Ship trajectory tracking control system and method with predetermined tracking accuracy and time

Abstract

The present invention discloses a ship trajectory tracking control system and method with predetermined tracking accuracy and time, the control system includes an expected trajectory input, a closed-loop system of the ship, the closed-loop system of the ship includes a feedback controller, and a model of the ship; the expected trajectory input inputs the expected motion trajectory of the ship, the closed-loop system of the ship subtracts the expected motion trajectory of the ship from the actual motion trajectory of the ship, and obtains the position error of the ship, the position error is obtained by the feedback controller to obtain the system input, the system input acts on the model of the ship, and obtains the actual motion trajectory of the ship. The present invention solves the control problem of underactuated ships under model uncertainty, environmental interference and potential actuator failure, and the computational burden problem brought by solutions such as neural networks, fuzzy logic systems or adaptive technologies.

Description

Technical Field

[0001] The present invention relates to a ship track tracking control system and method, and in particular to a ship track tracking control system and method with predetermined tracking accuracy and time. Background Art

[0002] Ships have received extensive attention in the field of control theory and engineering due to their huge commercial and military value. The commercial value is reflected in marine data collection, resource exploration and construction, and hydrological environment surveys. Military applications include intelligence, surveillance, reconnaissance, mine countermeasures, and anti-submarine warfare. Its functions are mainly divided into three categories: dynamic positioning, path tracking, and trajectory tracking. Dynamic positioning systems generally refer to the control system of ships in fully driven low-speed mode. The purpose is to maintain the position and heading of the ship at a fixed point or a prescribed waypoint along the track. Typical applications of dynamic positioning include pipeline laying and oil and gas exploration. Research in recent years has focused on dealing with model uncertainties and disturbances in ship systems to improve control performance. The purpose of path tracking control is to guide the ship (usually in underactuated mode) alone through a pre-assigned path with a satisfactory velocity profile. In high-speed applications, the sway direction of most ships cannot be directly driven. Therefore, the first challenge of path tracking control lies in the underactuation of the ship. This challenge was successfully overcome by backtracking and Lyapunov's direct method. Trajectory tracking refers to the ship tracking a spatiotemporal trajectory with strict time requirements, which is of great significance in marine navigation applications in terms of safety, emission reduction, and energy saving. Compared with path tracking, in addition to the steering control law, a specific speed law is also required. At present, there are still many challenging problems in the trajectory tracking control of ships. Summary of the invention

[0003] In order to solve the control problems of underactuated ships under model uncertainty, environmental interference and potential actuator failure, as well as the computational burden problems brought by solutions such as neural networks, fuzzy logic systems or adaptive technologies, the present invention provides a ship trajectory tracking control system and method with predetermined tracking accuracy and time.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] A ship trajectory tracking control system with predetermined tracking accuracy and time, including a desired trajectory input P d , a closed-loop system for ships, where:

[0006] The closed-loop system of the ship includes a feedback controller C and a model P of the ship;

[0007] The desired trajectory input P d Input the desired trajectory x of the ship d ,y d;

[0008] The closed-loop system of the ship is based on the actual motion trajectory x of the ship minus the expected motion trajectory x of the ship. d , and the ship's position error e is obtained x The closed-loop system of the ship is based on the actual motion trajectory y of the ship minus the expected motion trajectory y of the ship d , and the ship's position error e is obtained y ;

[0009] The position error e x 、e y The system input τ is obtained through the feedback controller C u , τ r , system input τ u , τ r Acting on the ship's model P, the actual motion trajectory x, y of the ship is obtained.

[0010] A ship trajectory tracking control method with predetermined tracking accuracy and time comprises the following steps:

[0011] Step (1) uses the following nonlinear output feedback system, which has the form:

[0012]

[0013]

[0014] Where (x, y) and ψ represent the position and yaw angle of the ship in the inertial system respectively; η = [u, v, r] T , u, v, r represent the ship's surge, sway and pitch speed respectively; τ u and τ r Respectively represent the system input; f u (η), f v (η) and f r (η) represents a nonlinear function; d u (t), d v (t) and d r (t) represents the bounded environmental disturbance caused by sea breeze and waves; g u and g r represents an unknown positive constant related to the mass of the ship;

[0015] Step (2) uses the following actuator failure form:

[0016] τ i =ρ i (t)α i (t)+σ i (t), i = u, r

[0017] Among them, α i (t), i = u, r is the command control signal to be designed; ρ i (t) and σ i (t), i = u, r represents multiplication and addition actuator faults, respectively;

[0018] Step (3) The control objective of the ship trajectory tracking control system is to output x(t) and y(t) to track the given desired motion trajectory x d (t), y d (t), the position error is described as:

[0019] e x (t) = x(t) - x d (t)

[0020] e y (t) = y(t) - y d (t)

[0021] The position error can be further described as:

[0022] z 1 =||col(e x , e y )||

[0023] Step (4) Feedback controller design

[0024] Step (41) designs the boundary function φ(t):

[0025] p(t)=γ 1 Φ(t)+γ 2

[0026]

[0027] Among them, γ 1 >0,γ 2 >0,t r >0 indicates design parameters, and γ 1 +γ 2 =1;

[0028] Step (42) Design auxiliary variable z 2 and ξ:

[0029]

[0030]

[0031] Step (43) converts the position error in the following manner:

[0032]

[0033]

[0034] Among them, k i Represents the controller parameters and satisfies the condition k i >0;z 3 (t) and z 4 (t) is the speed error, z 3 (t)=uu d , z 4 (t) = rr d ;

[0035] Step (44) is based on the backstepping design process to design the following controller:

[0036] u d (t) = -c 1 s ξ β 1

[0037] r d (t) = -c 2 s ξ β 2

[0038] α i (t) = -c m β j i=u,r,j=3,4

[0039] Among them, c m , m=1,2,3,4 represent controller parameters and satisfy c m >0;s ξ =sgn(ξ);u d (t) and r d (t) represents the virtual control rate;

[0040] Step (5) Ship trajectory tracking control

[0041] Step (51) The host computer inputs the desired motion trajectory x d (t), y d (t) provide propulsion for the vessel;

[0042] Step (52) When the position sensor on the ship detects the change in the position of the ship, it feeds back the position information to the feedback controller. After receiving the signal, the feedback controller performs a closed-loop operation and gives the operation result to the driver. The driver outputs current to control the output and direction of each motor to track the desired motion trajectory.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1. The present invention introduces a new boundary function into the constraint processing method, thereby ensuring that the positioning error converges to the specified set at a fixed time convergence speed.

[0045] 2. The controller design of the present invention does not involve the calculation of virtual control signal derivatives, nor does it rely on information related to vehicle dynamics parameters, interference boundaries or fault characteristics. No auxiliary tools (such as adaptive technology, neural networks, observers or filters) are used to collect this information, thereby significantly reducing the complexity of the structure.

[0046] 3. The present invention solves the control problem of underactuated ships under model uncertainty, environmental interference and potential actuator failure, and the computational burden problem brought by solutions such as neural networks, fuzzy logic systems or adaptive technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the principle of the ship position tracking control system of the present invention;

[0048] Figure 2 It is a path tracking trajectory diagram on a two-dimensional plane. The left one is the controller designed by the present invention, and the right one is based on the adaptive fast non-singular integral T-terminal sliding mode controller (AFNITSMC);

[0049] Figure 3 It is a position tracking error diagram of the controller presented in the present invention and the controller based on adaptive fast non-singular integral T terminal sliding mode controller (AFNITSMC), the left one is the controller designed by the present invention, and the right one is based on adaptive fast non-singular integral T terminal sliding mode controller (AFNITSMC);

[0050] Figure 4 It is a speed tracking error diagram of the controller presented by the present invention and the controller based on adaptive fast non-singular integral T terminal sliding mode controller (AFNITSMC), the left one is the controller designed by the present invention, and the right one is based on adaptive fast non-singular integral T terminal sliding mode controller (AFNITSMC);

[0051] Figure 5 It is a thrust diagram of the propeller output. The left one is the controller designed by the present invention, and the right one is based on the adaptive fast non-singular integral T-terminal sliding mode controller (AFNITSMC).

[0052] Figure 6 The controller designed by the present invention includes a tracking error map with upper and lower bounds. DETAILED DESCRIPTION

[0053] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0054] The present invention provides a ship trajectory tracking control system with predetermined tracking accuracy and time, such as Figure 1 As shown, the ship trajectory tracking control system includes a desired trajectory input P d , a closed-loop system for ships, where:

[0055] The closed-loop system of the ship includes a feedback controller C and a model P of the ship;

[0056] The desired trajectory input P d Input the desired trajectory x of the ship d ,y d ;

[0057] The closed-loop system of the ship is based on the actual motion trajectory x of the ship minus the expected motion trajectory x of the ship. d , and the ship's position error e is obtained x The closed-loop system of the ship is based on the actual motion trajectory y of the ship minus the expected motion trajectory y of the ship d , and the ship's position error e is obtained y ;

[0058] The position error e x 、e y The system input τ is obtained through the feedback controller C u , τ r , system input τ u , τ r Acting on the ship's model P, the actual motion trajectory x, y of the ship is obtained.

[0059] A method for ship trajectory tracking control using the above ship trajectory tracking control system comprises the following steps:

[0060] Step (1) uses a nonlinear output feedback system of the following form:

[0061]

[0062]

[0063] Where (x, y) and ψ represent the position and yaw angle of the ship in the inertial system respectively; η = [u, v, r] T , u, v, r represent the ship's surge, sway and pitch speed respectively; τ u and τ rThey represent the system input, including the thrust and torque generated by the propeller in the surge and yaw directions; f u (η), f v (η) and f r (η) represents a nonlinear function; d u (t), d v (t) and d r (t) represents the bounded environmental disturbance caused by sea breeze and waves; g u and g r Represents an unknown positive constant related to the mass of the ship.

[0064] Step (2) uses the following actuator failure form:

[0065] τ i =ρ i (t)α i (t)+σ i (t), i = u, r

[0066] Among them, α i (t) is the command control signal to be designed; i (t) and σ i (t) represent the multiplication and addition actuator failures, respectively.

[0067] Step (3) The control objective of the ship trajectory tracking control system is to output x(t) and y(t) to track the given desired motion trajectory x d (t), y d (t), the position error is described as:

[0068] e x (t) = x(t) - x d (t)

[0069] e y (t) = y(t) - y d (t)

[0070] The position error can be further described as:

[0071] z 1 =||col(e x , e y )||

[0072] Step (4) Feedback controller design

[0073] Step (41) designs the boundary function φ(t):

[0074] p(t)=γ 1 Φ(t)+γ 2

[0075]

[0076] Among them, γ 1 >0,γ 2 >0,t r >0 indicates design parameters, and γ 1 +γ 2 =1.

[0077] Step (42) Design auxiliary variable z 2 and ξ:

[0078]

[0079]

[0080] Step (43) converts the position error in the following manner:

[0081]

[0082]

[0083] Among them, k i Represents the controller parameters and satisfies the condition k i >0;z 3 (t) and z 4 (t) is the speed error:

[0084] z 3 (t) = uu d

[0085] z 4 (t) = rr d

[0086] Step (44) is based on the backstepping design process to design the following controller:

[0087] u d (t) = -c 1 s ξ β 1

[0088] r d (t) = -c 2 s ξ β 2

[0089] α i (t) = -c m β j i=u,r,j=3,4

[0090] Among them, c m , m=1,2,3,4 represent controller parameters and satisfy cm >0;s ξ =sgn(ξ);u d (t) and r d (t) represents the virtual control rate.

[0091] Step (5) Ship trajectory tracking control

[0092] Step (51) The host computer inputs the desired motion trajectory x d (t), y d (t) provide propulsion for the vessel;

[0093] Step (52) When the position sensor on the ship detects the change in the position of the ship, it feeds back the position information to the feedback controller. After receiving the signal, the feedback controller performs a closed-loop operation and gives the operation result to the driver. The driver outputs current to control the output and direction of each motor to track the desired motion trajectory.

[0094] Example:

[0095] Step (1) uses the following ship dynamics and kinematics equations:

[0096]

[0097] Among them, m 11 =21.5, m 22 =26.5, m 33 =8,X u =-70,X u|u| =-100, Y v =-100, Y v|v| =-200, N r =-50, N r|r| =-100.

[0098] Step (2) uses the following executor form:

[0099] τ i =ρ i (t)α i (t)+σ i (t), i = u, r, ω

[0100] In the formula, α i (t), i = u, r, ω is the command control signal to be designed; ρ i (t) and σ i (t), i = u, r, ω represent multiplication and addition actuator faults, respectively.

[0101] In this embodiment:

[0102]

[0103]

[0104] Step (3) The system control goal is to output x(t) and y(t) to track the desired motion trajectory x d (t), y d (t), the position error is described as:

[0105] e x (t) = x(t) - x d (t)

[0106] e y (t) = y(t) - y d (t)

[0107] Furthermore, the position error is described as:

[0108] z 1 =||col(e x , e y )||

[0109] In this embodiment,

[0110] Step (4) Feedback controller design

[0111] Step (41) designs the boundary function φ(t):

[0112] p(t)=γ 1 Φ(t)+γ 2

[0113]

[0114] In the formula, γ 1 =0.98,γ 2 =0.02, t r =20.

[0115] Step (42) Design auxiliary variable z 2 and ξ:

[0116]

[0117]

[0118] Step (43) converts the position error in the following manner:

[0119]

[0120]

[0121] In the formula, k2 =0.2, k 3 =0.035, k 4 =0.03; z 3 (t) and z 4 (t) is the speed error.

[0122] z 3 (t) = uu d

[0123] z 4 (t) = rr d

[0124] Step (44) is based on the backstepping design process to design the following controller:

[0125] u d (t) = -c 1 s ξ β 1

[0126] r d (t) = -c 2 s ξ β 2

[0127] α i (t) = -c j β j i=u,r,j=3,4

[0128] In the formula, c 1 =1, c 2 =1, c 3 =2, c 4 =8;s ξ =sgn(ξ);u d (t) and r d (t) represents the virtual control rate.

[0129] Step (5) uses the existing adaptive fast non-singular integral T-terminal sliding mode controller for comparative experiments. The controller is required to operate under the same conditions. The controller parameters are q 1 =5,q 2 =3,γ 1 =13,γ 2 =3, K 1 =diag(10,10,10),K 2 =diag(0.001, 0.001, 0.01), K 3 =diag(1.2,1.2),K 4 =diag(1,1).

[0130] Depend on Figure 2 It can be seen that both the controller designed by the present invention and the existing AFNITSMC can achieve tracking control of the ship. The two controllers behave differently in the initial stage. The tracking speed of the controller designed by the present invention from the initial state to the specified reference output is greater than that of the AFNITSMC. In addition, after the actuator fails, the controller designed by the present invention still accurately and continuously tracks the reference output; the tracking error of the AFNITSMC increases significantly.

[0131] Depend on Figure 3 It can be seen that after the actuator fails, under the same conditions, the position tracking error of the controller designed by the present invention does not produce obvious jitter, and the tracking error of AFNITSMC increases significantly.

[0132] Depend on Figure 4 It can be seen that the controller designed in the present invention ensures that the ship speed is continuous and has no sudden changes when realizing ship position tracking.

[0133] Depend on Figure 5 It can be seen that the thrust of the three thrusters of the controller designed by the present invention is always within the saturation limit of the thrusters and generates reasonable control force after the actuator failure, while the thrust of the three thrusters of AFNITSMC exceeds the saturation limit in the initial stage.

[0134] Depend on Figure 6 It can be seen that the tracking errors of the controller designed in the present invention are kept within the preset limits, and the output tracking error of the ship can be converged to a predetermined set within a fixed time period.

[0135] comprehensive Figure 2-Figure 6 It can be seen from the results that, compared with the existing methods, the present invention can not only ensure the control accuracy, but also achieve that the output tracking error of the ship converges to a predetermined set within a fixed time period, and the thrust of all thrusters does not exceed their saturation limit.

Claims

1. A ship trajectory tracking control method with predetermined tracking accuracy and time, characterized in that The method comprises the following steps: Step (1) uses the following nonlinear output feedback system, which has the form: Where (x, y) and ψ represent the position and yaw angle of the ship in the inertial system respectively; η = [u, v, r] T , u, v, r represent the ship's surge, sway and pitch speed respectively; τ u and τ r Respectively represent the system input; f u (η), f v (η) and f r (η) represents a nonlinear function; d u (t), d v (t) and d r (t) represents the bounded environmental disturbance caused by sea breeze and waves; g u and g r represents an unknown positive constant related to the mass of the ship; Step (2) uses the following actuator failure form: t i =ρ i (t)a i (t)+σ i (t), i=u,r Among them, α i (t), i = u, r is the command control signal to be designed; ρ i (t) and σ i (t), i = u, r represents multiplication and addition actuator faults, respectively; Step (3) The control objective of the ship trajectory tracking control system is to output x(t) and y(t) to track the given desired motion trajectory x d (t), y d (t), the position error is described as: e x (t)=x(t)-x d (t) e y (t)=y(t)-y d (t) The position error is further described as: z1=||col(e x ,And y )|| Step (4) Feedback controller design Step (41) designs the boundary function φ(t): p(t)=γ1Φ(t)+γ2 Among them, γ1>0, γ2>0, t r >0 indicates design parameters, and γ1+γ2=1; Step (42) designs auxiliary variables z2 and ξ: Step (43) converts the position error in the following manner: Among them, k i Represents the controller parameters and satisfies the condition k i >0; z3(t) and z4(t) are velocity errors; Step (44) is based on the backstepping design process to design the following controller: u d (t)=-c1s ξ β1 r d (t)=-c2s ξ β2 a i (t)=-c m b j i=u,r,j=3,4 Among them, c m , m=1,2,3,4 represents the controller parameters and satisfies c m >0;s ξ =sgn(ξ);u d (t) and r d (t) represents the virtual control rate; Step (5) Ship trajectory tracking control Step (51) The host computer inputs the desired motion trajectory x d (t), y d (t) provide propulsion for the vessel; Step (52) When the position sensor on the ship detects the change in the position of the ship, it feeds back the position information to the feedback controller. After receiving the signal, the feedback controller performs a closed-loop operation and gives the operation result to the driver. The driver outputs current to control the output and direction of each motor to track the desired motion trajectory.

2. The ship trajectory tracking control method with predetermined tracking accuracy and time according to claim 1, characterized in that z3(t)=uu d , z4(t)=rr d .

3. A ship trajectory tracking control system with predetermined tracking accuracy and time for implementing the method described in any one of claims 1-2, characterized in that The control system includes a desired trajectory input P d , a closed-loop system for ships, where: The closed-loop system of the ship includes a feedback controller C and a model P of the ship; The desired trajectory input P d Input the desired trajectory x of the ship d ,y d ; The closed-loop system of the ship is based on the actual motion trajectory of the ship x minus the expected motion trajectory of the ship x d , and the ship's position error e is obtained x The closed-loop system of the ship is based on the actual motion trajectory y of the ship minus the expected motion trajectory y of the ship d , and the ship's position error e is obtained y ; The position error e x 、e y The system input τ is obtained through the feedback controller C u , τ r , system input τ u , τ r Acting on the ship's model P, the actual motion trajectory x, y of the ship is obtained.

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