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UDC 681 5 9 7558
_DEVELOPMENT OF SHIP COURSE STABILIZATION SYSTEM_
Satybaldina Dana Karimtayevna
(Candidate of Engineering Sciences, Associate Professor Eurasian National University named after L.N. Gumilyev,
Astana, Kazakhstan) Zekenova Gulsanat Ziyashovna (Master's Degree student, Eurasian National University named after L.N. Gumilyev,
Astana, Kazakhstan)
_РАЗРАБОТКА СИСТЕМЫ СТАБИЛИЗАЦИИ МОРСКОГО СУДНА ПО КУРСУ_
Сатыбалдина Дана Каримтаевна
(кандидат технических наук, доцент, Евразийский национальный университет им. Л.Н. Гумилева,
г. Астана, Казахстан) Зекенова Гульсанат Зияшовна
(магистрант,
Евразийский национальный университет им. Л.Н. Гумилева,
г. Астана, Казахстан)
ABSTRACT
The development of ship course stabilization (autopilot) is addressed below. A mathematical model of a control system and a description of its elements are obtained. The results of modeling the ship's stabilization system are presented by using PD and PID regulators.
АННОТАЦИЯ
Рассматривается разработка системы стабилизации морского судна по курсу (авторулевого). Получены математическая модель систему управления и описание входящих в нее элементов. Представлены результаты моделирования системы стабилизации морского судна с применением ПД- и ПИД-регуляторов.
Keywords: control systems, ship stabilization systems, regulators, transient characteristics
Ключевые слова: системы управления, системы стабилизации судна, регуляторы, переходные характеристики
Guiding the ship from the port of departure to the port of destination refers to complex management tasks. Its peculiarities are the complexity of the ship as an object of control and the diversity of the influence of the external environment on it; the need to process a large amount of data, both from internal and external sources of information; complexity of navigation equipment and power means; limited time for decisionmaking and a number of other circumstances.
At the present stage, through electronic means, the problem of guiding the vessel from the initial point to the final one in accordance with the planned plan is usually solved [8]. It determines the route and time of arrival at its intermediate and final points. The fulfillment of the plan is to maintain a correspondence between the ship's kinematic parameters and the time functions
specified by the plan. In this control process, the driving along the route and the speed regulation are distinguished.
The first task is automatically solved by the onboard systems of driving on route, which have been officially named Track Control Systems (TCS). The TCS control the course and lateral deviation from the specified track line, reducing the latter to a zero value. In order to change or maintain the constant of the first coordinate only, the Heading Control System (HCS) is used. Traditionally it is called autopilot (AP).
On ships of the world fleet, many types of AP are exploited [1, 2, 6]. Depending on the element base, they are divided into electromechanical, electronic analog, electronic digital. The drawbacks of the traditional electromechanical AP are: obsolete element base, low
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Нацнонаflbнаa ассоцнацнa yneHbix (HAy) # 6(33), 2017
level of protection from the effect on the quality of wave yaw control, insufficient sensitivity to angular velocity in quiet weather for unstable high-tonnage vessels, low quality of course stabilization due to low manual tuning efficiency, automatic execution of turns to any angle in the required manner, the difficulty of including a route along the route in the contour of the vessel's navigation system. The greatest opportunities for optimizing ship control are provided by electronic digital APs. They usually include a control panel mounted in this remote processor and display for the helmsman.
controller
actuator
9n +
e C(s) u R(s) 8
* —K
The transition to computer technology in the AP expands the possibilities of applying effective algorithms for controlling the course [9].
On any vessel in real conditions there are disturbing forces caused by wind, sea waves and other causes. Some of them (for example, wind influence) contain a constant component, that is, their average value is not equal to zero. Nevertheless, the control system must maintain the prescribed course of the ship even in such conditions [7]. Perturbing forces and moments are applied directly to the input of the control object, the block diagram looks like in Figure 1: w
object
9
1
P(s)
H(s)
measuring system
Figure 1. Structural diagram of the ship course stabilization system
The suppression of perturbations (indicated in the diagram via w ) is determined by the transfer function of the system from the perturbation, that is, the transfer
function from the input w to the output p :
W (s) =_^_
w 1 + R(s) C (s) H (s) F (s)
If it contains zero at a point s = 0 , the corresponding AFC vanishes at zero frequency, that is, constant perturbations in the steady state are completely compensated. This requires integrator to be included in the drive, feedback, or regulator model. Thus, if the controller contains an integral channel (I-channel), there is no static error in the system under constant perturbation.
A linear mathematical model describing the yawing of a ship has the form [6]:
(P = ®y
1 K 5,
s s
where 9 is yaw angle (the angle of deviation from the specified course), 9 is the angular velocity of rotation about the vertical axis, 8 is the angle of rotation of the vertical rudder relative to the equilibrium position, Ts is the time constant, and K is the constant coefficient having the dimension rad / sec.
The transfer function from the angle of rotation of the rudder to the yaw angle is written in the form
K
P(s) =-, where K = 0.0694 rad /
s(Tss +1)
sec, T = 18.2 sec,
Linear model of the drive (steering machine) is an integrator with a transfer function
Ro(s)= 1
TRs
TR = 2 sec,
covered by a single negative feedback. At the rudder angle and the speed of the shift, nonlinear constraints are imposed
| 8(i) | < 3 ° / sec, |8(i )| < 30°.
To measure the yaw angle, a gyrocompass is used, the mathematical model of which is written in the form of an aperiodic link of the first order with a transfer function
H (s) = 1
Ts +1
T„ = 6
sec,
Let us investigate the system with PD and PID regulators [5]. Transients in systems with PD and PID controllers are shown in Figure 2 [3, 4]:
Ha^OHa^bHaa ассоцнацнa yneHbix (HAy) #6 (33), 2017
51
0 50 100 150 200 250 300 350 400 450 500
Time, sec
Figure 2. Transient processes
A glance at the graphs provided shows that the ship with the PD controller did not reach the preset rate of 10 degrees, because the transfer function does not have zero at the point s = 0. The static gain ks = 1.419, the steady-state value of the output signal should be equal = 12,843 , because time independent perturbation equal to 2, amplified 1.419 times, is directly summed with the steady-state value of the signal in the absence of a pertutbation equal to 10.
When using the PID controller, the vessel goes to the set course, because of the integrator entering the system, the perturbation transfer function takes the value 0 for a time independent disturbance. The static
gain k = 0, the steady-state value of the output signal
should be equal @rTJ = 10 , because the time independent perturbation is neutralized. When using the PID controller instead of the PD controller, the system became resistant to time independent perturbations, while the control signal remained practically unchanged, but at the same time the overshoot increased.
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