Auto Pilot Ship Heading Angle Control Using Adaptive Control Algorithm

In this paper discussed about development of an auto pilot system for ships using adaptive filter. Adaptive filter in the application of auto pilots for ships is presented for controlling the ship such that it follows its predetermined trajectory. Due to random environmental effects such as wind speed or direction and sea current, the path of the ship may alter. The objective of this research is to investigate that whether proposed system will adapts to the random changes and maintain the desired ship trajectory. The proposed auto pilot system is developed using Least Mean Square algorithm (LMS) adaptive filter. The performances of the system are analyzed based on accuracy and computational times. MATLAB Simulink model tool is used for execute the simulations of the auto pilot system for ships.


Introduction
The history of ships, boats and sailing is spread over centuries.Ship steering control has been an essential topic for researchers for more than 95 years.Early steering control systems were based on an instrument called gyroscope, which was used to determine the direction of travel.In 1911, Elmer Sperry invented an automatic mechanism for ship steering control based on the gyroscope (Sperry, 1992).
In 1922, Minorsky published his work on automatic ship steering, which was an essential breakthrough in the field (Minsky, 1954).Later in the same year, Sperry presented the first automatic ship control system.These early autopilot for ships were entirely mechanical in nature and had a very simple process, wherein the rudder was proportional to the heading error.
Major disadvantage s of traditional controllers such as PID and PD are their inability to adjust with alterations automatically in the environmental and operating conditions.These settings had to be adjusted manually by the user which in many cases may not be completely optimal.Moreover, these obligatory setting which had to be done repeatedly were exhausting and time consuming.

Steering Control Overview
Fig. 1 shows a general block diagram of a ship steering control system made up of reference model, sensor system and feedback control system.The reference model receives the data on the position and speed of the ship from the DGPS (Differential Global Position System) and also receives external data provided by an operator (Deck Officer) and other data concerning the environmental conditions (height and slope of the waves and speed and direction of the wind and currents).The control system also receives information that supplied by the measurement system and determines the forces and moments which are to be supplied to the ship in accordance with the established control objective in most cases together with the reference model system.In this thesis, we will be focusing only on the course keeping characteristics of the auto pilot controller.

Adaptive Controllers in Auto Pilot Ship System
Autopilot is one of the most important section used in ships.Autopilots are not just used to lead the ship on a desired trajectory, but also raise the safety level of the journey and control the ship economically.A good autopilot can help to avoid undesired situations on maneuvering and remarkably reduce the numbers of ship operators.In the last few decades, taking the advantage of drastic development of electronics and control theory, several new and effective methods have been proposed and developed for designing ship-autopilots (Barbos, 2008), (M.Kamran Joyo, 2014), ( Hussain, 2011).

Adaptive Filter
Fig. 2 represents the general block diagram of any adaptive filter.In this application i.e. the ship steering auto-pilot is designed using an adaptive filter and completely replacing the traditional controllers.

Least Mean Square (LMS)
The LMS algorithm was established by Widrow and Hoff in 1959.Compared to other algorithms, LMS algorithm is relatively simple; it does not require correlation function calculation nor does it require matrix inversions.This algorithm is basically the type of adaptive filter known as stochastic gradient-based algorithms and it consists of two major processes: Filtering process and adaptive process (A.T.Hussain, 2015).LMS algorithm worked on steepest decent method and also took help from the theory of Wiener solution (optimal filter tap weights).This algorithm is basically using the formulas which updates the filter coefficients by using the tap weight vectors w and also update the gradient of the cost function accordingly to the filter tap weight coefficient vector

P -732
In practice, the value of the expectation E { } is normally unknown, therefore we need to introduces the approximation or estimated as the sample mean.
With this estimate we obtain the updating weight vector as, And finally, the weight vector update equation become the simple form.

Ship Dynamics & Model
In this research, Norrbin Model of the ship is considered.This model is extension of the Nomoto's first-order model (Syed Faiz Ahmed, 2014) in an empirical way.To describe large rudder angles as well as course instability, the following model is proposed: (5) Where a 1 = +1 for course-stable and 1 1 for course-unstable ships.Of course, this model can also be extended with a constant and a quadratic term.This yield, in the steady state, when 0 0 1 With Eq. 5 and Eq. 6 can be rewritten as:

Ships Use for Simulation Purposes
For simulation purpose ROV Zeefakkel ship (ferry) is taken in account which is 45m ferry.The ship model of the ferry can be formed using table 1.The desired heading response is represented by the third order model of Eq 8 with am= 0.9341, bm= 0.2040 and cm= 0.0182.The maximum rudder limit selected is and the maximum rudder rate is.Where am, bm and cmare constants.Van Amerongen demonstrates that the motion of this ship can be described adequately by the Norrbin's nonlinear model with the following parameter values: When the speed of the ship changes, the values of K and T also vary as found out by Van Amerongen and illustrated in the table below:

Conclusions
The LMS filter gives very good results in terms of achieving the heading angle that is desired for both 20° and 50°.It is ascertained from the simulation results that the performance of LMS algorithm is better to minimize Mean Square Error (MSE) for different heading degree angles to maintain the desired trajectory using the performance function of the algorithm that minimized the average power in the error signal.As the degree of heading angle was switched from 20° to 50°, we can observe that the filter length and step size µ has to be changed to get an optimum performance from the controller.