Sliding mode control design for autonomous surface vehicle motion under the influence of environmental factor

Hendro Nurhadi1, Erna Apriliani2, Teguh Herlambang3, Dieky Adzkiya4 Department of Mechanical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember (ITS), Indonesia Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Indonesia Study Program of Information Systems, Faculty of Engineering, Universitas Nahdlatul Ulama Surabaya (UNUSA), Indonesia Center of Excellence Mechatronics and Industrial Automation Research Center, Institut Teknologi Sepuluh Nopember (ITS), Indonesia

INTRODUCTION Indonesia is one of the countries in the world where approximately 70% of the area is sea [1,2]. Such condition makes Indonesia a suitable place to develop marine and coastal tourism. There are many marine and coastal tourisms in Indonesia. One of them is Kenjeran Beach, that is located in Surabaya. At Kenjeran Beach, tourists can enjoy the view by riding a simple boat that is operated by humans. Boat operation by humans may cause accidents due to negligence, lack of professionalism and some other reasons. To reduce the number of accidents and along with technological developments, a vehicle called Autonomous Surface Vehicle (ASV) can be utilized as a support for marine and coastal tourisms.
In this paper, we discuss control design for ASV by using SMC. There are many advantages of using SMC, for example it is robust and it can be applied to nonlinear systems. The ASV model discussed in this paper has three degrees of freedom, namely surge, sway and yaw. The disturbances considered are wind speed and wave height. This paper is structured as follows. The modeling of ASV is discussed in Section 2. Then the general control design using SMC is described in Section 3. The control design of ASV by using SMC is explained in Section 4. The simulation results are discussed in Section 5. Finally, the conclusions are written in Section 6.

2.
AUTONOMOUS SURFACE VEHICLE Autonomous Surface Vehicle (ASV) is equipped with Global Positioning System (GPS), sensors, gas, pH sensors, bluetooth, and telemetry. When the location has been determined, the vehicle will move automatically in real-time. Besides research water vehicle, ASV can also be used for other purposes, such as survey vehicle, inspection of river conditions, seismic surveys, rescue operations etc. The profile and specification of Touristant ASV are listed in Figure 1 and Table 1.  In general, the water-vehicle motions are divided into two types, namely translational and rotational motions. Translational motion consists of surge, sway and heave, whereas rotational motion comprises of roll, pitch, and yaw [18]. In this paper, we use the equation of water-vehicle motions with 3 degrees of freedom (DOF), namely surge, sway and, yaw. The mathematical model for surge, sway and yaw motions is given by From (1)-(3), X ext , Y ext and N ext represent an interference from outside of the surge, sway and yaw motions. In this study, the external interference or environmental factors considered are the force on wind speed, force on wave height, moment of wind speed and force on wave height. It follows that the equations are as follows From the description of X ext , Y ext and N ext , the following nonlinear equations are obtained: In the following, we define three variables U surge , V sway and N yaw which will be used later Equations (7)-(9) are quite long and complicated. In order to simplify those three equations, we use the newly introduced U surge , V sway and N yaw , as follows The mathematical model of Touristant ASV is described in (13)- (15). In order to apply the sliding mode control design, it is better if the mathematical model is written in a state-space form. The state-space form of the mathematical model is as followṡ where T 1 , T 2 , . . . , T 5 are constants, δ 1 is the variable associated with sway and δ 2 is the variable associated with yaw. The state variables are u, v, r and the input variables are X prop , δ 1 and δ 2 .

SLIDING MODE CONTROL
In order to apply the Sliding Mode Control (SMC), we follow the flowchart shown in Figure 2. The detailed stages of SMC implementation can be summarized as follows [17,25]: 1. Determine switching function S(x, t) from the tracking error At the stage of determining the switching function, each ASV motion state is associated with a switching function using the following equations: where tracking error can be expressed asx(t) = x(t) − x d (t) and x d is the desired state.
Ì ISSN: 2088-8708 2. Determine the sliding surface The next step is to determine the sliding surface, namely S(x, t) = 0 from the switching function obtained.

Determine the controller estimation valueâ
The step to determine the controller estimation valueâ can be obtained from the equationṠ = 0. 4. Use control law a =â − K sgn(S) The next step is applying the control law by using the equation: To satisfy the sliding condition, the signum function is defined as follows:

Subtitute the value ofâ
Subtitute the valueâ to control law so that new control input is obtained as the subtitute of the previous control input. 6. Determine the value of K Determine the value K from control law a =â − K sgn(S) that has been obtained.

Saturation function
The last step is to change the signum function into a saturation function which aims is to minimize the chattering.

SLIDING MODE CONTROL DESIGN FOR AUTONOMOUS SURFACE VEHICLE MODELS
As mentioned in the previous section, the design of SMC for Nonlinear ASV model consists of three parts, namely for surge, sway and yaw motions.

SMC design for surge motion
In designing the control of surge motion, first of all notice that the tracking error of surge motion is u = u − u d , where the desired surge u d is constant. Because the system has order 1, the switching function is formed from (19) by defining n = 1 as follows: Since u d is a constant function,u d = 0. It follows that the derivative of S 1 (u, t) iṡ Then we substitute (16) to (20) to obtain the following equation: In order to compute the estimated value of X prop , denoted byX prop ,Ṡ 1 (u, t) is set to zero: We obtain the following expressionX Based on the control law that meets the sliding condition, the relationship between X prop andX prop shall be By substituting (23) into (24), we obtain Then we substitute (25) to (21), as followṡ Then K 1 is chosen such that the sliding condition is fulfilled, that is where η is a tuning parameter. After some simple algebraic manipulations, we obtain From (27), the value of K 1 is Then, a boundary layer is used to minimize chattering by changing the signum function (sgn) into saturation function as follows: Ì ISSN: 2088-8708 where φ is a tuning parameter. Finally the control input X prop is defined in the following equation

SMC design for sway motion
The procedure for designing sway input is similar with surge input. The switching function of sway motion is as follows: By performing the same steps as in the surge motion, the control system design for sway motion is as follows: where η and φ are tuning parameters.

SMC design for yaw motion
The procedure for designing yaw input has some similarities to that for surge inputs. The switching function of yaw motion is given by: By applying the same steps as for the surge motion, the design of the control system for yaw motion is as follows: where η and φ are tuning parameters.

RESULTS AND SIMULATION
After designing the motion control system using the SMC method, then we simulate the results on Matlab's Simulink. This control system is arranged in the form of block diagrams on the motion system of Autonomous Surface Vehicle (ASV) in the form of a closed loop with η = 1 and φ = 1. The block diagram of the nonlinear 3-DOF Autonomous Surface Vehicle (ASV) model using the SMC method is presented in Figure 3. From Figures 4 and 5, it can be seen that the higher wind speed and wave height, the steady-state error is higher and settling time is longer. But the level of the wind speed and the height of the wave has no effect on the overshoot. At a wind speed of 23 km/h and a wave height of 0.6 m, the graph shows that it goes away from the setpoint. It appears that the motion is stable and the steady-state error is very small with a setpoint of 4.6 m/s for surge, 1 m/s for sway and 1 rad/s for yaw. Figure 4 shows a surge motion response reaching the first time (settling time) at 11 seconds, a steady-state error of 0.17% and having a 0% overshoot by presenting an error between a setpoint and a stable position. Figure 4 is the result of a response by the SMC method for sway motion, where the sway motion response reaches settling time at 9.4 seconds, steady-state error of 0.2% and has a 0% overshoot. Figure 5 is the result of a response by the SMC method for yaw motion, where the yaw motion response reaches settling time in 8.1 seconds, steady state error 0.2% and has a 0% overshoot. The simulation results of the three conditions can be seen in Table 2.  6. CONCLUSIONS Based on the results and analysis related to the design of the ASV motion control system with the Sliding Mode Control (SMC) method for surge, sway and yaw motions, the study of 3-DOF nonlinear models came to the conclusion that if the environmental factor value is higher, then the error produced is also higher. The average error difference between the simulation without environmental factors and that using environmental factors is 0.05% for surge, sway and yaw motions.