IMPROVING THE ACCURACY AND RELIABILITY OF AUTOMATIC VESSEL MOUTION CONTROL SYSTEM

Context. There were considered the issues of improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. The object of research is the process of automatic vessel motion control in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. The subject of research is a method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. Objective. The aim of the research is development a method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. Method. This goal is achieved by using in onboard controller of the automatic vessel motion control systems an observer to estimation the parameters of the state vector in the linear motion channel by measurements of linear speed and position sensors; estimation the parameters of the state vector in the angular motion channel by measurements of rotational speed and angular position sensors; continuous monitoring of the measured information by comparing it with the obtained estimations; correction estimations in the linear motion channel by measurements of linear speed and position sensors that have passed control; correction estimations in the angular motion channel by measurements of rotational speed and angular position sensors that have passed control; formation of a sensor failure in the linear motion channel (linear speed sensor or position sensor), if its measurements differ from the corresponding estimations for a greater than permissible value, to parry the failure in the linear motion channel by disconnecting the failed sensor from the observer and further estimation according to another sensor working in pairs; formation of a sensor failure in the angular motion channel (rotation speed sensor or angular position sensor), if its measurements differ from the corresponding estimations for a greater than permissible value, to parry the failure in the angular motion channel by disconnecting the failed sensor from the observer and further estimation according to another sensor working in pair; formation of an actuators failure in the linear motion channel (engine, automation or other device) if a simultaneous or sequential failure of both sensors were detected – linear speed sensor and position sensor, actuator failure alarm in the linear motion channel; formation of an actuators failure in the angular motion channel (rudders, drives, other devices) if a simultaneous or sequential failure of both sensors were detected – rotation speed sensor and angular position sensor, actuator failure alarm in the angular motion channel. This method and algorithms make it possible to improve the accuracy and reliability of automatic vessel motion control processes in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. Results. The proposed method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators were verified by mathematical modeling in the MATLAB environment of the control object movement in a closed circuit with a control system for various types of vessels, navigation areas, weather conditions and cases of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. Conclusions. The results of mathematical modeling confirmed the efficiency of the developed method and algorithms and allow to recommend them for practical use in the development of mathematical support for automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.

starboard, the axis OZ complements the system to the "right" one.
GCS is a geographical coordinate system; is located in the vessel rotation center, the axis OXg is directed along the meridian towards the North, the axis OYg is directed along the parallel towards the East, the axis OZg complements the system to the "right" one.
is a vessel's maximum speed.

INTRODUCTION
Currently, more than 90% of all cargo in the world is transported by sea. If we also take into account the presence of a significant number of warships, we can say that the oceans have become quite "crowded". People and their ship management decisions have caused most maritime accidents. Thus, the Dutch study "100 Sea casualties" revealed that the human factor led to 96 out of 100 accidents. According to the United Kingdom Protection and Indemnity Club, the human factor accounts for 89-96% of ship collisions, 84-88% of tanker accidents, 79% of towing ship a grounds and costs the marine industry about $ 541 million a year. A detailed analysis of the causes of ship accidents at sea due to the human factor is given in [1]. The human factor is the weakest link in ship management. Studies of the influence of the human factor on management have been considered in the works of many authors, in particular [1][2][3][4][5]. Organizational measures taken to strengthen the training and retraining of skippers, amending the International Convention on Standards of Training, Certification, and Watch keeping for Seafarers [1] in terms of language requirements, other measures did not lead to a significant reduction in accident rates. Experts note that the only way to achieve the desired result is the development and implementation of automated decision support systems and automatic control systems.
Automated decision support systems suggest a person in the control loop and provide him with technical support, for example, in the form of monitoring the parameters of the ship's state vector and propulsion system, the formation of warning messages, control warnings, etc. In such systems, despite the technical support from automated decision support systems, the skipper makes the final decision on the control of the ship, which means , in the control chain there remains the link of the HF with partially indefinite behavior that generates a certain percentage of errors and has large delays in the processing and transmission of information [6][7].
In automatic control systems, the HF link is absent, which gives them great advantages: automatic systems are not subject to fatigue, emotions, stresses; no communication problems; information in the system is transmitted almost without delay, which is especially important when controlled inertial dimensional objects; the task can be solved optimally, which saves time and resources. In automatic systems can be achieved greater control accuracy and reliability. The accuracy of control, in the absence of a HF link, is determined only by the errors of technical devices (sensors and actuators), the scheme and accuracy of the calculations. Using mathematical methods can improve the characteristics of the input signals and increase the accuracy of control.
The work [1] gives an example of a failure of the navigation equipment of the MS Royal Majesty ship. None of the crew found a failure of the equipment and did not even respond to the warning of the Portuguese fishing boats that the vessel was in danger, which ultimately led to the ship's departure from the route for 17 miles and landing aground. In automatic systems, incorrect operation or failure of navigation equipment, equipment in linear motion control channels (automation, engine, propulsion), angular movement control equipment (automation, drives, rudder) can be detected automatically by analyzing the dynamics of the control object. Most modern ships use autopilots, which are representatives of automatic systems. Similarly to autopilots, other automatic control modules can be developed that solve more complex ap-plied problems, for example, automatic divergence with many targets [8][9], automatic wiring in narrowness, optimal maneuvering, etc. The skipper, as in the case of autopilot, only makes a decision about the involvement of the necessary module and controls the implementation of the task, and technical control of the vessel is provided automatically, according to the algorithms laid down in the on-board controller. As follows from the foregoing, automatic control systems have huge advantages over manual control, as well as ADSS systems. Therefore, the development of such systems is an urgent scientific and technical task.
The object of research is the process of automatic vessel motion control in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.
The subject of research is a method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.
The aim of the research is development a method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.

PROBLEM STATEMENT
Is given a mathematical model of the movement of the control object in the form of a system of nonlinear differential equations, taking into account the effects of wind, flow and waves, a mathematical model of actuators in the form of a system of linear differential equations with a model of errors and failures, as well as a mathematical model of sensors in the form of a system of algebraic equations with model of errors and failures. , It is required to form such controls  and  that would ensure control of the object (1) in conditions of measurement errors and failures of sensors (2) and actuators (3).

LITERATURE REVIEW
Article [10] investigated a model of the ship's dynamic positioning system by modeling real weather conditions in the laboratory, which allowed not only avoids the risks caused by direct experiments on a real ship, but also reduces the cost of the experiment. In order to implement high-precision positioning were used a highprecision mathematical model of the vessel and continuous position information with GPS. To improve positioning accuracy were analyzed the characteristics of many sensors, including radar, differential GPS, ultrasonic sen-sors, room temperature and others, followed by mathematical methods.
Article [11] considered the problems of wave filtration based on the Kalman filter, there were estimationd the noise covariance parameters, the Kalman filter was adjusted, using the obtained estimation, and its operation was verified in a dynamic positioning system by mathematical modeling.
Article [12] considered a new concept of navigation guidance, which allows to increase the reliability of the provided guidance on changing speed or course in automated decision support systems under conditions of incomplete information on the hydrodynamic model of the vessel and external influences.
Article [13] considered the issues of forecasting the movement of a vessel in a heeling channel. There was proposed an adaptive forecasting model as a combination of models with variable weights to improve the accuracy of forecasting and stability. To determine the weights there was used adaptive recursive identification.
Article [14] considered the issues of forecasting the movement of a vessel in maneuvering areas based on reference vectors. In contrast to forecasting methods based on an explicit mathematical model, there was built a black box model of a maneuvering ship. For the input values of the rudder and the variables of the state vector, as well as the output values of the hydrodynamic forces, there were identified complex nonlinear functions in the Abkowitz model, which were used to predict motion.
Article [15] considered the use of a mathematical model of full-circle propeller vessels for predicting their maneuverability. There was carried out propeller force analysis and synthesized the control of motion models. To test the effectiveness of the developed models and control algorithms, numerical modeling was carried out, the results of which are compared with field tests.
When creating modern aviation gas turbine engines, a significant complication of automatic control and monitoring systems is noted, which increases the probability of various violations in the measurement channel and complicates control tasks.
Article [16] considered the synthesis of a fault-tolerant flight control scheme based on a neural network. The proposed scheme involves diagnostics, fault detection and adaptation. The circuit was tested on an F-16 airplane model in case of drive failure.
As can be seen from the above review, the mathematical model of the control object was used to predict movement in control systems, including the ship, but there was not found Information about the methods: -improving the reliability of ship control systems by detecting sensor failures in the channels of linear and angular movement of the control object according to the results of analysis of its movement dynamics; -improving the reliability through parry failures of sensors by replacing their information (received from another sensor working in pair with a failure in one measurement channel, for example, if the linear speed sensor fails, its information can be replaced by position sensor information and vice versa, and if it fails the rotation speed sensor its information can be replaced by the information of the angular position sensor and vice versa); -improving reliability by detecting failures of actuators based on the analysis of the dynamics of movement of the control object; -improving accuracy when maneuvering the vessel by identifying unacceptable deviations of the sensors and replacing their information until the end of the maneuver (for example, during acceleration, braking, and turning the ship, the gyrocompass inertia deviates is present. During the maneuver, the gyrocompass date can be replaced by the rotation speed sensor in the jaw -channel). Figure 1 shows the block diagram of the control object and the control system.

MATERIALS AND METHODS
The movement of the control object is presented in a BCS, that moves relative to the GCS. The control object 1 moves under the action of external disturbances W and controls input to the observer 7. Observer 7 is a mathematical model of the control object and is used to estimate the state vector parameters of the control object. Due to the inaccuracy of the mathematical model and calculation errors, estimate of the state vector parameters with time will be more and more different from the state vector itself. To prevent this divergence, the observer's estimates are adjusted using the residuals between the measured parameters and their estimates.
In comparator 9, the measured state vector parameters m X are compared at each step of the calculations with the corresponding estimation vector parameters w X to form the residual vector w m X X X    , which is fed to the fault diagnosis unit 10.
The fault diagnosis unit 10 controls the excess of the residual vector parameters X  the permissible values * X  . to reset the jcolumn of the matrix L in order to prevent distortion of the state vector estimates by the j -sensor. In this case, a further estimate of the state vector w X is made according to the replacement information. Replacement information is the information of another sensor, operating in the same measurement channel, for example, speed and position sensors work in a linear motion channel and can replace each other when one of them failed, and angular rate sensor and angular position sensor also work in one channel angular motion and can replace each other when one of them failed.
The fault diagnosis unit 10 monitors the dates of the j -sensor, as well as other sensors, at each control interval b n . If the number of unreliable measurements . If at the same time or sequentially, after a short time interval, the fault diagnosis unit 10 detects a failure of the main and replacement sensors, then this is regarded as a failure in the control channel in which the failures of the main and replacement sensors were detected. For example, a simultaneous or sequential failure of the speed sensor and the position sensor in the linear motion channel is regarded as the failure of the linear control channel (engine, propulsion device, amplifiers, automation or any other device whose failure can violate the relationship between the screw force and telegraph position). Also, the simultaneous or sequential failure of the main and replacement sensors in the angular motion channel is regarded as a failure in the angular control channel (steering wheel, drive, amplifiers, automation, or any other device whose failure can violate the relationship between the control moment and the position of the steering wheel). Estimations of the yaw angle w  and yaw rate zw  from the output of the observer 7, as well as the required course * K and the required yaw rate * z  , from the block of motion programs 8, are fed to the inputs of the autopilot 6, where control  is formed The speed estimation Vxw from the output of the observer 7, as well as the required speed * x V from the block of motion programs 8 are fed to the inputs of engine automation unit 5, where control  is formed

EXPERIMENTS
Verification of the operability and effectiveness of the method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators, as well as the mathematical support developed on its basis, was verified by mathematical modeling in the MATLAB environment of a control object in a closed circuit with a control system including an observer and a fault diagnosis unit.
During all experiments, the following measurement errors were adopted: -linear speeds: systematic Y . Inadmissible deviations of measured linear speed, measured yaw angle and measured position from their estimations were revealed. To exclude the influence of unacceptable deviations of the sensors on the estimations, the matrix gains for these measurements are zeroed. After restoration of the sensors, the gain is restored. Fig, 3 shows results of detection and parry linear speed sensor failure during acceleration of the vessel from zero speed to maximum.
The graphs are shown (horizontally): -linear speed x V , measured speed xm V , estimated speed xw V ; -movement g X , measured movement gm X , estimated movement gw X ; -matrix gain coefficients lmd (1) for measured speed xm V and lmd (10) for measured movement gm X as well as telegraph deflection  . For 50 s was simulated linear speed sensor failure. As can be seen from the simulation results, this failure was detected and parried (matrix gain coefficients lmd (1) was reset to zero and further estimation xw V was carried out only by measurements gm X of the replacement sensor).  -matrix gain coefficients lmd (6) for measured yaw rate zm  and lmd (9) for measured yaw angle m  as well as the steering wheel deflection  . For 30 s was simulated the yaw angle sensor failure. As can be seen from the simulation results, this failure was detected and parried (matrix gain coefficients lmd (9) was reset to zero and further estimation w  was carried out only by measurements zm  of the replacement sensor. Fig. 5 shows the results of detection linear motion control channel failure, when the vessel was moving at maximum speed. The graphs are shown (horizontally): -linear speed x V , measured linear speed xm V , estimated linear speed xw V ; -movement g X , measured movement gm X , estimated movement gw X ; -matrix gain coefficients lmd (1) for measured linear speed xm V and lmd (10) for measured movement gm X as well as the telegraph deflection  .
For 50 s the engine failure was simulated (the screw force does not correspond to the telegraph deflection  ). As can be seen from the simulation results, this failure manifested itself through the failures of both sensorslinear speed sensor and movement sensor. Since the probability of simultaneous failure of two sensors is small, it was diagnosed not a sensors failure but linear motion control channel failure (engine, propulsion device, amplifiers, automation, or any other device, the failure of which may violate the relationship between the screw force and telegraph deflection  ). Fig. 6 shows the results of detection of angle motion control channel failure, when the vessel turns 45 degrees. For 50 s the engine failure was simulated (the screw force does not correspond to the telegraph deflection  ). As can be seen from the simulation results, this failure manifested itself through the failures of both sensorslinear speed sensor and movement sensor. Since the probability of simultaneous failure of two sensors is small, it was diagnosed not a sensors failure but linear motion control channel failure (engine, propulsion device, amplifiers, automation, or any other device, the failure of which may violate the relationship between the screw force and telegraph deflection  ).
The graphs are shown (horizontally): -yaw rate z  , measured yaw rate zm  , estimated yaw rate zw  ; -yaw angle  , measured yaw angle m  , estimated yaw angle w  ; -matrix gain coefficients lmd (6) for measured yaw rate zm  and lmd (9) for measured yaw angle m  as well as the steering wheel deflection  .
For 50 s simulated failure in the channel of angular motion (the control moment does not correspond to the steering wheel deflection  ). As can be seen from the simulation results, this failure manifested itself through the failures of both sensors -yaw rate sensor and yaw sensor. Since the probability of simultaneous failure of two sensors is small, it was diagnosed not a sensors failure but angular motion control channel failure (ruder, drive, amplifiers, automation, or any other device, the failure of which may violate the relationship between the control moment and the position of the steering wheel).

RESULTS
There were considered the issues of improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. There were analyzed the existing methods of increasing the accuracy and reliability of control in automatic systems, their shortcomings was identified and the relevance of solving this problem was substantiated.
There were developed the method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. The effectiveness of the proposed method and algorithms were verified by mathematical modeling of the control object in a closed circuit with a control system in the MATLAB environment for various types of ships, navigation areas, weather conditions and cases of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.

DISCUSSION
They were proposed the method and algorithms of the vessel linear and angular motion control system, which allow to increase the accuracy and reliability of control in the conditions of significant errors of the sensors during intensive maneuvering and possible failures of the sensors and actuators.
As can be seen from the results of mathematical modeling ( Fig. 1 -Fig. 6), the proposed method and algorithms, in comparison with the known solutions [10 -16], make it possible to detect and parry the failures of sensors and actuators in the channels of linear and angular movement of the vessel due to the use of an observer in the control system for assessing the parameters of the state vector by measuring the parameters of motion, constant monitoring of the measured information according to the estimates of state vector parameters, forming a failure of the sensor that did not pass the control, and replacing its data with the information of another sensor working with it in pair.
The failure of actuators in the control channel is detected if a simultaneous or sequential, after a short period of time, failure of the main and replacement sensors of this channel is detected.
The proposed method and algorithms can be used in the development of software for automatic vessel motion control systems.

CONCLUSIONS
There were proposed a method and algorithms to improve the accuracy and reliability of the automatic vessel control systems.
The scientific novelty of the obtained results consists in the fact that for the first time were proposed a method and algorithms for improving the accuracy and reliability of the automatic vessel control systems working in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. This is achieved by using in onboard controller of the automatic vessel motion control systems an observer to estimation the parameters of the state vector in the linear motion channel by measurements of linear speed and position sensors; estimation the parameters of the state vector in the angular motion channel by measurements of rotational speed and angular position sensors; continuous monitoring of the measured information by comparing it with the obtained estimations; correction estimations in the linear motion channel by measurements of linear speed and position sensors that have passed control; correction estimations in the angular motion channel by measurements of rotational speed and angular position sensors that have passed control; formation of a sensor failure in the linear motion channel (linear speed sensor or position sensor), if its measurements differ from the corresponding estimations for a greater than permissible value, to parry the failure in the linear motion channel by disconnecting the failed sensor from the observer and further estimation according to another sensor working in pairs; formation of a sensor failure in the angular motion channel (rotation speed sensor or angular position sensor), if its measurements differ from the corresponding estimations for a greater than permissible value, to parry the failure in the angular motion channel by disconnecting the failed sensor from the observer and further estimation according to another sensor working in pair; formation of an actuators failure in the linear motion channel (engine, automation or other device) if a simultaneous or sequential failure of both sensors were detected -linear speed sensor and position sensor, actuator failure alarm in the linear motion channel; formation of an actuators failure in the angular motion channel (rudders, drives, other devices) if a simultaneous or sequential failure of both sensors were detected -rotation speed sensor and angular position sensor, actuator failure alarm in the angular motion channel. This method and algorithms make it possible to improve the accuracy and reliability of automatic vessel motion control processes in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators. The proposed method and algorithms for improving the accuracy and reliability of automatic vessel motion control systems in conditions of large deviations in sensors measurements during maneuvering and failures of sensors and actuators were verified by mathematical modeling in the MATLAB environment of the control object movement in a closed circuit with a control system for various types of vessels, navigation areas, weather conditions and cases of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.
The practical value of the obtained results lies in the fact that the developed method and algorithms were tested by mathematical modeling in the MATLAB environment of the control object movement in a closed circuit with a control system for various types of vessels, navigation areas, weather conditions and cases of large deviations in sensors measurements during maneuvering and failures of sensors and actuators.
Mathematical modeling confirmed the efficiency of the developed method and algorithms and allows to recomend them for practical use in the development of mathematical support of vessel motion control systems.