Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Real-time Control and Hardware-in-the-Loop Simulation of Surface Vessels for Multitask Missions at Seas Điều khiển thời gian thực và mô phỏng phần cứng trong vòng lặp các tầu mặt nước để làm đa nhiệm vụ trên biển Hung Duc Nguyen University of Tasmania / Australian Maritime College e-Mail: nguyenhd@amc.edu.au Abstract This paper presents an experimental approach to develop a real-time control system and hardware-in- the-loop simulation of surface vessels for multitask missions at seas. A multitask mission control system has many functions as an autopilot, rudder-roll damping, speed control, dynamic positioning, automatic mooring and anchoring, berthing and unberthing. A model-scaled container vessel is used for this work. Model-scaled experiments are conducted using a model test basin in order to verify feasibility of the automatic multitask mission control system. The paper first summarises control algorithms, then describes the experimental facility and development of real-time control programs. Tóm tắt: Bài báo này trình bày phương pháp thử nghiệm phát triển hệ thống điều khiển thời gian thực và mô phỏng phần cứng trong vòng lặp cho tầu mặt nước thực hiện đa nhiệm vụ trên biển. Hệ thống điều khiển thực hiện đa nhiệm vụ có các chức năng như máy lái tự động, giảm lắc ngang, điều khiển tốc độ, định vị động, neo buộc tầu tự động và ra vào cầu tự động. Một tầu mô hình đuợc sử dụng cho công trình này. Các thí nghiệm mô hình được thực hiện sử dụng bể thử mô hình nhằm kiểm chứng tính khả thi của hệ thống điều khiển đa nhiệm vụ. Bài báo trước hết tóm tắt các thuật toán điều khiển và tiếp theo mô tả thiết bị thí nghiệm và phát triển chương trình điểu khiển thời gian thực. Nomenclature Symbol Unit Meaning U d m/s Desired velocity d rad Desired heading angle x i , y i m Position coordinates Abbreviation RRD/S Rudder roll damping/stabilisation IMO International Maritime Organization CCP Controllable pitch propeller LQG Linear quadratic Gaussian 1. Introduction Surface vessels are the main means of marine transport. New generation surface vessels require automation at a high level. Design of automatic control systems for surface vessels involves an understanding of their manoeuvrability, seakeeping and seaworthiness. The most important motions for surface vessels are surge, sway and yaw while unnecessary motions are heave, pitch and roll. Small autonomous surface vessels have recently been applied in various missions in rivers and seas in remote areas, for example, a river water sample taking vessel is used to take water samples at certain time and take measurement of water sample and send data to the control centre. Another example of autonomous surface vessel is for littoral surveillance [2]. This article is about the second step to realise an automatic multitask mission manoeuvring system for surface vessels. The article focuses on applied aspects of the system and experimental approach. The main purpose of this paper is to: do feasibility study of the automatic multitask mission manoeuvring systems by computer simulation; develop real-time control programs for the multitask mission manoeuvring system; describe experimental facilities; realise multitask mission manoeuvring system; and propose applications of autonomous surface vessels for some missions at remote sea areas where human being find it difficult to access. This article is organised as follows: Section 1 Introduction, Section 2 Mathematical background, Section 3 Brief description of AMC experimental facilities, Section 4 Software controller diagrams, Section 4 Development of software controller programs, Section 5 Design of experiment; Section 6 Possible applications and Section 7 Conclusions. 2. Mathematical Background for Multitask Mission Manoeuvrves Nguyen [12][14] proposed a multitask mission manoeuvring system based on the recursive optimal method in which a recursive estimation algorithm is combined with an optimal control algorithm. The main functions of the multitask mission manoeuvring system are: autopilot: course keeping and changing; 133 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 rudder-roll stabilisation; dynamic positioning; manoeuvre tests and estimation of manoeuvrability indices; ship motion information providing and monitoring; automatic berthing and unberthing manoeuvres; and Automatic mooring and anchoring manoeuvres The multitask mission manoeuvring system consists of three subsytems (guidance, navigation and control) as shown in Fig. 1. Fig. 1 Three subsystems (guidance, navigation and control) for a surface vessel 2.1 Guidance System – Waypoint positions/LOS technique The guidance system generating a reference trajectory includes desired courses, speed, way-points and position is constructed by using the waypoint and light of sight and exponential decay techniques [12][14]. The guidance system receives prior information data, position of waypoints and weather information. For various missions at seas the guidance system will generate trajectory for the following cases: IMO search and rescue expanding square pattern and sector pattern; weather routing navigation trajectory; trawling trajectory; dredging trajectory; subsea pipe and device laying and installation trajectory; and seismic survey trajectory. The outputs of the guidance system often are Desired way-point positions: wpt.pos: {(x 0 ,y 0 ), (x 1 ,y 1 ), , (x k ,y k )} (1) Desired speeds between way-points: wpt.speed: U d = {u 0 , u 1 , u 2 , , u k } (2) Desired heading angles: wpt.heading: d = { d1 , d2 , d3 , , dk } (3) The guidance system also receives navigation signals from the navigation system and computes errors including position errors (path tangential tracking and cross-track errors), heading error and speed error. 2.2 Navigation System The navigation system has the main function of providing accurate measurements of position and ship motion. The navigation is equipped with D-GNSS or RTK-GNSS and GNSS receivers when the surface vessel is running along a coast where D-GNSS and correction signals are available. A gyro- or satellite- compass is used to measure the ship’s heading. For autonomous surface vessels running in a lake or model test basin a 6-DOF IMU device is used. In the in-door model test basin where there is no GNSS signal, an indoor navigation device is applied to get the vessel’s measurement. The GNSS/IMU signals are often including noisy. A Kalman filter and/or low-pass filter may be used to estimate state variables that are not measured and to remove noisy, respectively. An adaptive observer is also applied for enhancement of accuracy and reliability of the obtained signals. 2.3 Control System As shown in Fig. 1 the control system consists of two blocks: motion control and controller allocation. The control system synthesises an appropriate control algorithm to compute control signals and allocate control actions by actuators. The control algorithms can be one of the following: conventional PID control; self-tuning PID control algorithm; recursive optimal control algorithm [11]; optimal control algorithm; model reference adaptive control; robust (H-infinity) control; fuzzy logic PID control; neural networks-based control; or genetic algorithm-based control. The control algorithm adopted in the control system is often complicated because of MIMO control system which controls many output variables. For an automatic multi-task control systems used in marine vessels equipped with a propeller and rudder the control program should include the following control modes: one control (autopilot) without RRD: course control by rudder; one control (autopilot) with RRD: course control and roll damping by rudder; two controls (course and speed) by rudder and engine shaft rpm or CCP pitch angle without and/or with RRD; and three controls (course, speed and positions) without and/or with RRD. The recursive optimal control algorithm is a combination of an optimal LQG control law and recursive identification algorithm. The recursive identification algorithm is either the recursive least squares algorithm or the recursive prediction error algorithm. Interested readers can find more information on this control algorithm in Appendix 1 and in [12][14]. 3. Brief Description of Model-scaled Vessel and Electronics Estimated position and velocities 134 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 2.1 Model-scaled Container Vessel In order to develop software control programs and verify the control algorithms for multitask mission control systems model-scaled surface vessels equipped with propulsion system and steering mechanisms and instrumentation electronics are needed. It is very ideal if a full-scaled vessel for experiments is available. However operating a full- scaled vessel costs a lot of money. A model-scaled container vessel named “P and O Nedlloyd” is shown in Fig. 2. The main particulars of the full-scaled vessel and the model are given in Table 1. Fig. 2 Model-scaled vessel for experiments Table 1 Vessel and model main particulars Full Scale Vessel Model (Scale 1:100) LBP 247 m 2470 mm B 32 m 320 mm Draught 12 m 120 mm Δ 64000 tonnes 62.4 kg L/B 7.72 7.72 B/T 2.67 2.67 Fig 3 shows onboard electronic devices. The model is equipped with a twin propeller operated by a dc motor, rudder controlled by a servo motor and controller, mass carriage mechanism operated by a dc motor, a mobile (target) computer (PC\104) with wireless/Ethernet and DAQ cards, a 6-DOF IMU and GPS device (Crossbow NAV420CA) and batteries. The mass carriage mechanism is used to investigate parametric roll motion and rudder-roll damping system. Fig. 3 Onboard electronic devices As shown in Fig. 3 the target computer communicates with a host computer via an Ethernet cable or wireless communication device. In the host computer there is an integrated environment of software that allows the user to develop control programs. Software includes MATLAB/Simulink, Real-time Workshop, RT-LAB (product of Opal-RT), MS Visual Studio, LabVIEW and Control Design and Simulation Module and Python. 2.2 Prototype “GreenLiner” with Electrically- operated Waterjet At the AMC propulsion lab there is a prototype of 11- metre boat equipped with an electrically-operated waterjet as shown in Fig. 4. The heading is control by a waterjet nozzle. This prototype allows one man to ride. GreenLiner’s principal particulars are given in Table 2. Fig. 4 GreenLiner, a prototype boat equipped with electrically-operated waterjet Table 2 Principal particulars of GreenLiner) Item Original Spec 48V Electric Spec 96V HiPo Config Built: 1999 Greg Cox, L.O.A: 7.75 m L.W.L: 6.15 m TBA TBA B.O.A: 1.06 m Draught: 164 mm 244 mm. 200 mm. Displacement: 348 kg 648 kg. 540 kg. Powering Fuel Petrol (a cup full) 4off 210A- hr LA Batteries 8off HiPo 80 A-hr. LA Batteries Engine/ motor B&S 18 hp Vanguard engine 2 cylinder, 4-stroke, air-cooled. 4hp HiTorque Industrial Technik DC electric Motor. Parallel fields 10 hp HiTorque Industrial Technik DC electric motor Series fields Construction Ply (Australian Plantation Hoop Pine) Cruise Speed: 17 knots 7 knots. 11 knots. Propulsor: Doen DJ60 water-jet 16B5. 12A4. 16B5. 135 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 In order to develop automatic control systems for GreenLiner, the current steering system must be upgraded with an electro-hydraulic steering machine and data acquisition card. 2.3 Full-scaled and Model-scaled Bluefin AMC has a training fishing vessel that can be used for full-scaled experiments as shown in Fig. 5. Main particulars of full-scaled Bluefin are given in Table 3. Fig. 5 Full scaled Bluefin Table 3 Main particulars of Bluefin Length OA 34.50 m Length BP 32.00 m Breadth 10.00 m Maximum draft 4.40 m Deadweight 53.60 t AMC also has a model scaled Bluefin as shown in Fig. 6. Fig. 6 Model-scaled Bluefin (scale 1:20) 4. Development of Software Controller Programs Computer simulation study done with non-linear mathematical models of two vessels in [11] has shown the feasibility of the automatic multitask manoeuvring system using recursive optional control algorithm. As the second step to realise the multitask manoeuvring system, model-scaled experiments need to be conducted to verify the methods. Real-time measurement and control of a surface vessel is done by MATLAB/Simulink and RT-LAB software. The equipment for real-time measurement and control is shown in Fig. 6. The model-scaled boat with target computer and electronics is shown in Fig. 9. The target computer is installed with real-time operating system QNX 6.3 and RT-LAB software, and the host PC (with Windows) is installed with MATLAB/Simulink and RT-LAB software. Controller programs are developed with Simulink. A sample real-time control program is given in Fig. 8. Fig. 7 Arrangement of target and host PCs with sensors and actuators Fig. 8 Real-time control program developed with Simulink Target computer & DAQ Host computer Ethernet or wireless Actuators (propeller motor drive, mass carriage motor drive, rudder servo motor controller Sensors: GPS/6-DOF IMU, encoders etc. Sensors: Required software: MATLAB/Simulink, Real- time Workshop, RT-LAB 136 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 A real-time control program was made with Simulink in the RT-LAB environment. An RT-LAB program of Oral-RT (www.opal-rt.com), fully integrated with MATLAB/Simulink®, is a real-time simulation software environment that provides with a revolutionised way in which model-based design is performed. Fig. 9 shows the RT-LAB window. The software required consists of RT-LAB software, MATLAB/Simulink, Real-time Workshop and a C/C++ Compiler. Using the RT-LAB software the real-time control program is made and run in the following procedure: create and edit Simulink model compile the Simulink model to C code; assign nodes (target) for the Simulink program; load the Simulink program to the target computer, then the user-interface console window (as shown in Fig. 11) that allows user to run the control program appears; and execute the Simulink program. Fig. 9 RT-LAB Window Fig. 10 P and O Netlloyd with electronics Fig. 11 Real-time control program (SC-Console window) developed with Simulink 137 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 A series of real-time control programs have been developed with Simulink and RT-LAB as follows: Program 1: Simulink model to control propeller; Program 2: Simulink model to control servo motor (rudder angle); Program 3: Simulink model to control both propeller and servo motor Program 4: Simulink model to receive data from Crossbow NAV420CA (GPS/IMU) Program 5: Simulink model to control load carriage mass to investigate effect of changing load. Program 6: Combined program for tasks in 1, 2, 3, 4, and 5 to test functionality of the open- loop system; Program 7: Simulink model for autopilot (e.g. PID control, recursive optimal control); Program 8: Simulink model for autopilot and rudder-roll damping, to investigate of mass carriage mechanism on roll motion; Program 9: Simulink model for autopilot, rudder-roll damping and speed control, to investigate effect of mass carriage mechanism, speed and course on roll motion (parametric roll); Program 10: Simulink model for trajectory tracking manoeuvres (search and rescue mission); Program 11: Simulink model for trajectory tracking (trawling); Program 12: Simulink model for automatic berthing and unberthing manoeuvres; Program 13: Simulink model for automatic mooring and anchoring; Program 14: Simulink model for an integrated bridge with all above functions; 5. Design of Experiments Experiments can be conducted using a free-running model in the AMC model test basin (MTB) (Fig. 11). Fig. 11 Model test basin and free-running model Table 4 General specifications of MTB Length 35 metres Width 12 metres Water depth 0 to 1.0 metres Model towing carriage speed 0 to 3.8 metres/second Typical model lengths 2 to 6 metres The MTB has been equipped with the following ancillary equipment and instrumentation devices: multi-element wave generator; non-contact digital video motion capture system; variable speed model towing mechanism; variable speed wind generator; votating arm mechanism; multiple wave damping devices; wide array of single and multi-axis force transducers; wide array of wave measurement devices wide array of video cameras (including underwater); acoustic Doppler Velocimeter (measurement of currents); pressure transducers; displacement transducers; accelerometers; and multi-channel digital data acquisition systems. The following experiments will be conducted: Experiment 1: zigzag test (open-loop system); Experiment 2: turning circle test (open-loop system); Experiment 3: Course keeping and changing (autopilot); Experiment 4: Autopilot and rudder-roll damping Experiment 5: Autopilot, rudder-roll damping and speed control; Experiment 6: Trajectory tracking control for search and rescue mission; Experiment 7: Trajectory tracking control for trawling; Experiment 8: Automatic berthing and unberthing manoeuvres; and Experiment 9: Automatic mooring and anchoring manoeuvres. Some proposed experiments are shown in Fig. 12 through 15. Fig. 12 IMO expanding square pattern with 1 and 2 controls 138 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Fig. 13 IMO sector search pattern with 1 and 2 controls Fig. 14 Rudder roll stabilisation to reduce parametric roll in head seas Fig. 15 Berthing and unberthing 6. Possible Applications The automatic multitask manoeuvring system is suggested to be working in some modes as follows autopilot and RRD at high seas; the function of manoeuvres for maritime search and rescue mission should be compulsory for all merchant vessels in order to enhance safety at seas; manoeuvring information and monitoring system for the captain (deck officers) and pilot; and manoeuvrability test system. Fig. 17 illustrates a proposed multi-task automatic manoeuvring system with an LCD and Control Panel in which there are different working mode buttons and keyboard. The multitask manoeuvring system can be developed with a microcontroller and/or embedded computer. Fig 17 A proposed application for various modes (AUTO = autopilot, RRS = rudder-roll stabiliser, MT = manoeuvrability tests, SAR = maritime search and rescue mission, INFO = information when manoeuvring, GNSS = global navigation satellite system receiver In addition to the above proposed system the multitask manoeuvring system can be developed further to the following for educational and research purposes: automatic berthing/unberthing system; automatic mooring and anchoring system; dynamic positioning system; water sample taker; spilling area measuring autonomous vessel; power control and management system. In comparison with ROVs/AUVs, advantages of using autonomous surface vessels for various missions at seas are: solution to energy issue; solar energy; and difficulty in communication between the target computer and the host computer. 7. Conclusions In conclusion the paper has discussed the following points: background of the multitask manoeuvring system; description of experimental facilities; development of software controller programs; proposed experiments using model-scaled vessel and model test basin; and proposal of possible applications. Recommendations for future work are: continue to develop real-time control programs with Simulink and LabVIEW; conduct model-scaled experiments and collect data for analysis; analyse experimental data and develop nonlinear mathematical models for vessels; and develop hardware and software for a multitask mission manoeuvring system and test its functionalities under lab conditions. 139 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Acknowledgements This paper is a continuity of the AMC IGS granted research project financially supported by the AMC Research and Higher Degrees by Research Committee during 2005-2007. The author would like to thank the Research Office for financial support. References [1] Leonessa, A., Madello, J., Morel, Y. and Vidal, M Design of a Small, Multi-Purpose, Autonomous Surface Vessel. DOI: 0-933957- 30-0. [2] Caccia, M Autonomous Surface Craft: Prototypes and Basic Research Issues. [3] Baumann, M. and Baur, O Autonomous Surface Vessel for Toxic Cynobacteria Bloom Examination. [4] Caccia, M., Bono, R., Bruzzone, Ga., Bruzzone, Gi. And Stortini, A.M Design and Exploitation of an Autonomous Surface Vessel for the Study of Sea-Air Interatcions. IEEE Explore. 0-7803- 8914-x/05. 2005. [5] Munjal, A Development of Automatic Manoeuvring Systems for Surface Vessels – Simulation and Design of Model Scale Experiments, BE (MOS) Thesis. AMC, Launceston, 2011. [6] Roberts, G.N. and Sutton, R (Editors). Advances in Unmanned Marine Vehicles. The Institute of Electrical Engineers, 2006. [7] Fossen, T.I Nonlinear Modelling and Control of Underwater Vehicles, PhD Thesis. Norwegian Institute of Technology, 1991. [8] Fossen, T.I Handbook of Marine Craft Hydrodynamics and Motion Control. John Wiley and Sons Inc. 2011. [9] Fossen, T.I Marine Control Systems – Guidance, Navigation and Control of Ships, Rigs and Underwater Vehicles. Marine Cybernetics, Trondheim, Norway, 2002. [10] Fossen, T.I Guidance and Control of Ocean Vehicles. John Wiley and Sons, 1994. [11] Wadoo, S.A. and Kachoroo, P Autonomous Underwater Vehicles: Modeling, Control Design, and Simulation. CRC Press, 2011. [12] Nguyen, H.D Multitask Manoeuvring Systems Using Recursive Optimal Control Algorithms. Proceedings of HUT-ICCE 2008, pp. 54-59 Hoi An, Vietnam, 2008. [13] Nguyen, H.D Recursive Identification of Ship Manoeuvring Dynamics and Hydrodynamics. Proceedings of EMAC 2007 (ANZIAM), pp. 681-697, 2008. [14] Nguyen, H.D Recursive Optimal Manoeuvring Systems for Maritime Search and Rescue Mission, Proceedings of OCEANS'04 MTS/IEEE/TECHNO-OCEAN'04 (OTO’04), pp. 911-918, Kobe, Japan, 2004. [15] West, W.J. Remotely Operated Underwater Vehicle, BE Thesis. Australian Maritime College, UTAS, Launceston, 2009. [16] Gaskin, C.R Design and Development of ROV/AUV, BE Thesis. Australian Maritime College, UTAS, Launceston, 2000. [17] Woods, R.L. and Lawrence, K.L Modeling and Simulation of Dynamic Systems. Prentice-Hall Inc. Upper Saddle River, NJ, 1997. [18] Kulakowski, B.T., Gardner, J.F. and Shearer, J.L Dynamic Modeling and Control of Engineering Systems. Cambridge University Press, 2007. [19] Antonelli, G Underwater Robots – Motion and Force Control of Vehicle-Manipulated Systems, 2 nd Edition. Springer, 2006. [20] Bose, N., Lewis, R., Adams, S Use of an Explorer Class Autonomous Underwater Vehicle for Missions under Sea Ice, 3rd International Conference in Ocean Engineering, ICOE 2009, IIT Madras, Chennai, India. Keynote presentation, 2009. [21] Burcher, R. and L. Rydill Concepts in Submarine Design. Cambridge University Press. [22] Christ, R.D. and R.L. Wernli Sr (2007). The ROV Manual – A User Guide for Observation Class Remotely Operated Vehicles. Butter- Heinemann (Elsevier). Oxford, 1994. [23] Griffiths, G. (Editor) (2003). Technology and Applications of Autonomous Underwater Vehicles. Taylor and Francis. [24] Groves, P.D GNSS, Inertial, and Multisensor Integrated Navigation Systems. Artech House, 2008. Biography Dr. Hung Nguyen is a lecturer in Marine Control Engineering at National Centre for Maritime Engineering and Hydrodynamics, Australian Maritime College, Australia. He obtained his BE degree in Nautical Science at Vietnam Maritime University in 1991, then he worked as a lecturer there until 1995. He completed the MSc in Marine Systems Engineering in 1998 at Tokyo University of Marine Science and Technology and then the PhD degree in Marine Control Engineering at the same university in 2001. During April 2001 to July 2002 he worked as a research and development engineer at Fieldtech Co. Ltd., a civil engineering related nuclear instrument manufacturing company, in Japan. He moved to the Australian Maritime College, Australia in August 2002. His research interests include guidance, navigation and control of marine vehicles, self-tuning and optimal control, recursive system identification, 140 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 real-time control and hardware-in-the-loop simulation of marine vehicles and dynamics of marine vehicles. Appendix 1 Summary of Control Algorithms The desired trajectory is one of the following manoeuvres: IMO expanding square pattern for search and rescue mission (Fig. A1); IMO sector pattern for search and rescue mission (Fig. A2) Williams’ turning circle manoeuvre; Any trawling trajectory; and Any planned manoeuvres; The reference trajectory generator in the guidance system is a vessel simulator using the Nomoto’s first- order manoeuvring model. Details can be found in [12][14]. The desired heading angle d is calculated by the LOS technique as follows: k+1 dk k1 yy atan2 xx (A1) When the ship is moving along the desired trajectory, a switching mechanism for selecting the next way- point is necessary. The next way-point (x k+1 ,y k+1 ) is selected when the ship lies within a circle of acceptance with a radius R0 around the current waypoint (x k ,y k ) satisfying: 22 2 k k 0 x x y y R (A2) Fig. A1 IMO expanding square pattern The value of R 0 is often chosen as two ship lengths, i.e. R 0 = 2L pp in [8][12][14]. A reference trajectory generator using a vessel simulator is constructed. The vessel model used in this paper is of Nomoto’s first-order model with forward speed dynamics and described as follows: d d d x U cos (A3) d d d y U sin (A4) where (x d, y d ) is the desired position, U d > 0 is the desired speed and ψ d is the desired heading. The forward speed dynamics is 2 x d w d d x m m U 0.5 C AU (A5) Fig. A2 IMO sector pattern Fig. A3 LOS technique where ρ w is the density of sea water, C d is the drag coefficient, A is the projected cross-sectional area of the submerged hull of ship in the x-direction, and (m – mx) is the mass included hydrodynamic added mass. The course dynamics is chosen as dd r (A6) d d r Tr r K (A7) where T and K are ship manoeuvrability indices, r d is the desired yaw rate and δ r is rudder angle. The guidance system has two inputs, thrust τ x and rudder angle δr. The guidance controllers can be chosen as PI and/or PID types. When the ship goes along the desired trajectory, the reference heading angle can be adjusted by the exponential decay technique as shown in Fig. A4. Heading and position errors when the ship is moving along the desired trajectory are calculated as follows 141 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 1 d d 2 d d 3d e (x x)cos (y y)sin e (x x)sin (y y)cos e e (A8) where e 1 = path tangential tracking error e 2 = cross-track error (normal to path) e 3 = heading error Fig. A4. Exponential decay technique If the rudder-roll damping controller is switched on the vector of errors including roll error (e 4 ) becomes 1 dd 2 dd 3 d 4 e (x x)cos (y y)sin e (x x)sin (y y)cos e e 0 e (A9) If the speed controller is on the speed error will be calculated 5d e U U (A10) Recursive Optimal Control Algorithm In order to design control systems with multitask missions, mathematical models for the steering and manoeuvring dynamics are applied. For example, the ship steering dynamics for the automatic manoeuvring system is represented by an MAXR as follows (t 1) ( ) (t) ( ) (t) xFθ xGθ u (A11) (t) ( ) (t)yCθ x (A12) where x(t) is the state vector, u(t) is the input vector, y(t) the output vector and F(θ), G(θ) and C(θ) are system matrices dependent on parameter vector θ. The unknown system parameters are estimated by one of appropriate recursive estimation methods. An optimal control law is applied. The optimal recursive control algorithm is illustrated by the flowchart as shown Fig. A5. Summary of RPE Algorithm: The RPE algorithm is to minimize the following criterion function: T1 1 V t t t 2 θ ε Λε (A13) where Λ is a positive definite matrix, and Gauss- Newton search direction is chosen as: 11 f t t t, t, H ψ θ Λε θ (A14) where H(t) is the Hessian, the second derivative of the criterion function with respect to θ and ψ(t,θ) is the gradient of the predicted output with respect to θ and ε(t,θ) is the vector of the predicted errors. The RPE algorithm consists of the following steps: Fig. A5 Flowchart for the optimal recursive control algorithm [12] Step 1: Calculate the predicted error vector using ˆ t t tε yy (A15) Step 2: Update the weighting matrix by T t t 1 t t t t 1 Λ Λ ε ε Λ (A16) Step 3: Update the Hessian: 1T t t 1 t t t t t 1 HH ψ Λψ H (A17) Step 4: Update the estimated parameters: 11 t t 1 t t t t t θ θ H ψ Λε (A18) Step 5: Update the predicted output: T ˆ t t ty (A19) Step 6: Calculate the gradient of the predicted output by d ˆ t t, d y (A20) Step 7: Update data and loop back to Step 1. Note that the step size factor α(t) is calculated as 1 t 1t (A21) 142 . triển hệ thống điều khiển thời gian thực và mô phỏng phần cứng trong vòng lặp cho tầu mặt nước thực hiện đa nhiệm vụ trên biển. Hệ thống điều khiển thực hiện đa nhiệm vụ có các chức năng như. Multitask Missions at Seas Điều khiển thời gian thực và mô phỏng phần cứng trong vòng lặp các tầu mặt nước để làm đa nhiệm vụ trên biển Hung Duc Nguyen University of Tasmania / Australian Maritime. của hệ thống điều khiển đa nhiệm vụ. Bài báo trước hết tóm tắt các thuật toán điều khiển và tiếp theo mô tả thiết bị thí nghiệm và phát triển chương trình điểu khiển thời gian thực. Nomenclature