce the size and shape of the S-AUV, represented as follows: which can be changed when moving, will have several benefits including (i) reducing the drag impact on the η=[, ηηT TT ] ∈ R6 1* 2* (2) S-AUV, (ii) increasing solar energy collection  T TT 6  v=[,] vv12 ∈ R efficiency, (iii) reducing energy consumption and (iv) supporting the S-AUV to operate for a long time where: without recharging steps. T 3 T 3 η1* =[,xyz ,] ∈ R v1 =[,, uvw ] ∈ R  T 3 and  T 3 η2* =[,, φθψ ] ∈ R v2 =[,,] pqr ∈ R The first-order derivative of the position vector is related to the velocity vector through the below transformation: =ηη Jv( )  1* 1 2* 1 (3) ηη2*= Jv 2( 2*) 2 Combining (2) and (3) creates equations that describe the position and direction of S-AUV: Fig. 1. The dynamic coordinate system xyz and fixed ηη1*  Jv 1( 2*) 0 3x 3 1 coordinate system abc  =⇔=ηη Jv( ) (4) ηη2*  03x 3Jv 2( 2*)  2 2. Dynamics of S-AUV Model 2.1. Coordinates with: The dynamic model of the S-AUV is built on the c(θψ) .c ( ) JJ12 13  basis of mechanical theory, the principles of kinetics η= θψ J1( 2* ) c( ) .s ( ) JJ22 23 and statics. Hydrodynamic models of the S-AUV are −sθ s φθ .c c φθ .c used to design control systems for the S-AUV that ( ) ( ) ( ) ( ) ( ) 76
3. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 with: c=cos; s=sin 00−mr −− mxg r a2  J = sφθψ .s .c− c φψ .s mr 00−+myg r a1 12 ( ) ( ) ( ) ( ) ( ) C = , 0 00 0 = φθψ+ φψ  J13 c( ) .s( ) .c( ) s( ) .s ( ) +− mxgg r a21 my r a 00 J22 = s(φθψ) .s( ) .s( ) + c( φψ) .c ( ) D11 0 00  J = cφθψ .s .s− s φψ .c 0D22 00 23 ( ) ( ) ( ) ( ) ( ) Dv( ) =   Zu0 0 D33 0 1s ()tan()φθ cs ()tan() φθ  0 00D44 η=  φφ− J2( 2* ) 0 cs () () with: 0sc ()sec(φθ ) ()sec( φθ ) D= X + Xu 2.2. Dynamics with 4 Degrees of Freedom 11 u uu To simplify the small types of AUV we can D22 = YYvv + vv remove 2 unnecessary degrees of freedom: angle θ ( pitch) and angle φ (roll) . Hence the equations of D33 = ZZww + ww movement of the S-AUV 4 degrees of freedom are = + expressed through the quantities (propulsion, a D44 KKpp pp steering wing, two auxiliary rudders combined with a pump system for floating diving). Coordinate position In this case the S-AUV is an underactuated (x, y), direction of S-AUV (ψ- yaw) and position on system, consisting of 2 input signals and 4 output axis z (diving depth). signals. Therefore, we separate the mathematical model into two parts, including the underactuated and In this study, the authors focus on constructing full actuated system. Position vector η will be the hierarchical sliding mode controller with the S- T T AUV's parameter model which is appropriately separated into 2 parts η= [ ηη12] and η1 = [xy] T calculated and selected. Four degrees of freedom for a state of full actuated and ηψ= [z ] for a state movement model of S-AUV include following: 2 T of underactuated. Similarly, velocity vector v is ηψ= [xyz,,, ] is the position vector of the device in T divided into two parts with v= [ vv] . The diving axes Ox,, Oy Oz and the directional angle of the S- 12 T gear dynamic equation was rewritten as follows: AUV rotates around the axis Oz ; v= [ uvwr,, ,] is a  η1=Jv 11 1 + Jv 12 2 vector of long velocity in the directions Ox,, Oy Oz   η2=Jv 21 1 + Jv 22 2  (6) and the rotational velocity around axis Oz . ++ + ++ =τ  Mv11 1( C 11 D 11) v 1 Mv 12 2( C 12 D 12) v 2 The general dynamic equation for a S-AUV with  Mv21 1++( C 21 D 21) v 1 + Mv 22 2 ++( C 22 D 22) v 2 =0 4 degrees of freedom is as follows: with: =ηη Jv( )  * (5) − MvCvv++ Dvv =τ mX+ u 0 Xwg my   ( ) ( ) M = ; M = ; 11 12 + 0 mY+ v 0 Yrg mx where: Zu 0 mZ+ w 0 m+− X u0 Xwg my M 21 = ; M 22 =  −+my mx N + 00m++ Y Y mx g gv 0 INzr M = vrg, + Zuw00mZ −− 0 −mr 0 mxg r a2 −+ + Cv11 ( ) = ; Cv12 ( ) = ; myg mx gv N 0 INzr  −+ mr 0 0 myg r a1 cos(ψψ )− sin( ) 0 0 00 00 ψψ Cv( ) = ; Cv( ) = ; sin( ) cos( ) 0 0 21 +−22  J (η ) = ’ mxgg r a21 my r a 00 0 0 10  cos(ψψ )− sin( ) 00 0 0 01 Jv11 ( ) = ; Jv12 ( ) = ; sin(ψψ ) cos( ) 00 77
4. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 00 10 Replace (10) and (11) into the system of Jv21 ( ) = ; Jv22 ( ) = ; equations (6), we have the system of dynamic 00 01   equations of S-AUV as follows: Xu + Xuuu 0  η1= Jv 11 1 Dv11 ( ) = ; 0 YYv+  −−11 v vv v1= M( −− Cv11 Cv 2 2) + M τ  (12) 00  η2= Jv 22 2 Dv12 ( ) = ; 00    v2 = fv( ) with Zu0 0 −− Dv21 ( ) = ; 11 f( v) =− M22 M 21 M( −− Cv1 1 Cv 2 2 ) 00  ++(C21 Dv 21) 1 ++( C 22 Dv 22) 2 ZZww + ww 0 −−11 Dv22 ( ) = ; −M MMτ 0 KKp+ 22 21 p pp 00 00 τ= ττ [ 12, ,0,0] where : Jv12 ( ) =  ; Jv21 ( ) =  00 00 a1w=++ Xuuq Xw Xq  To solve the above problem, the paper proposes a2 =++ Yvvp Y p Yr r  to use HSMC controller because this is the most suitable method to control underactuated systems. Since M is the positive definite matrix so from 22 Therefore, the algorithm structure is used to ensure the the fourth equation in (6), we have: stability of the system while still sticking to the given −1 value as shown in Fig. 2. v2 =− M22 MvCDvCDv 21 1 ++( 21 21) 1 ++( 22 22) 2 (7) Replace (7) into the third equation in (6): Mv11 1++( C 11 D 11) v 1 −MMMvCDvCDv−1  ++( ) ++( ) 12 22 21 1 21 21 1 22 22 2 Fig. 2. HSMC controller structure block diagram ++(C Dv) =τ 12 12 2 From the system of equations (12), we rewrite the (8) generalized form as follows: Simplify equation (8) we get:  η1= Jv 11 1  MvCvCv ++ =τ (9)  v = fX() + GX ()τ 1 11 2 2  11 1 (13) η = Jv with:  2 22 2  v22= fX() + GX 2 ()τ = − −1 M M11MM 12 22 M 21 with: −1 T C1=+−( C 11 D 11) MM 12 22( C 21 + D 21 ) X= [ηη11 vv 2 2] −1 −1 C2=+−(C 12 D 12) MM 12 22( C 22 + D 22 ) f1() X= M ( −− Cv11 Cv 2 2 ) With the assumption that we can choose the GX()= M−1 1 parameters for assuring that the M is positive definite f() X=− M−−11 M M() −− Cv Cv matrix, from the equation (9), we have: 2 22 21 1 1 2 2 ++(C Dv )( ++ C D ) v] −−11 21 21 1 22 22 2 v1= M( −− Cv11 Cv 2 2) + M τ (10) −−11 GX2 ()= − M22 MM 21 Replace (10) into the equation (7): The definition of the error vector between the −−11 output signal and the set signal is: v2 =− M22 M 21 M(τ −− Cv1 1 Cv 2 2 )  ηη− ++(C Dv) ++( C Dv) ] e1  11d  21 21 1 22 22 2    ev −−11 21   v2 =− M22 M 21 M( −− Cv1 1 Cv 2 2 ) et( ) = = (14)  e ηη−  3  22d  ++(CD21 21)v 1 ++( C 22 Dv 22) 2 ] (11) ev42   −−11 − MM22 21M τ 78
5. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 The definition of the sliding surface is as follows: 1 V= SST .  (24) 2  s1=+> ke 11 e 2, ( k 1 0)  Taking derivative V over time, we get:  s2=+> ke 23 e 4, ( k 2 0) (15)  Ss=+>λ1 β s 2, ( λβ , 0) ∂V = SST .  (25) ∂t According to the control method HSMC for underactuated system, the controller signal is divided From (13), (14), (15) and (25) we have below into two components: equation: ττn= eqn + τ swn (16) ∂V = SST .  ∂t where: T =Sss.[λβ12 + ] + τeqn is the signal that is used to control the λ ++τη − subsystem in the controller structure Hierarchical T (kJ1 11 v 1 f 1 () X G1 () X k1 1d ) = S . Sliding Mode Controller. +β(kJ2 22 v 2 ++ f 2 () X G2 () Xτη − k2 2d ) + τswn is the signal that is used to control the Since ηη, are constant values so: ηη= = 0 . switching of the system sliding surface. 12dd 12dd Consider the first subsystem model: Hence: η = ∂V T  1Jv 11 1 = SS.   (17) ∂t v11= fX() + GX 1 ()τ T λτ(kJ1 11 v 1++ f 1 () X G1 ()) X Applying equation (16), we have the control = S . +βτ(kJ v ++ f () X G ()) X signal for the first and second subsystem as follows: 2 22 2 2 2 λ(kJ1 11 v 1++ f 1 () X ττ1=eq 1 + τ s w1   (18) GX1 ( )(ττeq1+++ s w1 ττ eq 2 s w2 )) ττ= + τ T   2eq 2 s w2 = S . +β (kJ v ++ f () X 2 22 2 2 The sliding surface derivative S1 with respect to ττ+++ ττ GX2 ( )( eq1 s w1 eq 2 s w2 )) time we get: λτ(kJ1 11 v 1++ f 1 () X G1 () X eq 1 ) s1= ke 11  + e 2 =++ke11 f 1() X G 1 () X τ 1  +βτ(kJ2 22 v 2 ++ f 2 () X G2 () X eq 2 ) =++ke f() X G ()( X ττ + ) 1 1 1 1 eq1 s w1 ++τλ(GX () β GX ()) = T sw1 1 2 =k11 e + f 1() X + G 1 () Xτ eq 1 −− as 1 bsign() s1 S . (26) (19) ++τλsw2(GX 1 () β GX2 ()) ++as bsign() s + G ( X )τ  1 1 1s w1 ++λ τβ τ GX1()eq 22 GX ()eq 1  We choose the control signal for the first ++kS.δδ sgn( S ) − ( kS . + sgn( S )) subsystem as follows: To ensure the stability of the system through the τ =−+(G−1 (X))( kJ v f (X))  eq1 1 1 11 1 1 (20) principle of stability of Lyapunov so that ∂∂Vt/ is τ =−+−1  sw1(G 1 (X))( as1 bsign ( s1 )) negative definite, we choose the following control signals: Substituting the system of equations (20) into equation (19) we have: τ =−+G−1 ( X )( kJ v f ( X ))  eq1 1 1 11 1 1 s =−− as bsign() s (21) −1 11 1 τ eq2=−+G 2( X )( kJ 2 22 v 2 f 2 ( X ))  −1 The control signal for the system consists of two τsw2 =−+( λGX1 () β GX2 ())( λτ GX1 ()eq 2 (27)  subsystems: +−βτλ  GX21()eq )( GX 1 () τττ= +  −1 12 (22) +β +− δτ  G2 ( X )) ( kS . sgn( S )) sw1 Select the sliding surface for the first and second subsystems as follows: With values corresponding to (27) and s1=+=+ ke 11 e 2, s 2 ke 2 3 e 4 and through the Lyapunov Ss=λβ12 + s (23) function choose the values for ee12→→0; 0; To ensure stability for the S-AUV, consider ee34→→0; 0. Then we get s1 → 0 , s2 → 0 . Lyapunov function for the closed system as follows: 79
6. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 Replacing (27) into equation (26) we have: ∂V ==−+ST. S ( kS . TT Sδ S sgn( S )) ≤ 0 ∂t This suggests that the system stability is guaranteed. Control signals are determined by the following formula: ττ=+++eq1 τ sw 1 τ eq 2 τ sw 2 −1 =−+(G1 (). X) ( kJ1 11 v 1 f 1 () X ) Fig. 6. Solar energy collection chart with solar wing −1 closed and opened at Hai Phong City (2020 Aug) −+(G2 (). X) ( kJ2 22 v 2 f 2 () X ) (28) −1 −+(λβGX12() g () X) ×(λG1( X ) τβeq 22 + G ( X ) τeq 1 ++ kS . δ sgn( S )) 3. Simulation and Experimental Results 3.1. Performance of the Collection Solar Energy Test The S-AUV has been tested to collect solar energy at some localities such as Hai Phong City, Quang Ninh Province (Ha Long Bay) and Hanoi City, as shown in Fig. 5. S-AUV in case of closing and opening as shown in Fig. 3, Fig. 4. Fig. 7. Solar energy collection chart with solar wing closed and opened at Quang Ninh City (2020 Aug) Fixed solar wing Fig. 3. S-AUV in closed solar wing case Retractable solar Fig. 8. Solar energy collection chart with solar wing closed and opened at Ha Noi City (2020 Aug) Fig. 4. S-AUV in opened solar wing case Fig. 9. Solar energy collection with solar wing closed Fig. 5. Testing in Quang Ninh Province at Hai Phong, Quang Ninh, Hanoi (2020 Aug) 80
7. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 3.2. Simulation Hierarchical Sliding Mode Controller To verify the quality of the HSMC, the simulation was performed for the new S-AUV with parameters as shown in Table 2, 3. The simulation results for S-AUV with HSMC controller are shown in Figs.11-18: Table 2. Modeling parameter S-AUV − − m 18.5 Yr 1.03 Nr 12.32 0.15 −0.85 0.32 Fig. 10. Solar energy collection with solar wing xygg, Yv Nv opened at Hai Phong, Quang Ninh, Hanoi (2020 Aug) − − zg 0 Yvv|| 0.62 Nr 2.15 Test conditions: The S-AUV's solar capture X u 6.53 Zw 4.57 I z 1.57 capacity measurement was made in the period from X −0.58 Z 0.23 Y 0.08 12:00 to 13:00, to avoid the influence of the angle of uu u v sunlight. Time to measure sunny days without clouds Table 3. Parameters of HSMC controller in August 2020. The average of total radiation in August measured in Quang Ninh Province, Hai Phong k 100 City was 17.56 -17.82 MJ/m2/day; in Hanoi City is δ 5 2 18.23 MJ/m /day [3]. k1 0.05 Fig. 6 , Fig. 7, Fig. 8, Fig. 9, Fig. 10 show that when k2 5 S-AUV increases the depth of diving, the solar λ 500 collecting capacity of S-AUV in both fields when β 2.5 T opening and closing the energy wing decreases linearly. η1d [14 7] Opening the retractable energy wing, the solar collector T η2d [-12 0] capacity increases, the largest increase is 2.7 times. 16 0 14 -2 12 -4 10 -6 8 -8 6 -10 x-postion (m) 4 z-position (m) 2 -12 0 -14 0 20 40 60 80 100 0 20 40 60 80 100 Time (seconds) Time (seconds) Fig. 11. Position in the Ox direction Fig. 13. Position in the Oz direction 8 0.2 7 0.15 6 5 0.1 4 0.05 3 y-position (m) 2 0 1 ψ-swing angle (rad) 0 -0.05 0 20 40 60 80 100 0 20 40 60 80 100 Time (seconds) Time (seconds) Fig. 12. Position in the Oy direction Fig. 14. Navigation angle of S-AUV 81
8. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 0.6 1 0.5 0 0.4 0.3 -1 0.2 -2 u-velocity (m/s) w-velocity (m/s) 0.1 0 -3 0 20 40 60 80 100 0 20 40 60 80 100 Time (seconds) Time (seconds) Fig. 15. Velocity in the Ox direction Fig. 17. Velocity in the Oz direction 0.4 4 3 0.3 2 0.2 1 0.1 v-velocity (m/s) 0 0 r-angular velocity (rad/s) -1 0 20 40 60 80 100 0 20 40 60 80 100 Time (seconds) Time (seconds) Fig. 16. Velocity in the Oy direction Fig. 18. Angular velocity of S-AUV navigation According to Figs. 11-18, the HSMC applied to References the new S-AUV gives good control quality in terms of [1]. U.S. Commission on Ocean Policy, An ocean blueprint grip position, directional angle, long velocity and for the 21st century, final report, Washington D.C., maneuverability and angle velocity in 3-dimensional 2004, ISBN# 0-9759462-0-X. space. Specifically, the set time of the system of the grip position in the direction Ox, Oy are respectively [2]. Denise M. Crimmins, Christopher T. Patty. Long- 84s and 86s, and the setting time of the position in the Endurance Test Results of the Solar-Powered AUV System, 2006, 1-4244-01 15-1/06. IEEE. direction Oz is 20s and navigation angle is 40s. [3]. 4. Conclusion nang-luong-tai-tao/cap-nhat-so-lieu-khao-sat-cuong- The paper presents an Autonomous Underwater do-buc-xa-mat-troi-o-viet-nam.html. Vehicles with solar energy supplemented. Applying [4]. Nguyen Van Tuan, Dinh Van Phong, Nguyen Chi the analysis and experimental results, when collecting Hung and Hoang The Phuong. Studying the effects of solar energy, the S-AUV floats as close to the water the energy wing on the motion resistance of the AUV th surface as possible. Especially, when integrating when integrating the solar collection system. The 10 retractable solar wing increases the solar collector National Mechanical Conference, December 2017. capacity when the S-AUV's energy wing is opened to ISBN 978-604-913-719-8. pp309-318. about 2.7 times compared to the closed solar wing. [5]. T. I. Fossen, O.-E. Fjellstad (1995) Nonlinear According to the simulation results, the HSMC modelling of marine vehicles in 6 degrees of freedom. controller performs control good quality. Although the Mathematical Modelling of Systems, 1995, vol. 1 no. setting time is rather large and the oscillation still 1, pp. 17–27 remains when switching around the sliding surface, the simulation values approach closely to the desired [6]. Wadoo S, Kachroo , Autonomous underwater vehicles: setting and the overshoot is acceptable. The controller modeling, control design and simulation. CRC Press, follows the desired signal with a negligible transient of February 2011. ISBN 978-1439818312. less than 5%. In the future, applying the Adaptive [7]. Cooney LA, Dynamic response and maneuvering Neural Network Controller to approximate the strategies of a hybrid autonomous underwater vehicle parameters might be a proper solution to improve the in hovering. Thesis of Master of Science in ocean quality of control. engineering, Massachusetts Institute of Technology, 2009. 82
9. JST: Smart Systems and Devices Volume 31, Issue 2, September 2021, 075-083 [8]. Buckham BJ, Podhorodeski RP, Soylu S , A automation and systems, ICCAS 2011, Gyeonggi-do, chattering-free sliding-mode controller for underwater Republic of Korea, 2011, pp 1682–1684. vehicles with fault tolerant infinity-norm thrust allocation. J Ocean Eng, 2008, 35(16):1647–1659. [11]. Medagoda L, Williams SB, Model predictive control of an autonomous underwater vehicle in an in situ estimated water current profile. Oceans, 2012, Yeosu, [9]. Qi X, Adaptive coordinated tracking control of pp 1–8. multiple autonomous underwater vehicles. Ocean Eng, 2014, 91:84–90. [12]. Xu B, Pandian SR, Sakagami N, Petry F, Neurofuzzy control of underwater vehicle-manipulator systems. J [10]. Jun SW, Kim DW, Lee HJ, Design of T-S fuzzy model Franklin Institute, 2012, 349(3):1125–1138. based controller for depth control of autonomous underwater vehicles with parametric uncertainties. In: 2011 11th international conference on control, 83