A robust adaptive heading angle control method for underwater glider based on event-triggered strategy

Abstract

The present invention proposes a method for robust adaptive control of the heading angle of an underwater glider based on an event-triggered strategy. The method regards the roll angle as a virtual control and the differential rudder angle as an actual control input, and designs a controller based on a fourth-order nonlinear model and a backstepping method. First, the heading angle tracking error of the underwater glider is calculated, and a virtual control law of the roll angle is designed. Secondly, based on the virtual control law and the current roll angle of the underwater glider, the roll angle tracking error is calculated to obtain the differential rudder angle control command input. In order to reduce the actuator action frequency, a relative threshold event trigger condition is designed. Only when the trigger condition is met, the command signal is transmitted to the steering gear to power the steering gear. At the same time, a robust adaptive damping term is designed to stabilize the model uncertainty and external disturbances. From the simulation results, the system can track the expected signal relatively well, and the action frequency of the steering gear is significantly reduced, the number of controls is effectively reduced, and the energy consumption of the heading control system is saved.

Description

Technical Field

[0001] The invention relates to the technical field of underwater glider control, in particular to an underwater glider robust adaptive heading angle control method based on an event triggering strategy. Background Art

[0002] Underwater glider is a new type of underwater vehicle that is purely buoyancy-driven and has no external propulsion. As a long-range underwater vehicle with its own power supply, its endurance is the guarantee for long-term gliding and observation missions. The energy consumption of the control system has a significant impact on the endurance of the glider. It is of great significance to reduce the control energy consumption and realize energy-saving motion control of underwater gliders.

[0003] The existing underwater glider heading angle control strategy is highly dependent on accurate mathematical models, and the most obvious drawback is that continuous steering is required to maintain the heading in the presence of environmental disturbances and unmodeled dynamics, which not only causes a large amount of control system energy consumption, but also increases the wear of the actuator, which is not conducive to the long-term mission execution of the underwater glider. Therefore, it is of great significance to design an underwater glider heading controller with good adaptability and robustness and low actuator action frequency. Summary of the invention

[0004] The present invention proposes a method for robust adaptive control of the heading angle of an underwater glider based on an event-triggered strategy to overcome the above-mentioned defects, so that the underwater glider can reduce the number of controls while achieving precise heading angle tracking control, and reduce the action frequency of the servo to save energy consumption of the control system.

[0005] The technical solution of the present invention is:

[0006] The method for robust adaptive control of the heading angle of an underwater glider based on an event-triggered strategy is characterized by comprising the following steps:

[0007] Step 1: Establish a mathematical model of the lateral motion of the underwater glider, including the state equations of heading angle, yaw angular velocity, roll angle and roll angular velocity;

[0008] Step 2: Continuously collect the underwater glider state variables, including heading angle, yaw angular velocity, roll angle, roll angular velocity and longitudinal velocity;

[0009] Step 3: Calculate the yaw rate, roll angle, intermediate virtual control law of roll rate and actual control law of differential rudder according to the collected state variables;

[0010] Step 4: Determine whether the heading error is stable, and calculate the difference between the actual control law signal and the current signal of the differential rudder, and compare it with the designed event trigger threshold to determine whether the event trigger condition is met; if the heading error is stable and does not meet the event trigger condition, the differential rudder signal remains unchanged, and the differential rudder servo is powered off; if the event trigger condition is violated, the differential rudder signal is updated, the differential rudder servo is powered on, and the control signal is transmitted from the controller to the differential rudder servo;

[0011] Step 5: The differential rudder generates a corresponding differential rudder angle according to the judgment result of step 4 and the new control signal, or maintains the current state unchanged to complete the control of the heading angle of the underwater glider.

[0012] Furthermore, the lateral motion model of the underwater glider established in step 1 is:

[0013]

[0014]

[0015]

[0016]

[0017] Where ψ is the heading angle, ω y is the yaw angular velocity, is the roll angle, ω x is the rolling angular velocity; J yy , J xx is the moment of inertia, λ 55 , 44 is the additional inertia moment; G is the gravity of the underwater glider; y c is the vertical coordinate of the underwater glider's center of gravity, x c is the longitudinal coordinate of the underwater glider's center of gravity, z c is the lateral coordinate of the underwater glider’s center of gravity; S and L represent the cross-sectional area and total length of the underwater glider; and is the hydrodynamic coefficient, β is the sideslip angle, δ d is the differential rudder angle, which is the actual control input.

[0018] Furthermore, in step 1, the established underwater glider lateral motion model is standardized into a high-order nonlinear model with a strict feedback form

[0019]

[0020]

[0021]

[0022]

[0023] Where g1=(J yy +λ 55 ) -1 Gx c and is the unknown control gain function;

[0024]

[0025] as well as

[0026]

[0027] is the model uncertainty term.

[0028] Furthermore, in step 3, the yaw rate, roll angle, intermediate virtual control law of the roll rate and the actual control law of the differential rudder are specifically:

[0029]

[0030]

[0031]

[0032]

[0033] Among them, α1 is the virtual control law of yaw angular velocity, α2 is the virtual control law of roll angle, α3 is the virtual control law of roll angular velocity, u(t) is the differential rudder control command signal; z1 = x1-x d is the heading angle tracking error, z2=x2-β1 is the yaw angular velocity tracking error, z3=x3-β2 is the roll angle tracking error, and z4=x4-β3 is the roll angular velocity tracking error; is an adaptive parameter, Φ is a robust adaptive damping term; β1, β2, β3 are the first-order filter outputs of the virtual control law; k1, k2, k3, k4 and κ are positive adjustment parameters.

[0034] Furthermore, in step 3, the dynamic surface technology is used to calculate the filtered output of the virtual control law:

[0035]

[0036]

[0037]

[0038] Where τ1, τ2 and τ3 are the time constants of the first-order filter.

[0039] Furthermore, in step 3, the adaptive parameters The adaptive law is:

[0040]

[0041] γ and σ are adjustment parameters greater than 0; Φ is the robust adaptive damping term, and its specific expression is:

[0042]

[0043] For Z = [z2,z4,x2,x3,x4,v] T is the basis function vector of the input radial basis neural network.

[0044] Furthermore, in step 4, the basis for judging whether the heading error has reached stability is:

[0045] The time during which the heading error remains within plus or minus 3° is defined as the stabilization time. If the stabilization time t st If it is greater than 15 seconds, the heading error is considered to be stable.

[0046] Furthermore, in step 4, the event triggering condition refers to a condition derived from the stability of the closed-loop system and using the difference between the command signal and the actuator signal to determine whether to perform control.

[0047] Furthermore, in step 4, the condition for stopping the heading control and powering off the servo is that the heading error is stable and does not meet the event triggering condition, that is, there is:

[0048] t st >15&&|e(t)|<λ|z1(t)|+m t

[0049] The condition for starting to control the heading is set to the event trigger condition being met, that is:

[0050]

[0051] t k+1 = inf{t>t k ||e(t)|≥λ|z1(t)|+m t}

[0052] Among them, λ and m t The event trigger adjustment parameter is greater than 0; at t k ≤t<t k+1 In the time interval, δ d (t) is not updated, u(t) will not be transmitted to the differential rudder; once the event trigger condition is met, δ d(t) is immediately updated to u(t); even if the heading deviation is less than 3° after the event triggering condition is met, the stabilization time calculation is still performed again.

[0053] Beneficial Effects

[0054] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0055] 1. The event trigger strategy is used to effectively reduce the power supply time of the servo, reduce the number of actuator actions, save control system energy, and reduce actuator wear.

[0056] 2. It does not rely on accurate mathematical models, but uses robust adaptive technology to compensate for model uncertainties and external disturbances. The controller has good robustness and adaptability.

[0057] 3. Dynamic surface technology is used to avoid repeated derivation of virtual control laws in backstepping design, reducing the calculation complexity of the control law.

[0058] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0060] Figure 1 It is a flow chart of the method of the present invention.

[0061] Figure 2 This is the logic diagram of the event triggering strategy of the present invention

[0062] Figure 3 It is the heading angle control effect curve.

[0063] Figure 4 is the differential rudder angle input curve.

[0064] Figure 5 It is the horizontal plane motion trajectory of the underwater glider under heading angle tracking control. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] In this embodiment, the given heading angle command signal is ψ d =135°, the specific method for robust adaptive control of the heading angle of an underwater glider based on an event-triggered strategy comprises the following steps:

[0067] Step 1: Establish a mathematical model of the lateral motion of the underwater glider, including the state equations of heading angle, yaw angular velocity, roll angle, and roll angular velocity, and standardize the obtained motion mathematical model into a strict feedback system form.

[0068]

[0069]

[0070]

[0071]

[0072] Where ψ is the heading angle, ω y is the yaw angular velocity, is the roll angle, ω x is the rolling angular velocity. yy , J xx is the moment of inertia, λ 55 , 44 is the additional inertia moment. G is the gravity on the glider. c is the vertical coordinate of the glider's center of gravity, x c is the longitudinal coordinate of the glider's center of gravity, z c is the transverse coordinate of the glider's center of gravity. S and L represent the cross-sectional area and total length of the glider. and is the hydrodynamic coefficient, β is the sideslip angle, δ d is the differential rudder angle, which is the actual control input.

[0073] The standardized mathematical model with strict feedback system form is:

[0074]

[0075] in, and is the unknown control gain function.

[0076] as well as is the model uncertainty term.

[0077] Step 2: Continuously collect the underwater glider state variables, including heading angle, yaw angular velocity, roll angle, roll angular velocity and longitudinal velocity.

[0078] Step 3: Calculate the yaw rate, roll angle, intermediate virtual control law of roll rate and actual control law of differential rudder according to the collected state variables.

[0079] Specifically, the design of virtual control law and actual control law includes the following steps:

[0080] Step 1: Calculate the virtual control law of heading deviation and yaw rate according to the heading instruction:

[0081] z1=ψ-ψ d (2)

[0082]

[0083] k1 is a positive tuning parameter.

[0084] Calculate the filtered output of the virtual control law for yaw rate based on dynamic surface technology

[0085]

[0086] τ1 is the time constant of the first-order filter.

[0087] Step 2: Calculate the yaw rate tracking error and roll angle virtual control law based on the filtered virtual control law

[0088] z2=x2-β1 (5)

[0089]

[0090] k2 is a positive tuning parameter.

[0091] Use a sign function to change the direction of the roll angle when switching between up / down gliding.

[0092] Based on the dynamic surface technology, the filtered output of the virtual control law of the roll angle is calculated:

[0093]

[0094] τ2 is the time constant of the first-order filter.

[0095] Step 3: Calculate the roll angle tracking error and roll angular velocity virtual control law based on the filtered virtual control law

[0096] z3=x3-β2 (8)

[0097]

[0098] k3 is a positive adjustment parameter.

[0099] Calculate the filtered output of the virtual control law for yaw rate based on dynamic surface technology

[0100]

[0101] τ3 is the time constant of the first-order filter.

[0102] Step 4: According to the filtered virtual control law, calculate the rolling angular velocity tracking error and the actual control law of the differential rudder:

[0103] First calculate the rolling angular velocity tracking error

[0104] z4=x4-β3 (11)

[0105] Defining model composite uncertainties Using an input Z = [z2,z4,x2,x3,x4,v] T The radial basis neural network is used to approximate it and the robust adaptive damping term is calculated as follows

[0106]

[0107]

[0108]

[0109] k4 and κ are positive adjustment parameters, is the adaptive parameter, and Φ is the robust adaptive damping term.

[0110] Step 4: Determine whether the heading error has reached stability, and calculate the difference between the actual control law signal and the actuator current signal, and compare it with the designed event trigger threshold to determine whether the trigger condition is met.

[0111] The time during which the heading error remains within plus or minus 3° is defined as the stabilization time. If the stabilization time t st If it is greater than 15 seconds, the heading error is considered to be stable. The condition derived from the stability of the closed-loop system and using the difference between the command signal and the actuator signal to determine whether to control is called the event trigger condition.

[0112] The conditions for stopping heading control and powering off the servo are that the stability conditions are met and the event triggering conditions are not met, that is:

[0113] t st >15&&|e(t)|<λ|z1(t)|+m t

[0114] The condition for starting to control the heading is set to the event trigger condition being met, that is:

[0115]

[0116] t k+1 = inf{t>t k ||e(t)|≥λ|z1(t)|+m t}

[0117] Among them, λ and m t is an event trigger adjustment parameter greater than 0. Obviously, at t k ≤t<t k+1 In the time interval, δ d (t) is not updated, and u(t) is not sent to the executor. Once the event triggering condition is met, δ d (t) will be updated to u(t) immediately. Even if the heading deviation is less than 3° after the event trigger condition is met, the stabilization time calculation should still be performed again.

[0118] Step 5: Based on the above judgment, the servo generates a corresponding differential rudder angle according to the new control signal, or maintains the current state unchanged to complete the control of the glider's heading angle.

[0119] The logical structure of the control algorithm proposed by the present invention is as follows: Figure 1 As shown in the figure, the logic diagram of the event trigger condition is as follows Figure 2 shown.

[0120] Taking a certain type of underwater glider as the controlled object, simulation experiments are carried out to verify the effectiveness of the control algorithm proposed in the present invention.

[0121] The simulation time is set to 5200s, the sampling period is 0.01s, and the Euler method is used for numerical calculation. The glider is expected to dive to a depth of 800m, with an expected pitch angle of 30° and an expected heading angle of 135°. The maximum net buoyancy during ascent / descent is plus or minus 4L. The controller parameters are selected as follows:

[0122]

[0123] In addition, white noise is used to drive the second-order transfer function to simulate unknown environmental disturbances.

[0124] from Figure 3 Judging from the heading control effect shown, the control algorithm designed in this study can achieve stable, accurate and fast control effects in the presence of model uncertainty and external interference in the glider. When the event trigger strategy is used, the heading error can be controlled within plus or minus 5°. From the perspective of the horizontal motion trajectory, the heading deviation caused by the event trigger strategy has little effect on the glider's tracking task. This is because the glider itself has a slow navigation speed, and the heading deviation within a certain range will not cause a huge track deviation. Figure 4It can be seen from the differential rudder angle output curve that the differential rudder angle output is step-shaped and remains unchanged within the trigger interval. The event trigger strategy greatly reduces the action frequency of the servo and reduces the control number limit. The servo can be powered off during the trigger interval, thereby reducing the energy consumption of the heading control system and the wear of the actuator. If the trigger interval greater than 80 seconds is defined as the effective power-off time, the total effective power-off time exceeds 3810 seconds, indicating that the power-off time within a profile exceeds 71%. Figure 5 It shows that the maximum event trigger interval exceeds 450 seconds, and the energy saving effect is obvious. Since the system is essentially in an open-loop control state during the event trigger interval, a slightly larger control input is required to reduce the deviation after the event is triggered, but it can be seen that the control input amplitude is still reasonable.

[0125] The event-triggered robust adaptive controller designed in the present invention effectively reduces the actuator action frequency while ensuring the heading control effect, thereby reducing the energy consumption of the control system, which is conducive to realizing energy-saving gliding control of the underwater glider.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for robust adaptive control of heading angle of underwater glider based on event triggering strategy, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the lateral motion of the underwater glider, including the state equations of heading angle, yaw angular velocity, roll angle and roll angular velocity; Step 2: Continuously collect the underwater glider state variables, including heading angle, yaw angular velocity, roll angle, roll angular velocity and longitudinal velocity; Step 3: Calculate the yaw rate, roll angle, intermediate virtual control law of roll rate and actual control law of differential rudder according to the collected state variables; In step 3, the intermediate virtual control law of the yaw rate, the roll angle, the roll rate and the actual control law of the differential rudder are specifically: Among them, α1 is the virtual control law of yaw angular velocity, α2 is the virtual control law of roll angle, α3 is the virtual control law of roll angular velocity, u(t) is the differential rudder control command signal; z1 = x1-x d is the heading angle tracking error, z2=x2-β1 is the yaw angular velocity tracking error, z3=x3-β2 is the roll angle tracking error, and z4=x4-β3 is the roll angular velocity tracking error; is an adaptive parameter, Φ is a robust adaptive damping term; β1, β2, β3 are the first-order filter outputs of the virtual control law; k1, k2, k3, k4 and κ are positive adjustment parameters; Step 4: Determine whether the heading error has reached stability, and calculate the difference between the actual control law signal and the current signal of the differential rudder, and compare it with the designed event trigger threshold to determine whether the event trigger condition is met; If the heading error is stable and does not meet the event triggering condition, the differential rudder signal remains unchanged and the differential rudder servo is powered off. If the event triggering condition is violated, the differential rudder signal is updated, the differential rudder servo is powered on, and the control signal is transmitted from the controller to the differential rudder servo; Step 5: The differential rudder generates a corresponding differential rudder angle according to the judgment result of step 4 and the new control signal, or maintains the current state unchanged to complete the control of the heading angle of the underwater glider.

2. The method for robust adaptive control of heading angle of underwater glider based on event-triggered strategy according to claim 1, characterized in that: The lateral motion model of the underwater glider established in step 1 is: Where ψ is the heading angle, ω y is the yaw angular velocity, is the roll angle, ω x is the rolling angular velocity; J yy , J xx is the moment of inertia, λ 55 , 44 is the additional inertia moment; G is the gravity of the underwater glider; y c is the vertical coordinate of the underwater glider's center of gravity, x c is the longitudinal coordinate of the underwater glider’s center of gravity, z c is the lateral coordinate of the underwater glider’s center of gravity; S and L represent the cross-sectional area and total length of the underwater glider; and is the hydrodynamic coefficient, β is the sideslip angle, δ d is the differential rudder angle, which is the actual control input.

3. The method for robust adaptive control of heading angle of underwater glider based on event-triggered strategy according to claim 2, characterized in that: In step 1, the established underwater glider lateral motion model is standardized into a high-order nonlinear model with a strict feedback form Where g1=(J yy +λ 55 ) -1 Gx c and is the unknown control gain function; as well as is the model uncertainty term.

4. The method for robust adaptive control of heading angle of underwater glider based on event-triggered strategy according to claim 3, characterized in that: In step 3, the dynamic surface technique is used to calculate the filtered output of the virtual control law: Among them, τ1, τ2 and τ3 are the time constants of the first-order filter.

5. The method for robust adaptive control of heading angle of underwater glider based on event-triggered strategy according to claim 3, characterized in that: In step 3, the adaptive law of the adaptive parameter is: γ and σ are adjustment parameters greater than 0; Φ is the robust adaptive damping term, and its specific expression is: For Z = [z2,z4,x2,x3,x4,v] T is the basis function vector of the input radial basis neural network.

6. The method for robust adaptive control of heading angle of underwater glider based on event-triggered strategy according to claim 1, characterized in that: In step 4, the basis for judging whether the heading error has reached stability is: The time during which the heading error remains within plus or minus 3° is defined as the stabilization time. If the stabilization time t st If it is greater than 15 seconds, the heading error is considered to be stable.

7. The method for robust adaptive control of heading angle of underwater glider based on event triggering strategy according to claim 6, characterized in that: In step 4, the event triggering condition refers to a condition derived from the stability of the closed-loop system and using the difference between the command signal and the actuator signal to determine whether to perform control.

8. The method for robust adaptive control of heading angle of underwater glider based on event triggering strategy according to claim 7, characterized in that: In step 4, the heading control is stopped and the servo is powered off when the heading error is stable and the event triggering condition is not met, that is, t st >15&&|e(t)|<λ|z1(t)|+m t The condition for starting to control the heading is set to the event trigger condition being met, that is: t k+1 =inf{t>t k ||e(t)≥λ|z1(t)|+m t } Among them, λ and m t The event trigger adjustment parameter is greater than 0; at t k ≤t<t k+1 In the time interval, δ d (t) is not updated, u(t) will not be transmitted to the differential rudder; once the event trigger condition is met, δ d (t) will be updated to u(t) immediately; even if the heading deviation is less than 3° after the event triggering condition is met, the stabilization time calculation should still be performed again.

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