Robust reliable H-infinity control method for offshore steel frame platform model

Abstract

The invention provides a robust and reliable H-infinity control method for an offshore steel frame platform model, which comprises the following steps of: firstly, establishing a mathematical model of OSJPs, and considering a first main vibration mode; then, a memory SDC-based controller is designed that enables efficient control by reducing the amount of data transmission when the continuous time system state is available only at the sampling time. Furthermore, a loopback function method and a free matrix (FMB)-based integral inequality and linear matrix inequality (LMI) technology are introduced to obtain sufficient conditions about an uncertain offshore platform system, thereby solving the stabilization problem of OSJPs and realizing a reliable SDC design with an interference suppression level. Simulation results show that the method not only can effectively reduce vibration of OSJPs, but also can keep stability of the system under the condition that model uncertainty and actuator faults exist, and effectiveness and importance of the control strategy are proved.

Description

Technical Field

[0001] The present invention belongs to the technical field of controllers, and is specifically a robust and reliable H∞ controller for an offshore steel frame platform model.

[0002] Control method. Background Art

[0003] The steel jacket frame is the most typical mode of fixed offshore platform, which is usually transformed into an adaptable and intelligent super platform with functions such as storage and transportation, drilling, and oil and gas extraction. This kind of frame is often in dangerous environments and is often attacked by waves. In general, multi-purpose and advanced deep-sea structures usually generate strong nonlinear hydrodynamic forces and cause highly nonlinear responses in terms of building deformation. The structural vibration caused by these forces may lead to an unstable atmosphere and endanger all personnel on the platform. Therefore, effective control schemes have emerged, and the vibration system is an exciting research topic. Many researchers are committed to developing control strategies to minimize the vibration of the structure in order to improve the stability of the structure and safeguard the interests of the offshore platform. Various researchers have focused on the stability criteria of such platforms to seek effective methods to reduce the structural vibration of OSJP.

[0004] In most engineering systems, it is challenging to measure continuous information about the state in real equipment. In this case, to analyze the behavior of the device between sampling moments, both the individual operating mode and the continuous response of the device must be considered. The sampled data control (SDC) strategy is one of the most effective control means, which provides a suitable control scheme for dynamic systems to maintain their stability. In addition, SDC only needs to know the state of the continuous-time system at the sampling time (discrete time), which attempts to reduce the amount of data transmitted. In addition, the SDC system uses both continuous-time and discrete-time signals. The main advantage of SDC is that it only requires system state information at the sampling moment within the sampling interval. Therefore, the amount of data transmitted is greatly reduced, making supervision more effective in practice. Therefore, many researchers have been paying attention to the SDC problem of dynamic systems in recent years. Among the key methods of SDC systems, the input delay method is the most widely used method in SDC systems because it does not require a constant sampling interval. In this method, the SDC system can be considered as a modern continuous system whose control input has a specific time delay within the time interval.

[0005] On the other hand, the presence of actuator faults cannot be ignored as they may disrupt highly automated industrial systems. In this context, a reliable control scheme can provide better performance for possible actuator and sensor faults. Sakthivel et al. specifically studied the problem of reliable dissipative SDC for uncertain systems. In addition, Sakthivel et al. also adopted a reliable dissipative SDC scheme for OSJP with active tuned mass dampers (TMDs), where the actuator fault matrix is ​​considered to be known. Another important issue is that the parameters of the platform model may undergo some changes during its service life. Although various control schemes for OSJP have been proposed in the literature, many of them do not consider the uncertainties in the platform model. Therefore, the problem of robust and reliable H∞ storage SDC for OSJP with parameter uncertainties is studied.

[0006] The differences from the prior art are as follows;

[0007] Technical comparison with patent CN113504729A "H∞ robust control method and system for bionic flapping-wing aircraft based on LMI"

[0008] Patent CN113504729A is aimed at the H∞ robust control problem of bionic flapping-wing aircraft. By establishing a time-varying longitudinal dynamic model of bionic flapping-wing aircraft and performing a series of processing on it, an H∞ controller is finally designed based on the LMI method to achieve robust stability and robust performance. This patent is aimed at the vibration control problem of offshore steel frame platforms (OSJPs). By establishing a mathematical model of OSJPs and introducing a memory sampled data control (SDC) strategy, combined with LMI technology, loop function method and free matrix (FMB) integral inequality, the stabilization control of OSJPs with parameter uncertainty and actuator failure is achieved. There are essential differences between the two in terms of application scenarios and technical issues.

[0009] Patent CN113504729A mainly uses the LMI method to solve the H∞ controller. It converts the generalized state space model of the controlled object into the standard form for solving the H∞ controller, and then solves the linear matrix inequality based on the LMI method to obtain a controller that meets the robust stability and robust performance. This patent not only considers the application of LMI technology when designing the controller, but also introduces the memory SDC strategy, as well as the loop function method and FMB integral inequality to establish sufficient conditions for the memory SDC design. In addition, this patent also specifically considers the parameter uncertainty and actuator failure conditions of OSJPs, so that the designed controller has better adaptability and robustness in a more complex and practical working environment. Therefore, there are significant differences between the two at the algorithm level, and the algorithm of this patent is more complex and comprehensive.

[0010] Technical comparison with patent CN114879481A "A robust H∞ control method for ship dynamic positioning with resistance to hydrodynamic interference"

[0011] Patent CN114879481A is aimed at the ship dynamic positioning system with complex hydrodynamic parameters and nonlinear characteristics. By establishing a three-degree-of-freedom dynamic model and a kinematic model and converting it into a robust H∞ control problem, a robust H∞ anti-interference control method is designed. This patent is aimed at the vibration control problem of offshore steel frame platforms (OSJPs). It also uses the H∞ control theory, but by establishing a mathematical model of OSJPs and introducing a memory sampled data control (SDC) strategy, combined with LMI technology, loop function method and free matrix (FMB) integral inequality, it realizes the stabilization control of OSJPs with parameter uncertainty and actuator failure. There are significant differences between the two in application scenarios and technical issues.

[0012] Patent CN114879481A constructs a storage function to satisfy the dissipative inequality, and gives sufficient conditions for the robust H∞ performance of a nonlinear system with uncertainty, and obtains a state feedback control rate for a closed-loop system with local robust disturbance suppression performance. This method mainly relies on H∞ control theory and dissipative inequality to overcome the nonlinearity and uncertainty of the system. However, when designing the controller, this patent not only considers the application of LMI technology, but also introduces a memory SDC strategy, as well as a loop function method and FMB integral inequality to establish sufficient conditions for the design of the memory SDC, and especially considers the parameter uncertainty of OSJPs and actuator failure conditions. Therefore, there are significant differences between the two at the algorithm level. Summary of the invention

[0013] In order to solve the above technical problems, the present invention proposes a robust and reliable H∞ method for the offshore steel frame platform model.

[0014] The control method, by adopting the memory sampling data control strategy, effectively reduces the vibration caused by waves and improves the stability and reliability of the platform.

[0015] To achieve the above object, the technical solution adopted by the present invention is:

[0016] The robust and reliable H∞ control method for the offshore steel frame platform model is as follows:

[0017] S1: Establish a mathematical model of OSJPs, considering the first main vibration mode;

[0018] S2: Introducing the memorized SDC strategy, including the delay of the control input;

[0019] S3: To stabilize the OSJP in S1, sufficient conditions for the memory SDC design are established based on linear matrix inequality techniques, loop function method, and free matrix integral inequality;

[0020] S4: Apply the stability condition to achieve stabilization of the offshore steel frame platform with parameter uncertainty and actuator failure, obtain a stable feedback gain, and ensure that the system reaches asymptotic stability under the maximum sampling period.

[0021] As a further improvement of the present invention, in step S1, the mathematical model of OSJPs established is:

[0022]

[0023] Among them, ξ j ,m j and ω j denote the damping ratio, mass and frequency of the offshore platform j = 1 and the active damping device j = 2, respectively; z1(t) is the generalized modal coordinate, which refers to the deck motion of the offshore structure; z2(t) is the displacement of the active damping device; u F (t) is the control input of the marine structure, which may contain actuator failure; It is the wave force on an offshore platform generated by external disturbances.

[0024] As a further improvement of the present invention, step S2 is specifically as follows:

[0025] Introducing a memorized SDC strategy, including delays in control inputs:

[0026] Define ψ1(t)=z1(t), ψ2(t)=z2(t), And said

[0027]

[0028] Then the equation of motion when the actuator in the system fails is;

[0029]

[0030] in;

[0031]

[0032] for And the known matrix Assume that the output vector satisfies;

[0033] y(t)=Cψ(t)+Ff(t).

[0034] If there are parameter uncertainties, the dynamic equations of the offshore platform become;

[0035]

[0036] For a known constant matrix and Assume the following relationship holds:

[0037]

[0038] The uncertain time-varying matrix Ξ(t) is assumed to satisfy , the control input in the case of actuator failure is defined as

[0039]

[0040] where u(t) is the control input, is the actuator fault matrix (AFM), defined as in g j and is a constant, g j = 0 means the jth actuator fails completely, g j =1 means the jth actuator is normal, when 0 <g j <1 indicates that the jth actuator has a partial failure. Consider the following memristive SDC input with zero-order hold (ZOH):

[0041] u(t)=Kψ(t k -β),t k ≤t <t k+1 ,k=0,1,2,…,

[0042] in is the SDC gain matrix to be determined. β is the signal transmission delay. t k is satisfied 0 <t1<t2<...<t k <… and The sampling time, for any k ≥ 0, assuming that the sampling interval is variable and bounded in is the sampling interval, the lower bound and upper bound is a positive scalar. By substituting the control law and the memory SDC, the system becomes;

[0043]

[0044] y(t)=Cψ(t)+Ff(t),t k ≤t<t k+1 ,k=0,1,2.

[0045] As a further improvement of the present invention, step S3 is specifically as follows:

[0046] In order to stabilize the OSJP in S1, sufficient conditions for the memory SDC design are established, based on the linear matrix inequality technique, the loop function method, and the free matrix integral inequality;

[0047] As a preliminary preparation, there are two lemmas:

[0048] Lemma 1. Assume is a differentiable signal, for the vector matrix as well as The following inequality is satisfied:

[0049]

[0050] Lemma 2. Given real compatible dimension matrices M, N and Ξ T (t), satisfying ΞT(t)Ξ(t)≤I, then:

[0051] MΞ(t)N+N T Ξ T (t)M T ≤∈MM T +∈ -1 N T N,

[0052] The following symbols are defined:

[0053]

[0054] Select the following LKF:

[0055]

[0056] in

[0057]

[0058] because Obviously, V(t) is not necessarily positive in the sampling interval, nor is it necessarily continuous at the sampling time. This can be obtained by calculating the time derivative of V(t) along the system trajectory;

[0059]

[0060] According to Lemma 1, we get;

[0061]

[0062] For the matrix and the scalar α m>0,(m=1,2,3),written as:

[0063]

[0064] From the time derivative of V(t) along the system trajectory and the above formula, we get;

[0065]

[0066] in;

[0067]

[0068] Using Lemma 2, rewrite Ω;

[0069]

[0070] By convex combination method, for any t∈[tk,tk+1), if and only if:

[0071]

[0072] and

[0073]

[0074] There is Ω<0.

[0075] Therefore, for a given scalar ρ L >0,ρ U >0,α m >0,m=1,2,3,β>0,γ>0,fault matrix G,and control gain matrix K,the control system is said to be asymptotically stable when there exists a matrix P

[0076]

[0077] and a scalar ∈>0, such that

[0078]

[0079] For all ρ k ∈{ρ L ,ρ U} established.

[0080] As a further improvement of the present invention, step S4 is specifically as follows:

[0081] The stability condition is applied to stabilize the offshore steel frame platform with parameter uncertainty and actuator failure, and a stable feedback gain K is obtained to ensure that the system reaches asymptotic stability under the maximum sampling period: given a scalar α m>0,(m=1,2,3),β>0,γ≥0, when there exists the following matrix:

[0082] The control system is considered to be asymptotically stable and the scalar ∈>0, such that

[0083]

[0084] for

[0085] Compared with the prior art, the present invention has the following advantages:

[0086] 1. This invention ensures the stability and safety of the offshore steel frame platform in the face of parameter uncertainty and actuator failure by adopting advanced H∞ control theory and memory sampling data control strategy.

[0087] 2. By using linear matrix inequality technology and loop function method, the external interference is effectively suppressed and the system is ensured to be asymptotically stable within the maximum sampling period, thereby improving the control accuracy and response speed.

[0088] 3. The control strategy is not only applicable to offshore steel frame platforms, but can also be extended to other dynamic systems such as wind turbines. At the same time, it allows the use of variable sampling intervals, making the control strategy adaptable to diverse working environments and operating conditions.

[0089] 4. By reducing structural vibration and improving platform stability, the invention reduces maintenance costs, enhances environmental adaptability, and at the same time improves the safety and comfort of workers on the platform, with significant economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 This is a model diagram of an offshore platform based on AMD;

[0091] Figure 2 is the curve of wave force applied to OSJP;

[0092] Figure 3 Figure 1 is the sampling moment;

[0093] Figure 4 It is the acceleration response waveform of the structure in Case 1;

[0094] Figure 5 This is the acceleration response waveform of the structure in Case 2;

[0095] Figure 6 is u in Case 1 F (t) Control intensity waveform diagram;

[0096] Figure 7 is u in case 2 F (t) Control intensity waveform diagram;

[0097] Figure 8 The displacement response diagrams of OSJP with and without control in Case 1;

[0098] Fig. 9 The displacement response diagram of OSJP with and without control in Case 2. DETAILED DESCRIPTION

[0099] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0100] The following describes the implementation of the present invention in conjunction with the accompanying drawings. The present invention is verified using Matlab simulation. An example including two cases is given to demonstrate the effectiveness and feasibility of the proposed OSJP model control scheme. Figure 1 A model diagram of an offshore platform based on AMD is given.

[0101] In order to obtain the expected results, the parameters of the offshore structure in Table 1 are adopted.

[0102]

[0103]

[0104] The simulation results will demonstrate the effectiveness of the proposed robust and reliable H∞ memory SDC strategy. To do this, two cases are considered: Case 1 illustrates the OSJP results without uncertainty when the AFM is known, while Case 2 deals with the OSJP with uncertainty of unknown AFM.

[0105] The matrix in formula (2) is as follows:

[0106]

[0107] When 0≤t≤60, the wave force is expressed as f(t)=2×10 6 ((0.8sin(0.7t)×sin(0.2t)+0.9cos(1.7t)+0.6sin(0.4t)sin(0.8t))).

[0108] Case 1. First, assume that AFM is known The value of The lower and upper limits of the sampling interval are fixed to and Select the remaining parameters α1=0.001, α2=0.09, α3=0.001, β=0.01. For the H∞ performance index γ=0.5, use the LMI in the Matlab Yalmip toolbox to apply Theorem 2, and you can get the feasible solution and the H∞ memory SDC gain matrix:

[0109] K=10 7 ×[1.6068 -0.0007 0.0730 -0.0332].

[0110] Case 2. The values ​​in Table 1 may vary slightly due to the typicality of the parameters. Assume that the mass of OSJP has a tolerance of 2% and 1%, respectively, that is, m1 = 7825307 ± 156510 and m2 = 78253 ± 782.53 kg. Then, the values ​​of the matrix in formula (5) are as follows:

[0111]

[0112] Assuming AFM The value range is The lower and upper limits of the sampling interval are fixed to and Select the remaining parameters α1 = 0.001, α2 = 0.5. α3 = 2, β = 0.01. For the H∞ performance index γ = 0.5, use the LMI in the Matlab Yalmip toolbox to apply Theorem 2, and you can get the feasible solution and the H∞ sampled data controller gain matrix:

[0113] K=10 7 ×[1.4631 0.0041 0.1104 -0.0288].

[0114] Figure 2 The wave force applied to the OSJP is shown as an external disturbance. The figure depicts the sampling moments. Figure 3 The sampling time is plotted, Figure 4 and Figure 5 The acceleration responses of OSJP in Case 1 and Case 2 are shown in Figure 1 and Figure 2, respectively. The control forces generated in Case 1 and Case 2 are shown in Figure 1 and Figure 2, respectively. Figure 6 and Figure 7 middle. Figure 8 and Fig. 9 The displacement responses of the OSJP in the controlled and uncontrolled cases are shown. These graphs show that the vibration is significantly reduced.

[0115] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A robust and reliable H∞ control method for an offshore steel frame platform model, characterized by: Specifically: S1: Establish a mathematical model of OSJPs, considering the first main vibration mode; S2: Introducing the memorized SDC strategy, including the delay of the control input; S3: To stabilize the OSJP in S1, sufficient conditions for the memory SDC design are established based on linear matrix inequality techniques, loop function method, and free matrix integral inequality; S4: Apply the stability condition to achieve stabilization of the offshore steel frame platform with parameter uncertainty and actuator failure, obtain a stable feedback gain, and ensure that the system reaches asymptotic stability under the maximum sampling period.

2. The robust and reliable H∞ control method for an offshore steel frame platform model according to claim 1 is characterized in that: In step S1, the mathematical model of OSJPs is established as: Among them, ξ j ,m j and ω j denote the damping ratio, mass and frequency of the offshore platform j = 1 and the active damping device j = 2, respectively; z1(t) is the generalized modal coordinate, which refers to the deck motion of the offshore structure; z2(t) is the displacement of the active damping device; u F (t) is the control input of the marine structure, which may contain actuator failure; It is the wave force on an offshore platform generated by external disturbances.

3. The robust and reliable H∞ control method for an offshore steel frame platform model according to claim 1, characterized in that: Step S2 is specifically as follows: Introducing a memorized SDC strategy, including delays in control inputs: Define ψ1(t)=z1(t), ψ2(t)=z2(t), And said Then the equation of motion when the actuator in the system fails is; in; for And the known matrix Assume that the output vector satisfies; y(t)=Cψ(t)+Ff(t). If there are parameter uncertainties, the dynamic equations of the offshore platform become; For a known constant matrix and Assume the following relationship holds: The uncertain time-varying matrix Ξ(t) is assumed to satisfy The control input in the case of actuator failure is defined as where u(t) is the control input, is the actuator fault matrix (AFM), defined as in g j and is a constant, g j = 0 means the jth actuator fails completely, g j =1 means the jth actuator is normal, when 0 <g j <1 indicates that the jth actuator has a partial failure. Consider the following memristive SDC input with zero-order hold (ZOH): u(t)=Kψ(t k -b),t k ≤t <t k+1 ,k=0,1,2,…, in is the SDC gain matrix to be determined. β is the signal transmission delay. k is satisfied 0 <t1<t2<...<t k <… and The sampling time, for any k ≥ 0, assuming that the sampling interval is variable and bounded in is the sampling interval, the lower bound and upper bound is a positive scalar. By substituting the control law and the memory SDC, the system becomes; y(t)=Cψ(t)+Ff(t),t k ≤t<t k+1 ,k=0,1,2。 4. The robust and reliable H∞ control method for an offshore steel frame platform model according to claim 1, characterized in that: Step S3 is as follows: In order to stabilize the OSJP in S1, sufficient conditions for the memory SDC design are established, based on the linear matrix inequality technique, the loop function method, and the free matrix integral inequality; As a preliminary preparation, there are two lemmas: Lemma 1. Let x: is a differentiable signal, for the vector matrix as well as The following inequality is satisfied: Lemma 2. Given real compatible matrices M, N and Ξ T (t), satisfying Ξ T (t)Ξ(t)≤I, then: MΞ(T)N+N T Ξ T (t)M T ≤∈MM T +∈ -1 N T N, The following symbols are defined: Select the following LKF: in because Obviously, V(t) is not necessarily positive in the sampling interval, nor is it necessarily continuous at the sampling time. This can be obtained by calculating the time derivative of V(t) along the system trajectory; According to Lemma 1, we get; For the matrix and the scalar α m >0,(m=1,2,3),written as: From the time derivative of V(t) along the system trajectory and the above formula, we get; in; Using Lemma 2, rewrite Ω; By convex combination methods [306], Ω^<0 for any t∈[tk,tk+1) if and only if: and Therefore, for a given scalar ρ L >0,ρ U >0,α m >0,m=1,2,3,β>0,γ>0,fault matrix G,and control gain matrix K,the control system is said to be asymptotically stable when there is a matrix and a scalar ∈>0, such that For all ρ k ∈{ρ L ,ρ U } established.

5. The robust and reliable H∞ control method for an offshore steel frame platform model according to claim 1, characterized in that: Step S4 is specifically as follows: Apply the stability condition to stabilize the offshore steel frame platform with parameter uncertainty and actuator failure, and obtain a stable feedback gain K to ensure that the system reaches asymptotic stability under the maximum sampling period: Given a scalar α m >0,(m=1,2,3),β>0,γ≥0, when there exists the following matrix: The control system is considered to be asymptotically stable and the scalar ∈>0, such that for Depend on The SDC gain can be obtained.

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