Self-adaptive reverse clearance active boundary control method for marine flexible riser

Abstract

The invention discloses a self-adaptive reverse clearance active boundary control method for a marine flexible riser, and relates to the field of marine oil and gas development, and the method comprises the following steps: obtaining a control equation of a marine flexible riser system, and determining boundary conditions of the marine flexible riser system; updating boundary conditions; a barrier Lyapunov function is constructed; proposing a designed expected vibration control strategy, and designing an adaptive law based on the expected vibration control strategy; verifying that the system stability is bounded based on a barrier Lyapunov function; and acquiring the actual vibration offset of the marine flexible riser system, substituting the actual vibration offset into the adaptive law to obtain actual control output, and applying a control acting force to the top end of the marine flexible riser. The method is used for solving the problem that in the prior art, input nonlinearity caused by an input gap cannot be overcome in the control process of the marine flexible riser, the defect of an unknown input gap is overcome, and the purpose of compensating the input nonlinearity through a self-adaptive reverse gap algorithm is achieved.

Description

Technical Field

[0001] The invention relates to the field of marine oil and gas development, and in particular to an adaptive reverse clearance active boundary control method for marine flexible risers. Background Art

[0002] Marine flexible risers are important equipment that connects underwater oil wells with oil and gas gathering and transportation ships and production platforms on the sea surface. They are called the "lifeline" connecting offshore platforms and wellheads. Due to the harsh operating environment, marine flexible risers are affected by various environmental loads in the ocean and their own elastic properties, causing riser deformation and vibration, affecting the performance of production risers, and leading to fatigue failure. In severe cases, it may even cause oil and gas leakage, causing irreversible damage to the marine environment.

[0003] The internal fluid of the marine flexible riser and external environmental factors such as ocean current wave force, sea breeze, top tension, offshore platform drift, and the material of the riser itself can cause vibration of the flexible riser. If the vibration frequency is close to the frequency of the external load, resonance may occur. Excessive vibration can cause fatigue problems caused by cyclic loads, wear damage, crack propagation, and even damage to the upper and lower joints. Therefore, it is very necessary to conduct theoretical research on vibration control of marine flexible risers.

[0004] Active boundary control is an effective vibration suppression method. Compared with passive control, active control is easy to implement in practical applications and has better effects. Therefore, it is widely used in actual production and life. On the other hand, in actual systems, input nonlinearity is common in system structures or actuators, such as input gaps, which weaken the accuracy and sensitivity of control and even cause system instability. In the prior art, such as the applicant's prior applications "A multi-constraint adaptive control method for marine flexible risers" (CN114895570B) and "Marine flexible riser boundary vibration control method for model uncertainty" (CN114442481B), etc., are unable to overcome the input nonlinearity problem caused by input gaps. Summary of the invention

[0005] The object of the present invention is to provide an adaptive reverse clearance active boundary control method for marine flexible risers, so as to solve the problem of input nonlinearity caused by input clearance that cannot be overcome in the prior art during the control process of marine flexible risers, and to achieve the purpose of overcoming the defect of unknown input clearance and compensating input nonlinearity through an adaptive reverse clearance algorithm.

[0006] The present invention is achieved through the following technical solutions:

[0007] Model the marine flexible riser, conduct dynamic analysis, obtain the control equation of the marine flexible riser system, and determine the boundary conditions of the marine flexible riser system;

[0008] updating the boundary condition based on the nonlinear input gap;

[0009] Construct barrier Lyapunov functions;

[0010] The desired vibration control strategy is proposed, and the fuzzy logic system and adaptive law are designed based on the desired vibration control strategy; the system is verified to be stable and bounded based on the barrier Lyapunov function;

[0011] The actual vibration offset of the marine flexible riser system is obtained, the actual vibration offset is substituted into the adaptive law to obtain the actual control output, and the control force is applied to the top of the marine flexible riser.

[0012] During the research process, the applicant found that in the actual system of marine flexible risers, input nonlinearity represented by input gap is commonly present in the system structure or actuator, which will weaken the accuracy and sensitivity of control and even cause system instability; based on this, the present application proposes an adaptive reverse gap active boundary control method for marine flexible risers.

[0013] The present application first establishes a flexible riser model, obtains the control equation of the entire system based on dynamic analysis, and determines its boundary conditions; then introduces a nonlinear input gap, updates the boundary conditions of the model, and obtains updated boundary conditions; then constructs an obstacle Lyapunov function based on the updated boundary conditions; then proposes the designed expected vibration control strategy, and designs an adaptive law based on the expected vibration control strategy. After verifying that the system is stable and bounded, the adaptive law can be used as a basis to actually control the flexible riser of the offshore drilling and production platform.

[0014] The present application introduces a nonlinear input gap update boundary condition and designs a subsequent adaptive algorithm, which can overcome the problems of reduced system accuracy, sensitivity and control instability caused by input nonlinearity in the prior art, and can actively compensate for input nonlinearity in the active control process of the marine flexible riser, thereby improving control stability, sensitivity and accuracy.

[0015] Furthermore, the control equation of the marine flexible riser system is:

[0016]

[0017] The boundary conditions of the marine flexible riser system are:

[0018] u(0,t)=v(0,t)=w(0,t)=0

[0019] u′(0,t)=v′(0,t)=w′(0,t)=0

[0020] u″(l,t)=v″(l,t)=w″(l,t)=0

[0021]

[0022] Where: ρ is the unit riser mass; t is the time variable; s is the space variable; L is the riser length; is the second-order partial derivative of u(s,t) with respect to t; is the first-order partial derivative of u(s,t) with respect to t; u(s,t) is the actual displacement of vibration in the x direction; is the second-order partial derivative of v(s,t) with respect to t; is the first-order partial derivative of v(s,t) with respect to t; v(s,t) is the actual displacement of vibration in the y direction; is the second-order partial derivative of w(s,t) with respect to t; is the first-order partial derivative of w(s, t) with respect to t; w(s, t) is the actual displacement of vibration in the z direction; EI is the riser bending stiffness; c is the structural damping coefficient; T is the riser tension; M is the ship mass; EA is the axial bending stiffness; d s is the ship damping coefficient; u″″(s,t) is the fourth-order partial derivative of u(s,t) with respect to s; u″(s,t) is the second-order partial derivative of u(s,t) with respect to s; u′(s,t) is the first-order partial derivative of u(s,t) with respect to s; v″″(s,t) is the fourth-order partial derivative of v(s,t) with respect to s; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s; v′(s,t) is the first-order partial derivative of v(s,t) with respect to s; w″(s,t) is the second-order partial derivative of w(s,t) with respect to s; w′(s,t) is the first-order partial derivative of w(s,t) with respect to s; f x is the distributed current load acting on the riser in the x direction; f y is the distributed current load acting on the riser in the y direction; f z is the distributed current load acting on the riser in the z direction; u(0,t) is the value of u(s,t) when s=0; u′(0,t) is the first-order partial derivative of u(s,t) with respect to s when s=0; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; v(0,t) is the value of v(s,t) when s=0; v′(0,t) is the first-order partial derivative of v(s,t) with respect to s when v=0; v″(L,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; w(0,t) is the value of w(s,t) when s=0; w′(0,t) is the first-order partial derivative of w(s,t) with respect to s when s=0; d x is the boundary disturbance in the x direction; d y is the boundary disturbance in the y direction; d z is the boundary disturbance in the z direction; U xis the boundary control quantity at the top of the riser acting in the x direction; U y is the boundary control quantity at the top of the riser acting in the y direction; U z is the boundary control quantity at the top of the riser acting in the z direction.

[0023] The existing control equations and boundary conditions only consider a one-dimensional model, that is, vibration only in the x-direction. However, in actual situations, the riser in the ocean not only vibrates in the x-direction, but may also vibrate in the y and z directions. Therefore, the control equations and boundary conditions of this patent are more comprehensive and more in line with actual application scenarios.

[0024] Further, the method for updating the boundary condition based on the nonlinear input gap includes:

[0025] Determine an input gap expression that includes a nonlinear input gap;

[0026] Based on the backlash dynamics, an adaptive backlash algorithm is designed;

[0027] Update boundary conditions.

[0028] Furthermore, the input gap expression is:

[0029]

[0030] Where: A(p(t)) is the nonlinear input gap; m is the constant slope of the input gap; b is the input gap spacing of unknown width; U(t) is the actual gap boundary control input; p(t) is the gap input variable; is the value of the first derivative of p(t) with respect to the time variable t.

[0031] Furthermore, the designed adaptive backlash algorithm is:

[0032] U x (t) = m x U x ′(t)+b x sign(ΔU x (t)+f x )+U x eq(t)+U x sw(t)

[0033] U y (t) = m y U y ′(t)+b y sign(ΔU y (t)+f y )+U y eq(t)+U y sw(t)

[0034] U z (t) = m z U z ′(t)+b z sign(ΔU z (t)+f z )+U z eq(t)+U z sw(t)

[0035] In the formula, m x is the unknown slope of the input gap in the x direction; m y Enter the unknown slope of the gap in the y direction; m z is the unknown slope of the input gap in the z direction; b x is the input gap spacing of unknown width in the x direction; b y is the input gap spacing of unknown width in the y direction; b z is the input gap spacing of unknown width in the z direction; U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; U x (t) is the actual boundary control in the x direction; U y (t) is the actual boundary control in the y direction; U z (t) is the actual boundary control in the z direction; U x eq(t) is the equivalent control in the x direction; U y eq(t) is the equivalent control in the y direction; U z eq(t) is the equivalent control in the z direction, U x sw(t) is the switching control in the x direction; U y sw(t) is the switching control in the y direction; U z sw(t) is the switching control in the z direction;

[0036] ΔU x (t) = U x (t)-U x (t-Δt), is the actual change of boundary control in the x direction;

[0037] ΔU y (t) = U y (t)-U y (t-Δt), is the actual change of boundary control in the y direction;

[0038] ΔU z (t) = U z(t)-U z (t-Δt), is the actual change of boundary control in the z direction;

[0039] Δt is the unit time variable.

[0040] This solution is based on reverse gap dynamics to deal with the impact of nonlinear input gap on the system. This solution adds equivalent control and switching control based on synovial control to gap processing, which not only simplifies the design and analysis process of the controller, but also has high reliability and long-term stability. It can also respond quickly to the dynamics of the offshore flexible riser. At the same time, the synovial control provides smooth and predictable motion characteristics, which can avoid the oscillation or vibration problems that may occur in traditional control. Fuzzy adaptation is used for uncertain parameters in the gap. Compared with traditional adaptation, the linguistic fuzzy information provided by the on-site operator can be used for adaptation. The fuzzy adaptive method can effectively combine this information and transform the fuzzy subjective cognition into a form that the system can handle, thereby providing a more accurate and practical control strategy.

[0041] Among them, the equivalent control and switching control in each direction are specifically implemented by the following formula:

[0042]

[0043] U x sw(t)=-k1·sign(μ x )

[0044] U y sw(t)=-k2·sign(μ y )

[0045] U z sw(t)=-k3·sign(μ z )

[0046] Where γ1, γ2, and γ3 are equivalent control gain coefficients; k1, k2, and k3 are switching control gain coefficients; u″(L, t) is the second-order partial derivative of u(s, t) with respect to s when s=L; v″(L, t) is the second-order partial derivative of v(s, t) with respect to s when s=L; w″(L, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; μ x is the sliding film control in the x direction; μ y is the sliding mode control in the y direction; μ z It is the sliding mode control in z direction.

[0047] The present invention adds equivalent control and switching control based on sliding film control to gap processing, which not only simplifies the design and analysis process of the controller and has high reliability and long-term stability; but also can perform rapid dynamic response to the marine flexible riser. At the same time, the sliding film control provides smooth and predictable motion characteristics, which can avoid the oscillation or vibration problems that may occur in traditional control.

[0048] Furthermore, the sliding mode control in each direction is implemented using the following strategy:

[0049]

[0050] In the formula, e x (t) is the difference between the expected displacement and the actual displacement in the x direction; e y (t) is the difference between the expected displacement and the actual displacement in the y direction; e z (t) is the difference between the expected displacement and the actual displacement in the z direction; for e x The first-order partial derivative of (t) with respect to t; for e y The first-order partial derivative of (t) with respect to t;

[0051] for e z The first-order partial derivative of (t) with respect to t; λ x , y , z is a constant coefficient;

[0052] The updated boundary conditions are:

[0053] u(0,t)=v(0,t)=w(0,t)=0

[0054] u′(0,t)=v′(0,t)=w′(0,t)=0

[0055] u″(L,t)=v″(L,t)=w″(L,t)=0

[0056]

[0057] This scheme adopts fuzzy adaptation for uncertain parameters. Compared with traditional adaptation, it can use the linguistic fuzzy information provided by the on-site operators for adaptation. The fuzzy adaptive method can effectively combine this information and transform the fuzzy subjective cognition into a form that the system can handle, thereby providing a more accurate and practical control strategy. At the same time, in the adaptation of disturbance interference, the three-direction disturbance error adaptation law is considered, and the projection mapping operator is added. The projection mapping operator can limit the update range of the parameters, ensure that the estimated parameters converge to a reasonable value, and avoid instability in the parameter estimation process or exceed the feasible range.

[0058] Furthermore, the fuzzy logic system designed based on the desired vibration control strategy is:

[0059]

[0060]

[0061] In the formula, ζ x is the first adaptive fuzzy logic system; y is the second adaptive fuzzy logic system; z is the third adaptive fuzzy logic system; is the fourth adaptive fuzzy logic system; is the fifth adaptive fuzzy logic system; is the sixth adaptive fuzzy logic system; is the first fuzzy basis vector; is the second fuzzy basis vector; is the third fuzzy basis vector; is the fourth fuzzy basis vector; is the fifth fuzzy basis vector; is the sixth fuzzy basis vector; for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of

[0062] Furthermore, the adaptive law designed based on the desired vibration control strategy is:

[0063]

[0064]

[0065] Where: is m x The value of the first derivative with respect to t; is m y The value of the first derivative with respect to t; is m z The value of the first derivative with respect to t; for b x The value of the first derivative with respect to t; for b y The value of the first derivative with respect to t; for bz The value of the first-order derivative with respect to t; β3 is the weight value of the adaptive law; for The value of the first derivative with respect to t; for The value of the first derivative with respect to t; for The value of the first-order derivative with respect to t; Proj m is the projection mapping operator; k 1u , k 2v , k 3w is the disturbance weight value; U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; is the first-order partial derivative of u(s,t) with respect to t when s=L; u′(L,t) is the first-order partial derivative of u(s,t) with respect to s when s=L; is the second-order partial derivative of u(s,t) with respect to t when s=L; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; is the first-order partial derivative of v(s,t) with respect to t when s=L; v′(L,t) is the first-order partial derivative of v(s,t) with respect to s when s=L; is the second-order partial derivative of v(s,t) with respect to t when s=L; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; is the first-order partial derivative of w(s,t) with respect to t when s=L; w′(L,t) is the first-order partial derivative of w(s,t) with respect to s when s=L; is the second-order partial derivative of w(s, t) with respect to t when s=L; w″(s, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; β2 is the desired control gain coefficient; is d x An estimated value of is d y An estimated value of is d z The estimated value of .

[0066] Furthermore, the barrier Lyapunov function is constructed as: V(t)=V1(t)+V2(t)+V3(t)+V4(t); where:

[0067]

[0068] Where: V(t) is the barrier Lyapunov function; V1(t) is the energy term, V2(t) is the cross term, V3(t) is the auxiliary term, and V4(t) is the adaptive term; β1 is a positive constant based on the system energy term; kb1 Output constraint boundary value for x direction; k b2 Output constraint boundary value for the y direction; k b3 Output constraint boundary value for z direction; is m x The error estimate of is m y The error estimate of is m z The error estimate of for b x The error estimate of for b y The error estimate of for b z The error estimate of is d x The error estimate of is d y The error estimate of is d z The error estimate of .

[0069] This version of the barrier Lyapunov function takes into account a larger number of state variables, each of which may be subject to different constraints. This version of the barrier Lyapunov function needs to consider how to effectively handle the constraints on state variables in the X, Y, and Z directions to ensure system stability. It also considers the mutual constraints or restrictions between different state variables in the X, Y, and Z directions.

[0070] Furthermore, the barrier Lyapunov function satisfies the following conditions:

[0071] 0≤ω1(V1(t)+V3(t)+V4(t))≤V(t)≤ω2(V1(t)+V3(t)+V4(t))

[0072] Where: The value is and Is a normal number.

[0073] Furthermore, the desired vibration control strategy is:

[0074]

[0075] Where: U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; is the first-order partial derivative of u(s,t) with respect to t when s=L; u′(L,t) is the first-order partial derivative of u(s,t) with respect to s when s=L; is the second-order partial derivative of u(s,t) with respect to t when s=L; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; is the first-order partial derivative of v(s,t) with respect to t when s=L; v′(L,t) is the first-order partial derivative of v(s,t) with respect to s when s=L; is the second-order partial derivative of v(s,t) with respect to t when s=L; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; is the first-order partial derivative of w(s,t) with respect to t when s=L; w′(L,t) is the first-order partial derivative of w(s,t) with respect to s when s=L; is the second-order partial derivative of w(s, t) with respect to t when s=L; w″(s, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; β2 is the desired control gain coefficient.

[0076] Furthermore, the disturbance interference adaptive law is:

[0077]

[0078] Where: for The value of the first derivative with respect to t; for The value of the first derivative with respect to t; for The value of the first-order derivative with respect to t; Proj m is the projection mapping operator; k 1u , k 2v , k 3w is the disturbance weight value.

[0079] In this scheme, considering that the marine flexible riser system is affected by unknown external disturbances, the adaptive law can be used to estimate the upper bound of the disturbance, which is convenient for designing an active vibration control strategy combined with the adaptive law to achieve vibration suppression of the flexible riser affected by boundary disturbances.

[0080] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0081] 1. The present invention provides an adaptive reverse clearance active boundary control method for marine flexible risers. The influence of unknown input clearance is taken into account, nonlinear input clearance update boundary conditions are introduced, and a subsequent adaptive algorithm is designed. The problems of reduced system accuracy, reduced sensitivity, and unstable control caused by input nonlinearity in the prior art can be overcome, and input nonlinearity can be actively compensated in the active control process of marine flexible risers, thereby improving the control stability, sensitivity, and accuracy.

[0082] 2. The present invention provides an adaptive reverse clearance active boundary control method for marine flexible risers, which takes into account the influence of unknown external disturbances, limits the output constraints, and proposes an obstacle Lyapunov function related to the constraint conditions, thereby ensuring that the displacement remains within a given range while achieving vibration suppression.

[0083] 3. The present invention provides an adaptive reverse clearance active boundary control method for marine flexible risers, designs an adaptive law to deal with the influence of unknown disturbances, facilitates the design of an active vibration control strategy combined with the adaptive law, and realizes vibration suppression of the flexible riser affected by boundary disturbances.

[0084] 4. The present invention uses a three-dimensional marine flexible riser for control. Compared with the prior art, its model is more complex. The three-dimensional flexible riser can be controlled in three directions (x, y, z axis), while the one-dimensional flexible riser can only be controlled in the x axis. This means that the requirements for marine flexible riser control can be accurately met.

[0085] 5. The present invention adds equivalent control and switching control based on sliding film control to the gap processing, which not only simplifies the design and analysis process of the controller, but also has high reliability and long-term stability. It can also make fast dynamic response to the marine flexible riser. At the same time, the sliding film control provides smooth and predictable motion characteristics, which can avoid the oscillation or vibration problems that may occur in traditional control.

[0086] 6. The present invention adopts fuzzy adaptation for uncertain gap parameters. Compared with traditional adaptation, it can use the language fuzzy information provided by the on-site operator for adaptation. The fuzzy adaptive method can effectively combine this information and convert fuzzy subjective cognition into a form that the system can process, thereby providing a more accurate and practical control strategy.

[0087] 7. In this application, the obstacle Lyapunov function considers a larger number of state variables, and each state variable may be subject to different constraints. Therefore, the obstacle Lyapunov function of this application needs to consider how to effectively handle the constraints of state variables in the X, Y, and Z directions to ensure system stability, rather than just considering the constraints in the X direction. At the same time, the mutual constraints or restrictions between different state variables in the X, Y, and Z directions are also considered.

[0088] 8. In the adaptation to disturbance interference, the adaptive law of disturbance error in three directions is considered, and a projection mapping operator is added. The projection mapping operator can limit the update range of parameters, ensure that the estimated parameters converge to reasonable values, and avoid instability in the parameter estimation process or exceeding the feasible range. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0090] Figure 1 It is a schematic diagram of a flow chart of a specific embodiment of the present invention;

[0091] Figure 2 It is a schematic diagram of a marine flexible riser in a specific embodiment of the present invention;

[0092] Figure 3 Schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the x direction without applying control in a specific embodiment of the present invention

[0093] Figure 4 Schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the y direction without applying control in a specific embodiment of the present invention

[0094] Figure 5 Schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the z direction without applying control in a specific embodiment of the present invention

[0095] Figure 6 It is a schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the x direction after control is applied in a specific embodiment of the present invention;

[0096] Figure 7 It is a schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the y direction after control is applied in a specific embodiment of the present invention;

[0097] Figure 8 It is a schematic diagram of the three-dimensional vibration offset of the marine flexible riser in the z direction after control is applied in a specific embodiment of the present invention;

[0098] Fig. 9 It is a schematic diagram of the comparison of the vibration offset amplitude of the marine flexible riser at 500m in the x direction in a specific embodiment of the present invention;

[0099] Fig.10 It is a schematic diagram of the comparison of the vibration offset amplitude of the marine flexible riser at 500m in the y direction in a specific embodiment of the present invention;

[0100] Fig.11It is a schematic diagram of the comparison of vibration offset amplitudes of the marine flexible riser at 500m in the z direction in a specific embodiment of the present invention;

[0101] Fig.12 It is a schematic diagram of the comparison of the vibration offset amplitude of the marine flexible riser at 1000m in the x direction in a specific embodiment of the present invention;

[0102] Fig.13 It is a schematic diagram of the comparison of the vibration offset amplitude of the marine flexible riser at 1000m in the y direction in a specific embodiment of the present invention;

[0103] Fig.14 It is a schematic diagram of the comparison of vibration offset amplitudes of the marine flexible riser at 1000m in the z direction in a specific embodiment of the present invention; DETAILED DESCRIPTION

[0104] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0105] Embodiment 1:

[0106] like Figure 1 An adaptive backlash active boundary control method for a marine flexible riser is shown, comprising the following steps:

[0107] Model the marine flexible riser, conduct dynamic analysis, obtain the control equation of the marine flexible riser system, and determine the boundary conditions of the marine flexible riser system;

[0108] updating the boundary condition based on the nonlinear input gap;

[0109] Construct barrier Lyapunov functions;

[0110] The desired vibration control strategy is proposed, and the adaptive law is designed based on the desired vibration control strategy; the system is verified to be stable and bounded based on the barrier Lyapunov function;

[0111] The actual vibration offset of the marine flexible riser system is obtained, the actual vibration offset is substituted into the adaptive law to obtain an actual control input, and according to the actual control output, the actuator is driven to apply a control force to the marine flexible riser, wherein the actuator is located at the top of the flexible riser.

[0112] Preferably, the actual vibration offset of the marine flexible riser system is obtained by measuring the values ​​u(s, t), v(s, t), w(s, t) of the actual vibration offset signal of the flexible riser at time t and then using a backward difference method.

[0113] Embodiment 2:

[0114] An adaptive backlash active boundary control method for marine flexible riser, a marine flexible riser system such as Figure 2 As shown, Figure 2 The dotted arrows in the figure represent the distributed currents, f(x, t) is the distributed current load acting on the riser, the origin of the coordinate system is located at the bottom of the riser, and the controller is located at the top (boundary) of the riser for control input to generate lateral force to suppress the vibration of the flexible riser.

[0115] The control process of this embodiment includes:

[0116] Step 1: Based on the Hamilton principle, the control equation of the flexible riser system is obtained as follows:

[0117]

[0118] The boundary conditions of the marine flexible riser system are:

[0119] u(0,t)=v(0,t)=w(0,t)=0

[0120] u′(0,t)=v′(0,t)=w′(0,t)=0

[0121] u″(l,t)=v″(l,t)=w″(l,t)=0

[0122]

[0123] Where: ρ is the unit riser mass; t is the time variable; s is the space variable; L is the riser length; is the second-order partial derivative of u(s,t) with respect to t; is the first-order partial derivative of u(s,t) with respect to t; u(s,t) is the actual displacement of vibration in the x direction; is the second-order partial derivative of v(s,t) with respect to t; is the first-order partial derivative of v(s,t) with respect to t; v(s,t) is the actual displacement of vibration in the y direction; is the second-order partial derivative of w(s,t) with respect to t; is the first-order partial derivative of w(s, t) with respect to t; w(s, t) is the actual displacement of vibration in the z direction; EI is the riser bending stiffness; c is the structural damping coefficient; T is the riser tension; M is the ship mass; EA is the axial bending stiffness; d sis the ship damping coefficient; u″″(s,t) is the fourth-order partial derivative of u(s,t) with respect to s; u″(s,t) is the second-order partial derivative of u(s,t) with respect to s; u′(s,t) is the first-order partial derivative of u(s,t) with respect to s; v″″(s,t) is the fourth-order partial derivative of v(s,t) with respect to s; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s; v′(s,t) is the first-order partial derivative of v(s,t) with respect to s; w″(s,t) is the second-order partial derivative of w(s,t) with respect to s; w′(s,t) is the first-order partial derivative of w(s,t) with respect to s; f x is the distributed current load acting on the riser in the x direction; f y is the distributed current load acting on the riser in the y direction; f z is the distributed current load acting on the riser in the z direction; u(0,t) is the value of u(s,t) when s=0; u′(0,t) is the first-order partial derivative of u(s,t) with respect to s when s=0; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; v(0,t) is the value of v(s,t) when s=0; v′(0,t) is the first-order partial derivative of v(s,t) with respect to s when v=0; v″(L,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; w(0,t) is the value of w(s,t) when s=0; w′(0,t) is the first-order partial derivative of w(s,t) with respect to s when s=0; d x is the boundary disturbance in the x direction; d y is the boundary disturbance in the y direction; d z is the boundary disturbance in the z direction; U x is the boundary control quantity at the top of the riser acting in the x direction; U y is the boundary control quantity at the top of the riser acting in the y direction; U z is the boundary control quantity at the top of the riser acting in the z direction.

[0124] Step 2: Update boundary conditions based on nonlinear input gap:

[0125] (1) First, the input gap is processed to obtain an input gap expression including nonlinear input gap.

[0126] (2) Based on the backlash dynamics, the influence of nonlinear input gap on the system is processed and the adaptive backlash algorithm is designed as follows:

[0127] U x (t) = m x U x ′(t)+b x sign(ΔU x (t))+U x eq(t)+U x sw(t)

[0128] U y (t) = m y U y ′(t)+b y sign(ΔU y (t))+U y eq(t)+U y sw(t)

[0129] U z (t) = m z U z ′(t)+b z sign(ΔU z (t))+U z eq(t)+U z sw(t)

[0130] In the formula, m x Enter the unknown slope of the gap in the x direction; m y Enter the unknown slope of the gap in the y direction; m z is the unknown slope of the input gap in the z direction; b x is the input gap spacing of unknown width in the x direction; b y is the input gap spacing of unknown width in the y direction; b z is the input gap spacing of unknown width in the z direction; U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; U x (t) is the actual boundary control in the x direction; U y (t) is the actual boundary control in the y direction; U z (t) is the actual boundary control in the z direction; U x eq(t) is the equivalent control in the x direction; U y eq(t) is the equivalent control in the y direction; U z eq(t) is the equivalent control in the z direction, U x sw(t) is the switching control in the x direction; U y sw(t) is the switching control in the y direction; U z sw(t) is the switching control in the z direction;

[0131] ΔU x (t) = U x (t)-U x (t-Δt), is the actual change of boundary control in the x direction;

[0132] ΔU y (t) = U y (t)-U y (t-Δt), is the actual change of boundary control in the y direction;

[0133] ΔU z (t) = U z (t)-U z (t-Δt), is the actual change of boundary control in the z direction;

[0134] Δt is the unit time variable.

[0135] Among them, equivalent control and switching control are realized by the following formula:

[0136]

[0137] U x sw(t)=-k1·sign(μ x )

[0138] U y sw(t)=-k2·sign(μ y )

[0139] U z sw(t)=-k3·sign(μ z )

[0140] Where γ1, γ2, and γ3 are equivalent control gain coefficients; k1, k2, and k3 are switching control gain coefficients; u″(L, t) is the second-order partial derivative of u(s, t) with respect to s when s=L; v″(L, t) is the second-order partial derivative of v(s, t) with respect to s when s=L; w″(L, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; μ x is the sliding film control in the x direction; μ y is the sliding mode control in the y direction; μ z It is the sliding mode control in z direction.

[0141] The sliding mode control is implemented using the following strategy:

[0142]

[0143] In the formula, e x (t) is the difference between the expected displacement and the actual displacement in the x direction; e y (t) is the difference between the expected displacement and the actual displacement in the y direction; e z (t) is the difference between the expected displacement and the actual displacement in the z direction; for e x The first-order partial derivative of (t) with respect to t; for e y The first-order partial derivative of (t) with respect to t; for e z The first-order partial derivative of (t) with respect to t; λ x ,λ y ,λ z is a constant coefficient;

[0144] (3) Update the boundary conditions to:

[0145] u(0,t)=v(0,t)=w(0,t)=0

[0146] u′(0,t)=v′(0,t)=w′(0,t)=0

[0147] u″(L,t)=v″(L,t)=w″(L,t)=0

[0148]

[0149] Step 3: Construct the barrier Lyapunov function: V(t) = V1(t) + V2(t) + V3(t) + V4(t); where:

[0150]

[0151] Where: V(t) is the barrier Lyapunov function; V1(t) is the energy term, V2(t) is the cross term, V3(t) is the auxiliary term, and V4(t) is the adaptive term; β1 is a positive constant based on the system energy term; k b1 Output constraint boundary value for x direction; k b2 Output constraint boundary value for the y direction; k b3 Output constraint boundary value for z direction; is m x The error estimate of is m y The error estimate of is m z The error estimate of for b x The error estimate of for b y The error estimate of for b z The error estimate of is d x The error estimate of is d y The error estimate of is d z The error estimate of .

[0152] The barrier Lyapunov function used in this embodiment is positive and bounded, that is, there are always constants ω1 and ω2, so that the barrier Lyapunov function satisfies the following inequality:

[0153] 0≤ω1(V1(t)+V3(t)+V4(t))≤V(t)≤ω2(V1(t)+V3(t)+V4(t))

[0154] Where: The value is

[0155] and Is a normal number.

[0156] Step 4: The designed desired vibration control strategy is proposed as follows:

[0157]

[0158] Where: U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; is the first-order partial derivative of u(s,t) with respect to t when s=L; u′(L,t) is the first-order partial derivative of u(s,t) with respect to s when s=L; is the second-order partial derivative of u(s,t) with respect to t when s=L; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; is the first-order partial derivative of v(s,t) with respect to t when s=L; v′(L,t) is the first-order partial derivative of v(s,t) with respect to s when s=L; is the second-order partial derivative of v(s,t) with respect to t when s=L; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; is the first-order partial derivative of w(s,t) with respect to t when s=L; w′(L,t) is the first-order partial derivative of w(s,t) with respect to s when s=L; is the second-order partial derivative of w(s, t) with respect to t when s=L; w″(s, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; β2 is the desired control gain coefficient.

[0159] The desired vibration control strategy based on this embodiment designs the adaptive law as follows:

[0160]

[0161] In the formula, ζ x is the first adaptive fuzzy logic system; yis the second adaptive fuzzy logic system; z is the third adaptive fuzzy logic system; is the first adaptive fuzzy logic system; is the second adaptive fuzzy logic system; is the third adaptive fuzzy logic system; is the fourth adaptive fuzzy logic system; is the fifth adaptive fuzzy logic system; is the sixth adaptive fuzzy logic system; for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of

[0162] The adaptive law designed based on the desired vibration control strategy is:

[0163]

[0164]

[0165] Where: for is the value of the first-order derivative with respect to t; for is the value of the first-order derivative with respect to t; for is the value of the first-order derivative with respect to t; for is the value of the first-order derivative with respect to t; for is the value of the first-order derivative with respect to t; for is the value of the first-order derivative with respect to t; β3 is the weight value.

[0166] Step 5: The disturbance interference adaptive law is:

[0167]

[0168] Where: for The value of the first derivative with respect to t; for The value of the first derivative with respect to t; for The value of the first-order derivative with respect to t; Projm is the projection mapping operator; k 1u , k 2v , k 3w is the disturbance weight value.

[0169] Embodiment 3:

[0170] An adaptive backlash active boundary control method for a marine flexible riser, based on Example 2, a method for verifying that the system is stable and bounded includes:

[0171] Determine whether the following inequality holds:

[0172] In the formula, ε is bounded interference, λ is a constant greater than 0;

[0173] If this inequality holds, it means that the range of the lateral vibration of the flexible riser in this embodiment will never exceed the value on the right side, and the system is considered to be stable and bounded;

[0174] If the inequality does not hold, the system is considered not stable and bounded. At this time, it is necessary to readjust the control parameters according to the actual situation until the system satisfies the requirement of stability and boundedness.

[0175] The control parameters in this embodiment include: γ1, γ2, γ3, k1, k2, k3, λ x , y , z β1, β2, k 1u , k 2v , k 3w This step proposes an effective method to verify the stability of the system in the flexible riser application field, which ensures the stability of the entire flexible riser system when the adaptive backlash active control algorithm is adopted, and provides sufficient guarantee for the subsequent control accuracy.

[0176] Embodiment 4:

[0177] An adaptive reverse clearance active boundary control method for marine flexible risers. Based on Embodiment 2 or 3, this embodiment conducts experimental verification on the control method of the present application. Let k b1 =k b2 =k b3 =0.3, so that the marine flexible riser is stable at [0, 0.3]m in the x, y, and z directions.

[0178] In this embodiment, the control parameters are set as follows: γ1 = 3 × 10 3 γ2=2×10 3 ,γ3=1×10 3 , k1=100, k2=200, k3=300, λ x=0.01,λ y =0.05,λ z =0.1, β1=1×10 -4 β2=1×10 -4 , k 1u =1×10 -3 , k 2v =1×10 -3 , k 3w =1×10 -3 .Other main parameters of offshore flexible riser are shown in the following table:

[0179]

[0180] The experimental results of this embodiment are as follows Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 , Fig.10 , Fig.11 , Fig.12 , Fig.13 and Fig.14 As shown. Those skilled in the art will understand that Figure 3-Figure 14 middle:

[0181] The coordinate axis marked u(x,t) / m is the actual displacement of vibration in the x direction, in meters;

[0182] The coordinate axis marked v(x,t) / m is the actual displacement of vibration in the y direction, in meters;

[0183] The coordinate axis marked w(x,t) / m is the actual displacement of vibration in the z direction, in meters;

[0184] The coordinate axis marked u(l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 1000 meters in the x direction, in meters;

[0185] The coordinate axis marked v(l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 1000 meters in the y direction, in meters;

[0186] The coordinate axis marked w(l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 1000 meters in the z direction, in meters;

[0187] The coordinate axis marked u(0.5l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 500 meters in the x direction, in meters;

[0188] The coordinate axis marked v(0.5l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 500 meters in the y direction, in meters;

[0189] The coordinate axis marked w(0.5l,t) / m is the actual displacement value of the lateral vibration of the marine flexible riser at 500 meters in the z direction, in meters;

[0190] The axis labeled x / m represents the spatial variable s, in meters;

[0191] The axis labeled Time / s represents the time variable t, in seconds;

[0192] In this example, Figure 3-Figure 5 is a simulation diagram of the flexible riser under free vibration. Figure 3-Figure 5 It can be seen that under free vibration conditions, the flexible riser oscillates periodically and produces a large offset; Figure 6-8 is a simulation schematic diagram of a flexible riser system using the control method provided by the present invention, Figure 6-8 It can be seen that the vibration displacement under control is about one percent of that under free vibration, and the control effect is obvious; further, Figure 9-11 and Figure 12-14 It is shown as a comparison diagram of the boundary deviation and middle deviation of the flexible riser under uncontrolled and boundary control. The results show that the boundary deviation of the riser is significantly reduced under the adaptive reverse clearance active boundary control for the offshore flexible riser, and the middle deviation is also well suppressed. It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0193] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An adaptive backlash active boundary control method for marine flexible risers, characterized in that: include: Model the marine flexible riser, conduct dynamic analysis, obtain the control equation of the marine flexible riser system, and determine the boundary conditions of the marine flexible riser system; updating the boundary condition based on the nonlinear input gap; Construct barrier Lyapunov functions; Propose a desired vibration control strategy, and design a fuzzy logic system and an adaptive law based on the desired vibration control strategy; Verify that the system is stable and bounded based on the barrier Lyapunov function; The actual vibration offset of the marine flexible riser system is obtained, the actual vibration offset is substituted into the adaptive law to obtain the actual control output, and the control force is applied to the top of the marine flexible riser.

2. The adaptive backlash active boundary control method for marine flexible riser according to claim 1, characterized in that: The control equation of the marine flexible riser system is: The boundary conditions of the marine flexible riser system are: u(0,t)=v(0,t)=w(0,t)=0 u′(0,t)=v′(0,t)=w′(0,t)=0 u″(l,t)=v″(l,t)=w″(l,t)=0 Where: ρ is the unit riser mass; t is the time variable; s is the space variable; L is the riser length; is the second-order partial derivative of u(s,t) with respect to t; is the first-order partial derivative of u(s,t) with respect to t; u(s,t) is the actual displacement of vibration in the x direction; is the second-order partial derivative of v(s,t) with respect to t; is the first-order partial derivative of v(s,t) with respect to t; v(s,t) is the actual displacement of vibration in the y direction; is the second-order partial derivative of w(s,t) with respect to t; is the first-order partial derivative of w(s, t) with respect to t; w(s, t) is the actual displacement of vibration in the z direction; EI is the riser bending stiffness; c is the structural damping coefficient; T is the riser tension; M is the ship mass; EA is the axial bending stiffness; d s is the ship damping coefficient; u″″(s,t) is the fourth-order partial derivative of u(s,t) with respect to s; u″(s,t) is the second-order partial derivative of u(s,t) with respect to s; u′(s,t) is the first-order partial derivative of u(s,t) with respect to s; v″″(s,t) is the fourth-order partial derivative of v(s,t) with respect to s; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s; v′(s,t) is the first-order partial derivative of v(s,t) with respect to s; w″(s,t) is the second-order partial derivative of w(s,t) with respect to s; w′(s,t) is the first-order partial derivative of w(s,t) with respect to s; f x is the distributed current load acting on the riser in the x direction; f y is the distributed current load acting on the riser in the y direction; f z is the distributed current load acting on the riser in the z direction; u(0,t) is the value of u(s,t) when s=0; u′(0,t) is the first-order partial derivative of u(s,t) with respect to s when s=0; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; v(0,t) is the value of v(s,t) when s=0; v′(0,t) is the first-order partial derivative of v(s,t) with respect to s when v=0; v″(L,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; w(0,t) is the value of w(s,t) when s=0; w′(0,t) is the first-order partial derivative of w(s,t) with respect to s when s=0; d x is the boundary disturbance in the x direction; d y is the boundary disturbance in the y direction; d z is the boundary disturbance in the z direction; U x is the boundary control quantity at the top of the riser acting in the x direction; U y is the boundary control quantity at the top of the riser acting in the y direction; U z is the boundary control quantity at the top of the riser acting in the z direction.

3. The adaptive backlash active boundary control method for marine flexible riser according to claim 2, characterized in that: The method for updating the boundary condition based on the nonlinear input gap includes: Determine an input gap expression that includes a nonlinear input gap; Based on the backlash dynamics, an adaptive backlash algorithm is designed; Update boundary conditions.

4. The adaptive backlash active boundary control method for marine flexible riser according to claim 3, characterized in that: The input gap expression is: Where: A(p(t)) is the nonlinear input gap; m is the constant slope of the input gap; b is the input gap spacing of unknown width; U(t) is the actual gap boundary control input; p(t) is the gap input variable; is the value of the first derivative of p(t) with respect to the time variable t.

5. The adaptive backlash active boundary control method for marine flexible riser according to claim 4, characterized in that: The designed adaptive backlash algorithm is: U x (t)=m x U x ′(t)+b x sign(ΔU x (t))+U x eq(t)+U x sw(t) U y (t)=m y U y ′(t)+b y sign(ΔU y (t))+U y eq(t)+U y sw(t) U z (t)=m z U z ′(t)+b z sign(ΔU z (t))+U z eq(t)+U z sw(t) In the formula, m x is the unknown slope of the input gap in the x direction; m y Enter the unknown slope of the gap in the y direction; m z is the unknown slope of the input gap in the z direction; b x is the input gap spacing of unknown width in the x direction; b y is the input gap spacing of unknown width in the y direction; b z is the input gap spacing of unknown width in the z direction; U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; U x (t) is the actual boundary control in the x direction; U y (t) is the actual boundary control in the y direction; U z (t) is the actual boundary control in the z direction; U x eq(t) is the equivalent control in the x direction; U y eq(t) is the equivalent control in the y direction; U z eq(t) is the equivalent control in the z direction, U x sw(t) is the switching control in the x direction; U y sw(t) is the switching control in the y direction; U z sw(t) is the switching control in the z direction; ΔU x (t) = U x (t)-U x (t-Δt), is the actual change of boundary control in the x direction; ΔU y (t) = U y (t)-U y (t-Δt), is the actual change of boundary control in the y direction; ΔU z (t) = U z (t)-U z (t-Δt), is the actual change of boundary control in the z direction; Δt is the unit time variable.

6. The adaptive backlash active boundary control method for marine flexible riser according to claim 5, characterized in that: The equivalent control and switching control are implemented by the following formula: AT x sw(t)=-k1 sign(μ x ) U y sw(t)=-k2·sign(μ y ) U z sw(t)=-k3·sign(μ z ) Where γ1, γ2, and γ3 are equivalent control gain coefficients; k1, k2, and k3 are switching control gain coefficients; u″(L, t) is the second-order partial derivative of u(s, t) with respect to s when s=L; v″(L, t) is the second-order partial derivative of v(s, t) with respect to s when s=L; w″(L, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; μ x is the sliding film control in the x direction; μ y is the sliding mode control in the y direction; μ z It is the sliding mode control in z direction.

7. The method for adaptive reverse clearance active boundary control for marine flexible riser according to claim 6, characterized in that: The sliding mode control is implemented using the following strategy: In the formula, e x (t) is the difference between the expected displacement and the actual displacement in the x direction; e y (t) is the difference between the expected displacement and the actual displacement in the y direction; e z (t) is the difference between the expected displacement and the actual displacement in the z direction; for e x The first-order partial derivative of (t) with respect to t; for e y The first-order partial derivative of (t) with respect to t; for e z The first-order partial derivative of (t) with respect to t; λ x , y , z is a constant coefficient; The updated boundary conditions are: u(0,t)=v(0,t)=w(0,t)=0 u′(0,t)=v′(0,t)=w′(0,t)=0 u″(L,t)=v″(L,t)=w″(L,t)=0 8. The method for adaptive reverse clearance active boundary control for marine flexible riser according to claim 7, characterized in that: The fuzzy logic system designed based on the desired vibration control strategy is: In the formula, ζ x is the first adaptive fuzzy logic system; y is the second adaptive fuzzy logic system; z is the third adaptive fuzzy logic system; is the fourth adaptive fuzzy logic system; is the fifth adaptive fuzzy logic system; is the sixth adaptive fuzzy logic system; is the first fuzzy basis vector; is the second fuzzy basis vector; is the third fuzzy basis vector; is the fourth fuzzy basis vector; is the fifth fuzzy basis vector; is the sixth fuzzy basis vector; for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of for The transpose of The adaptive law designed based on the desired vibration control strategy is: Where: is m x The value of the first derivative with respect to t; is m y The value of the first derivative with respect to t; is m z The value of the first derivative with respect to t; for b x The value of the first derivative with respect to t; for b y The value of the first derivative with respect to t; for b z The value of the first-order derivative with respect to t; β3 is the weight value of the adaptive law; for The value of the first derivative with respect to t; for The value of the first derivative with respect to t; for The value of the first-order derivative with respect to t; Proj m is the projection mapping operator; k 1u , k 2v , k 3w is the disturbance weight value; U x ′(t) is the desired boundary control in the x direction; U y ′(t) is the desired boundary control in the y direction, U z ′(t) is the desired boundary control in the z direction; is the first-order partial derivative of u(s,t) with respect to t when s=L; u′(L,t) is the first-order partial derivative of u(s,t) with respect to s when s=L; is the second-order partial derivative of u(s,t) with respect to t when s = L; u″(L,t) is the second-order partial derivative of u(s,t) with respect to s when s=L; is the first-order partial derivative of v(s,t) with respect to t when s=L; v′(L,t) is the first-order partial derivative of v(s,t) with respect to s when s=L; is the second-order partial derivative of v(s,t) with respect to t when s=L; v″(s,t) is the second-order partial derivative of v(s,t) with respect to s when s=L; is the first-order partial derivative of w(s,t) with respect to t when s=L; w′(L,t) is the first-order partial derivative of w(s,t) with respect to s when s=L; is the second-order partial derivative of w(s, t) with respect to t when s=L; w″(s, t) is the second-order partial derivative of w(s, t) with respect to s when s=L; β2 is the desired control gain coefficient; is d x An estimated value of is d y An estimated value of is d z The estimated value of .

9. The method for adaptive reverse clearance active boundary control for marine flexible riser according to claim 8, characterized in that: The barrier Lyapunov function constructed is: V(t) = V1(t) + V2(t) + V3(t) + V4(t); where: Where: V(t) is the barrier Lyapunov function; V1(t) is the energy term, V2(t) is the cross term, V3(t) is the auxiliary term, and V4(t) is the adaptive term; β1 is a positive constant based on the system energy term; k b1 Output constraint boundary value for x direction; k b2 Output constraint boundary value for the y direction; k b3 Output constraint boundary value for z direction; is m x The error estimate of is m y The error estimate of is m z The error estimate of for b x The error estimate of for b y The error estimate of for b z The error estimate of is d x The error estimate of is d y The error estimate of is d z The error estimate of .

10. The method for adaptive backlash active boundary control for marine flexible riser according to claim 9, characterized in that: The barrier Lyapunov function satisfies the following conditions: 0≤ω1(V1(t)+V3(t)+V4(t))≤V(t)≤ω2(V1(t)+V3(t)+V4(t)) Where: The value is and Is a normal number.

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