Sliding-mode control method for hydraulic system of jacket ocean platform integrated disassembly lifting arm

Abstract

According to the sliding mode control method for the hydraulic system of the integrated disassembly lifting arm of the jacket ocean platform, when the integrated disassembly lifting arm is subjected to disassembly operation under the high-amplitude and high-frequency extreme sea condition, due to the fact that the uncertainty of the hydraulic control system of the lifting arm is increased, the requirement for the timeliness of response to state observation is higher, and the reliability of the lifting arm is improved. In order to improve the control precision of a lifting arm hydraulic system under an extreme sea condition, a high-gain observer is introduced to estimate an unmeasurable system state and improve the timeliness of state estimation error convergence, and a designed controller approximates a switching item in sliding mode controller input by introducing a fuzzy adaptive algorithm; therefore, the buffeting problem of the sliding mode controller in the error convergence process is improved. The device is suitable for integrated disassembling operation of the jacket ocean platform under high-amplitude and high-frequency extreme sea conditions, and is simple in structure, small in calculation amount and high in response speed.

Description

Technical Field

[0001] The present invention relates to the technical field of electro-hydraulic servo control of hydraulic systems, and particularly to a sliding mode control method for a hydraulic system of an integrated disassembly and lifting arm of a jacket offshore platform. Background Art

[0002] The disassembly operation of a jacket offshore platform is difficult and the operation window period is short. At present, there are mainly "heavy lift semi-submersible ship" overall lifting, "float-over method" and "integral method" disassembly schemes. These disassembly schemes all have problems such as low operation efficiency and poor safety and environmental protection. In recent years, integrated disassembly equipment has gradually emerged. Its working scenario is as Figure 1 shown. The integrated disassembly equipment consists of three semi-submersible barges. The three ships cooperate to disassemble the upper module of the jacket offshore platform as a whole, with high operation efficiency and wide application range.

[0003] In the integrated disassembly operation, affected by uncertain factors such as wind and waves, the platform to be disassembled may be overturned, resulting in huge economic losses, environmental pollution and personal injury accidents. To ensure the safe and effective disassembly of the jacket offshore platform, the lifting system needs to maintain continuous and stable output during the disassembly process. As the core system of the integrated disassembly equipment of the jacket offshore platform, the control performance of the lifting arm hydraulic system determines the stability of the equipment operation. Therefore, high precision and robustness are required for its control performance.

[0004] Therefore, developing a lifting arm hydraulic control system with good engineering adaptability, flexibility and fault tolerance is the key to the successful development of the integrated disassembly equipment of the jacket offshore platform. Summary of the Invention

[0005] The present invention provides a sliding mode control method for a hydraulic system of an integrated disassembly and lifting arm of a jacket offshore platform. By introducing a high-gain observer, the control system can accurately estimate the unmeasurable system states and improve the timeliness of the convergence of the state estimation error. At the same time, the designed controller approximates the switching term in the input of the sliding mode controller by introducing a fuzzy adaptive algorithm, thereby improving the chattering problem existing in the error convergence process of the sliding mode controller.

[0006] A sliding mode control method for a hydraulic system of an integrated disassembly and lifting arm of a jacket offshore platform includes the following steps:

[0007] Step 1: Establish a mathematical model for the hydraulic system of the integrated disassembly and lifting arm of the jacket offshore platform;

[0008] Step 2: Construct a fuzzy adaptive sliding mode controller based on a high-gain observer, where the controller includes a high-gain state observer and a sliding mode controller;

[0009] Step 3: Use the constructed high-gain state observer and sliding mode controller to control the lifting arm hydraulic system to disassemble the jacket offshore platform integration;

[0010] The mathematical modeling of the lifting arm hydraulic system for the disassembly of the jacket offshore platform integration described in Step 1 includes:

[0011] Step 1-1: Simplify the lifting arm hydraulic system based on the idea of reducing the complexity of the hydraulic system to obtain a valve-controlled asymmetric cylinder system for the lifting arm. Among them, the idea of reducing the complexity of the hydraulic system is to regard the hydraulic pump as the output unit of the controller, establish a mathematical model of the lifting arm hydraulic system around the hydraulic cylinder and its associated hydraulic valves, and classify the influencing factors of the hydraulic cylinder, hydraulic valves and other components into the modeling uncertainty, and make unified processing and compensation for the complex modeling uncertainty and external interference in the controller;

[0012] Step 1-2: Based on the structure of the valve-controlled asymmetric cylinder system for the lifting arm, establish the load dynamics equation of the hydraulic cylinder in the lifting arm hydraulic system, the flow calculation equations of the rodless chamber and the rod chamber of the hydraulic cylinder, and the pressure-flow dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder, and comprehensively establish the state space equation of the lifting arm hydraulic system by combining these three equations;

[0013] The construction of the fuzzy adaptive sliding mode controller based on the high-gain observer described in Step 2 includes:

[0014] Step 2-1: Construct a high-gain state observer based on the established mathematical model;

[0015] Step 2-2: Use the system state estimated by the high-gain state observer to construct a sliding mode controller.

[0016] Optionally, the specific process of Step 1-2 is as follows:

[0017] For the valve-controlled asymmetric cylinder system of the lifting arm, with the extension direction of the hydraulic cylinder piston rod as the positive direction, establish the load dynamics equation of the hydraulic cylinder according to Newton's second law, as shown in formula (1):

[0018]

[0019] Among them, m is the lifting weight of a single lifting arm, A 1 and A 2 are the cross-sectional areas of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, P 1 and P 2 are the pressures in the rodless chamber and the rod chamber of the hydraulic cylinder respectively, g is the control gain of the lifting arm hydraulic system, b is the viscous damping coefficient of the hydraulic cylinder, is the piston rod speed of the hydraulic cylinder, F d is the unknown disturbing force received by the hydraulic cylinder, f cis the coupling force acting on the hydraulic cylinder;

[0020] Establish the flow equation of the proportional servo valve of the hydraulic cylinder, so as to establish a connection with the dynamic equation. In order to simplify the modeling process, the following assumptions need to be met:

[0021] Assumption 1: The proportional servo valve used in the lifting arm hydraulic system should be a four-way spool valve with an ideal zero-opening structure, and all four throttle windows are guaranteed to be completely matched and symmetrical;

[0022] Assumption 2: The liquid flow characteristics at the throttle window are turbulent flow, and the change in the density of the hydraulic oil is small. The compressibility of the hydraulic oil inside the valve is negligible;

[0023] Assumption 3: The oil supply pressure of the lifting arm hydraulic system is constant. The losses and dynamic characteristics of the oil supply pipeline are ignored, the return oil pressure is zero, and the pressures in the rodless cavity and the rod cavity of the hydraulic cylinder satisfy 0 ≤ P r ≤ P 1 ,P 2 ≤ P s ,where P r is the liquid supply pressure of the fuel tank, and P s is the liquid supply pressure of the system;

[0024] When the piston rod of the hydraulic cylinder extends, the flow rates of the rodless cavity and the rod cavity of the hydraulic cylinder are calculated as shown in formula (2):

[0025]

[0026] Among them, Q 1 and Q 2 are the flow rates of the rodless cavity and the rod cavity of the hydraulic cylinder respectively, C d is the throttle orifice flow coefficient of the proportional servo valve, ω is the area gradient of the throttle orifice, ρ is the density of the hydraulic oil, and x v is the spool displacement of the proportional servo valve;

[0027] Similarly, when the hydraulic cylinder retracts, the flow rates flowing into the rodless cavity and the rod cavity of the hydraulic cylinder through the proportional servo valve are calculated as shown in formula (3):

[0028]

[0029] To facilitate the expression of the flow equation of the proportional servo valve, define the flow gain coefficient k q of the proportional servo valve as shown in formula (4):

[0030]

[0031] Combining formulas (2)-(4), it can be obtained that the comprehensive calculation of the flow rates flowing into the rodless cavity and the rod cavity of the hydraulic cylinder through the proportional servo valve is as shown in formula (5):

[0032]

[0033] In the formula, represents the half-sign function, specifically:

[0034]

[0035] Since the response speed of the proportional servo valve is much higher than the bandwidth of the lifting arm hydraulic system, the telescopic process of the spool displacement of the proportional servo valve can be approximated as a proportional process in the control process. Then, the spool displacement x of the proportional servo valve v and the control input are approximately represented as shown in Equation (7):

[0036]

[0037] where k v is the voltage-spool displacement gain of the proportional servo valve;

[0038] Finally, the flow calculation equations for the rodless chamber and the rod chamber of the hydraulic cylinder containing the control input are shown in Equation (8):

[0039]

[0040] where k t = k q · k v is the total flow gain relative to the control input ;

[0041] According to the calculated flows Q 1 and Q 2 of the rodless chamber and the rod chamber of the hydraulic cylinder, the pressure-flow dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder can be further established. According to the sealing and internal liquid characteristics of the hydraulic cylinder, the following assumptions need to be satisfied when establishing the pressure-flow dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder:

[0042] Assumption 3: The pressures in each working chamber of the hydraulic cylinder are equal, and the hydraulic oil temperature and bulk modulus of elasticity are both constants;

[0043] Assumption 4: The internal and external leaks of the hydraulic cylinder are both laminar flows;

[0044] Considering the oil compressibility during the disassembly operation of the lifting arm hydraulic system, the pressure-flow dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder are shown in Equation (9):

[0045]

[0046] where β e is the elastic modulus of the hydraulic oil, C t is the internal leakage coefficient of the hydraulic cylinder, Δ1 and Δ 2 are the parameter uncertainties and modeling errors of the rodless chamber and the rod chamber, V 1 and V 2 are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, and their calculation process is shown in Equation (10):

[0047]

[0048] Among them, V 01 and V 02 are the initial volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, A 1 and A 2 are the cross-sectional areas of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, and y is the displacement of the piston rod of the hydraulic cylinder;

[0049] Define the system state variables According to the load dynamic equation (1) of the hydraulic cylinder, the flow calculation equations (8) of the rodless chamber and the rod chamber of the hydraulic cylinder, the pressure-flow dynamic equations (9) of the rodless chamber and the rod chamber of the hydraulic cylinder, and the defined state variable x, the state space equation of the lifting arm hydraulic system is obtained, as shown in Equation (11):

[0050]

[0051] Among them, f(x) represents the correlation coefficient of the lifting arm hydraulic system, and d(t) represents the lumped uncertainty caused by the external wind, wave and flow interference and the system nonlinearity of the lifting arm hydraulic system. The derivation results of the specific parameters in the state equation of the lifting arm hydraulic system are shown in Equation (12):

[0052]

[0053] In the expression of d(t), under the stable operating conditions of the system, Δ 1 and Δ 2 change little, the areas of the rodless chamber and the rod chamber are close, so the value of the nonlinear term (A 1 Δ 1 -A 2 Δ 2 ) / m is also small, and the interference expression term d(t) can be mainly regarded as the force change rate of the system caused by various internal and external uncertainties per unit mass, that is, the change degree of the internal and external forces when the lifting arm hydraulic system works;

[0054] Considering the system uncertainty, rewrite Equation (12) as

[0055]

[0056] Among them, Let \(f(x)\) denote the nominal value, \(\Delta f(x)\) denote the perturbation of \(f(x)\), \(g\) denote the nominal value of \(g\), and \(\Delta g\) denote the perturbation of \(g\).

[0057] Furthermore, the specific process of step 2-1 is as follows:

[0058] Define the extended state \(x\) 4 \(= w\), where \(w = \Delta f(x)+\Delta bu + d\) represents the total perturbation of the system, and this term is bounded;

[0059] Define the system state \(X=[x\) 1 , \(x\) 2 , \(x\) 3 \(x\) 4 , the system state observation value The system output \(y = x\) 1 represents the displacement vector of the hydraulic cylinder rod;

[0060] Design a high-gain observer as shown in formula (15):

[0061]

[0062] where, represents the estimation error of the extended state observer, \(\alpha\) i \((i = 1,2,3,4)\) and \(\varepsilon\) are positive constants;

[0063] Define the perception error of the high-gain observer as:

[0064]

[0065] Then the dynamic equation of the observation error between the actual perturbation and the estimated perturbation is as shown in formula (17):

[0066]

[0067] Further arranging it gives:

[0068]

[0069] where, If \(A\) satisfies the Hurwitz criterion, then its eigenvalues are negative. At this time, the observation error is stable. Therefore, it is necessary to select appropriate \(\alpha\) i \((i = 1,2,3,4)\) to satisfy the Hurwitz criterion;

[0070] \(\lambda(s)=|sI - A|=\lambda\) 4 +\(\alpha\) 1 \(\lambda\) 3 +\(\alpha\) 2 \(\lambda\) 2 +\(\alpha\) 3 \(\lambda+\alpha\) 4= 0 (20)

[0071] Select α 1 = 6, α 2 = 11, α 3 = 6, α 4 = 6, at this time the eigenvalue is λ 1 = -2.8805 + 0.8099i, λ 2 = -2.8805 - 0.8099i, λ 3 = -0.1195 + 0.8099i, λ 4 = -0.1195 - 0.8099i;

[0072] For any given symmetric positive definite matrix Q, there exists a symmetric positive definite matrix P satisfying the following Lyapunov equation:

[0073] A T P + PA + Q = 0 (21)

[0074] Define the Lyapunov function of the observer as:

[0075] V o = εη T Pη (22)

[0076] Taking the derivative gives

[0077]

[0078] And

[0079]

[0080] where λ min (Q) is the minimum eigenvalue of Q, and L is the upper bound;

[0081] From it can be obtained that the convergence condition of the observer is

[0082]

[0083] Furthermore, the specific process of step 2-2 is as follows:

[0084] Define the expected position of the hydraulic cylinder piston rod as x d , then the error is defined as

[0085]

[0086] Define the sliding mode surface as

[0087] s = λ 2 e 1 + 2λe2 +e 3 (24)

[0088] Derivation gives

[0089]

[0090] where

[0091]

[0092] Design

[0093]

[0094] where

[0095]

[0096] To prove the stability of the control system, define the Lyapunov function Derivation gives

[0097]

[0098] Define

[0099]

[0100] Then

[0101]

[0102] Define The upper bound of is Δ max , which represents the total error of the extended state observer, and is transformed into

[0103]

[0104] Furthermore, we can obtain

[0105]

[0106] Take Then

[0107]

[0108] Since V s ≥0, when t→∞, The convergence speed depends on the control gain k and the observer parameter ε;

[0109] Considering the closed-loop system composed of the observer and the controller comprehensively, the Lyapunov function is V = V s +V o , then

[0110]

[0111] By taking a sufficiently large \(k\) and a sufficiently small \(\varepsilon\), it can be ensured that so that when \(t\rightarrow\infty\), \(s\rightarrow0\) and \(e\rightarrow0\). The convergence rate depends on the control gain \(k\) and the observer parameter \(\varepsilon\).

[0112] After adopting the above technical solution, the present invention has at least the following beneficial effects:

[0113] (1) The present invention proposes a non-backstepping control method for a strictly-feedback hydraulic system, which reduces the complexity of the system, and the controller design only uses the system output. This control method is significantly different from most existing methods and does not have the problem of complexity explosion.

[0114] (2) The present invention introduces a high-gain observer to estimate the unmeasurable system state and improve the timeliness of the convergence of the state estimation error. The designed controller approximates the switching term in the input of the sliding mode controller by introducing a fuzzy adaptive algorithm, thereby improving the chattering problem existing in the sliding mode controller during the error convergence process. It is applicable to the integrated disassembly operation of jacket offshore platforms under high-amplitude and high-frequency extreme sea conditions, and has the advantages of simple structure, small computational amount, and fast response speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0116] Figure 1 It is a working scenario diagram of the integrated disassembly of a jacket offshore platform;

[0117] Figure 2 It is a schematic structural diagram of a lifting arm valve-controlled asymmetric hydraulic cylinder system;

[0118] Figure 3 It is a comparison diagram of the lifting trajectories and trajectory tracking errors of a sliding mode controller and a robust controller under simulated sea condition 1, where a is a comparison diagram of the lifting trajectories of the sliding mode controller and the robust controller under simulated sea condition 1, and b is a comparison diagram of the trajectory tracking errors of the sliding mode controller and the robust controller under simulated sea condition 1;

[0119] Figure 4For the comparison diagram of the lifting trajectories and trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 2, where a is the comparison diagram of the lifting trajectories of the sliding mode controller and the neural network controller under simulated sea condition 2, and b is the comparison diagram of the trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 2;

[0120] Figure 5 For the comparison diagram of the lifting trajectories and trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 3, where a is the comparison diagram of the lifting trajectories of the sliding mode controller and the neural network controller under simulated sea condition 3, and b is the comparison diagram of the trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 3;

[0121] Figure 6 For the comparison diagram of the lifting trajectories and trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 4, where a is the comparison diagram of the lifting trajectories of the sliding mode controller and the neural network controller under simulated sea condition 4, and b is the comparison diagram of the trajectory tracking errors of the sliding mode controller and the neural network controller under simulated sea condition 4. Specific implementation mode

[0122] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0123] As the core system of the integrated disassembly equipment for jacket offshore platforms, the electro-hydraulic servo system control performance of the lifting arm hydraulic system determines the stability of the equipment operation. Since the 1980s, electro-hydraulic servo systems have been widely used in various fields due to their advantages in volume, weight, energy efficiency, and noise. However, electro-hydraulic servo systems are complex systems covering multiple disciplines such as mechanics, hydraulics, electricity, and thermodynamics, with characteristics such as complex models, nonlinearity, strong coupling, and time-variation. There are problems such as large hydraulic oil loss, complex system modeling due to high-precision hydraulic components, and uncertainties faced in the control process of electro-hydraulic servo systems. Considering the mechanical characteristics and working conditions requirements of the integrated disassembly equipment for jacket offshore platforms, the following difficulties in the electro-hydraulic servo control of the lifting arm hydraulic system are summarized:

[0124] (1) One is the strong nonlinear problem of the hydraulic system itself

[0125] There are problems such as hydraulic oil compression, leakage, mechanical wear, and sensor time delay, which make it impossible to accurately model the hydraulic system and require overcoming complex system uncertainties during the control process.

[0126] (2) The second is the multi-variable coupling problem of the hydraulic system

[0127] The hydraulic system is a complex nonlinear system with multiple inputs and outputs. There are complex coupling relationships among various variables. To achieve precise control of the hydraulic system, it is necessary to decouple the above-mentioned coupling variables, and complex control algorithms need to be designed to meet the requirements of accuracy and response speed.

[0128] (3) Thirdly, the hydraulic system faces complex wind and wave disturbances and the problem of sensor measurement errors caused by the disturbances.

[0129] During the lifting operation of the lifting arm hydraulic system, complex wind, wave and current disturbances bring new external uncertainties to the electro-hydraulic servo control of the hydraulic system. At the same time, the increase of external disturbances will also cause an increase in the sensor measurement errors of the hydraulic system, resulting in distorted measurement results, and then leading to the problem that the state of the electro-hydraulic servo control system is unmeasurable, which increases the design difficulty of the controller.

[0130] To solve the uncertainty problem of the hydraulic system and ensure the stable operation of the system and the accuracy of the actuator, many control technologies have been developed, such as adaptive control, H ∞ control, robust control and backstepping control. Among them, due to its online learning ability, adaptive control can cope with parameter changes. To further deal with the unknown nonlinearity of the system, function approximators such as neural network control and fuzzy control can be introduced. However, the computational cost of function approximators is relatively high, and the convergence speed is slow. At the same time, the system performance is affected by the adaptive law and learning gain. Therefore, using the adaptive control method in the practical application of the hydraulic system is still not an easy task. In addition to the above methods, the method based on the disturbance observer has also been proposed and used. Various observer structures have been developed and efforts have been made to estimate and compensate uncertainties. However, for most classical disturbance observer-based methods, it is difficult to select the observer parameters, and a compromise needs to be made between the system robustness and the control response.

[0131] On the other hand, since hydraulic systems generally have a strict feedback form, most of the existing hydraulic system control methods adopt the backstepping design method. In the backstepping design, the derivative of the virtual control law needs to be calculated repeatedly, resulting in the "complexity explosion" problem. Although dynamic surface control was developed to solve this problem, the introduced filtering operation increases the extra complexity and computational load. In addition, in these backstepping designs, the complete state of the system must be known or measurable, and this assumption is particularly strict in practice because parameters such as the pressure of the hydraulic system are usually unmeasurable. Additionally, some hydraulic system parameters (such as leakage coefficient and effective bulk modulus, etc.) cannot be accurately identified, and it is difficult to model the dynamics of the fluid in the cylinder and servo valve. In some literature, the hydraulic actuator is regarded as an ideal actuator, and this simplification leads to inevitable mismatches compared with the real system. The above difficulties have, to a certain extent, caused the gap between the theoretical research and practical application of hydraulic systems. Therefore, developing simple control for hydraulic systems (for example, without the backstepping method and function approximation) is worthy of further research. In addition, the internal and external uncertainties of the hydraulic system need to be considered, and only output feedback should be used to facilitate practical applications.

[0132] Through research, it can be obtained that the sliding mode control strategy based on the full-dimensional state observer can well observe the system state, and effectively improves the robustness of the system while suppressing the interference. However, this method usually requires constructing a system identical to the original system in the control loop, and the performance of the observer depends greatly on the model accuracy. Moreover, in the designed sliding mode controller, due to the frequent switching of the switching term in the sliding mode control input, it may reduce the service life of the hydraulic system actuator. Therefore, in order to reduce the dependence on the modeling accuracy and at the same time improve the convergence speed of the observation error of the state observer, many studies have introduced high-gain observers into the controller design process. The high-gain observer can decompose the nonlinear modeling error into a linear part and a nonlinear part, and by designing the observer gain to control the nonlinear part with the linear part, the system observation error can be converged to an arbitrarily small value. In addition, considering the strong suppression effect of sliding mode control on external complex wind, wave and current, especially high-frequency interference, and the chattering problem existing in itself, in the design process of the integrated disassembly and lifting arm hydraulic system controller, a robust control scheme combining low-chatter backstepping sliding mode control and high-gain observer is introduced, which has strong engineering practical significance for the integrated disassembly operation of the jacket offshore platform under extremely complex sea conditions.

[0133] Based on the above discussion, the inventors propose a new output feedback control design for a high-order hydraulic system. This method does not require the use of function approximators and backstepping design methods, can handle unknown nonlinear problems, and has fewer adjustable parameters and a fast convergence rate. To avoid using the backstepping method, the unknown dynamics and disturbances are regarded as lumped terms, and then Levant's differentiator is used to reconstruct the unmeasurable system states to ensure the finite-time convergence of the system, which helps to enhance the convergence of the observer error and the control error. Then, an unknown dynamic estimator is proposed, which has only one adjustable parameter. Finally, a control scheme without the backstepping method is constructed using the estimated system states and uncertainties. Through simulations and experiments, the effectiveness of the proposed scheme is verified. In this control, only the system output (hydraulic cylinder displacement) is required, while avoiding the use of complex function approximators (e.g., neural networks and FSs) and lengthy backstepping strategies. Therefore, the proposed scheme requires fewer sensors and has a lower computational cost, and the above characteristics make the proposed control scheme particularly suitable for applications.

[0134] An embodiment of the present disclosure provides a sliding mode control method for a hydraulic system of an integrated disassembly and lifting arm of a jacket offshore platform, including the following steps:

[0135] Step 1. Perform mathematical modeling on the hydraulic system of the integrated disassembly and lifting arm of the jacket offshore platform;

[0136] Step 1-1. Simplify the lifting arm hydraulic system based on the idea of reducing the complexity of the hydraulic system

[0137] The hydraulic cylinder is the power execution unit of the lifting arm hydraulic system, and the hydraulic valve is the core of the lifting arm control. Therefore, when designing the controller, more attention should be paid to modeling around these two units. The hydraulic system is a very complex high-order nonlinear system, with complex interactions and dynamic behaviors between different components. Moreover, there are many nonlinear characteristics in fluid mechanics in the hydraulic system, such as the nonlinear relationship between pressure, flow rate, and valve opening. These all exacerbate the difficulty of hydraulic system modeling. In addition, the parameters in the hydraulic system are often affected by various factors, such as temperature, frictional loss, and leakage. Therefore, there are modeling uncertainties in the process of hydraulic system modeling, which also pose challenges to the precise control of the hydraulic system. To sum up, in order to reduce the complexity of hydraulic system modeling, the hydraulic pump is regarded as the output unit of the controller, avoiding the additional uncertain impacts on the controller design caused by the complexity of hydraulic pump modeling. On this basis, a simplified model of the hydraulic system is established around the hydraulic cylinder and its associated hydraulic valve, and the influencing factors of the hydraulic cylinder, hydraulic valve, and other components (such as the stability and time delay of the hydraulic pump, and the structure and leakage of the oil pipe) are classified into modeling uncertainties. While facilitating the subsequent controller design, the complex modeling uncertainties and external disturbances are jointly processed and compensated in the controller. Therefore, based on the above simplified idea, the structure of the simplified lifting arm valve-controlled asymmetric hydraulic cylinder system is as Figure 2 shown.

[0138] Step 1-2: Based on the structure of the lifting arm valve-controlled asymmetric hydraulic cylinder system, establish the load dynamics equation of the hydraulic cylinder in the lifting arm hydraulic system, the flow calculation equations of the rodless chamber and the rod chamber of the hydraulic cylinder, and the pressure-flow dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder. Then, synthesize these three equations to establish the state space equation of the lifting arm hydraulic system;

[0139] (1) Hydraulic cylinder load dynamics equation

[0140] For the lifting arm valve-controlled asymmetric hydraulic cylinder system, with the extension direction of the hydraulic cylinder piston rod as the positive direction, the hydraulic cylinder load dynamics equation is established according to Newton's second law, as shown in formula (1):

[0141]

[0142] Among them, m is the lifting weight of a single lifting arm, A 1 and A 2 are the cross-sectional areas of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, P 1 and P 2 are the internal pressures of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, g is the control gain of the lifting arm hydraulic system, b is the viscous damping coefficient of the hydraulic cylinder, is the piston rod speed of the hydraulic cylinder, F d is the unknown disturbing force acting on the hydraulic cylinder, fc is the coupling force acting on the hydraulic cylinder;

[0143] (2) Flow calculation equations for the rodless chamber and the rod chamber of the hydraulic cylinder

[0144] Establish the flow calculation equations for the rodless chamber and the rod chamber of the hydraulic cylinder, so as to establish a connection with the dynamic equation. To simplify the modeling process, the following assumptions need to be met:

[0145] Assumption 1: The proportional servo valve used in the lifting arm hydraulic system should be a four-way spool valve with an ideal zero-opening structure, and all four throttle windows are guaranteed to be completely matched and symmetric;

[0146] Assumption 2: The liquid flow characteristics at the throttle window are turbulent flow, and the change in the density of the hydraulic oil is small, and the compressibility of the hydraulic oil inside the valve is negligible;

[0147] Assumption 3: The oil supply pressure of the lifting arm hydraulic system is constant, the losses and dynamic characteristics of the oil supply pipeline are ignored, the return oil pressure is zero, and the pressures in the rodless chamber and the rod chamber of the hydraulic cylinder satisfy 0 ≤ P r ≤ P 1 , P 2 ≤ P s , where P r is the liquid supply pressure of the fuel tank, and P s is the liquid supply pressure of the system;

[0148] When the piston rod of the hydraulic cylinder extends, the flow calculations for the rodless chamber and the rod chamber of the hydraulic cylinder are shown in formula (2):

[0149]

[0150] Among them, Q 1 and Q 2 are the flows of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, C d is the throttle orifice flow coefficient of the proportional servo valve, ω is the area gradient of the throttle orifice, ρ is the density of the hydraulic oil, and x v is the spool displacement of the proportional servo valve;

[0151] Similarly, when the hydraulic cylinder retracts, the flows flowing into the rodless chamber and the rod chamber of the hydraulic cylinder through the proportional servo valve are calculated as shown in formula (3):

[0152]

[0153] To facilitate the expression of the proportional servo valve flow equation, define the proportional servo valve flow gain coefficient k q as shown in formula (4):

[0154]

[0155] Combining equations (2)-(4), the comprehensive calculation of the flow rates flowing into the rodless chamber and the rod chamber of the hydraulic cylinder through the proportional servo valve is shown in equation (5):

[0156]

[0157] In the formula, represents the half-sign function, specifically:

[0158]

[0159] Since the response speed of the proportional servo valve is much higher than the bandwidth of the lifting arm hydraulic system, the telescopic process of the spool displacement of the proportional servo valve can be approximated as a proportional process in the control process. Then, the spool displacement x v of the proportional servo valve and the control input are approximately expressed as shown in equation (7):

[0160]

[0161] where k v is the voltage-spool displacement gain of the proportional servo valve;

[0162] Finally, the flow rate calculation equations for the rodless chamber and the rod chamber of the hydraulic cylinder containing the control input are shown in equation (8):

[0163]

[0164] where k t = k q ·k v is the total flow rate gain with respect to the control input ;

[0165] (3) Pressure-flow dynamic equations for the rodless chamber and the rod chamber of the hydraulic cylinder

[0166] Based on the calculated flow rates Q 1 and Q 2 of the rodless chamber and the rod chamber of the hydraulic cylinder, the pressure-flow dynamic equations for the rodless chamber and the rod chamber of the hydraulic cylinder can be further established. According to the sealing and internal liquid characteristics of the hydraulic cylinder, the following assumptions need to be satisfied when establishing the pressure-flow dynamic equations for the rodless chamber and the rod chamber of the hydraulic cylinder:

[0167] Assumption 3: The pressures in each working chamber of the hydraulic cylinder are equal, and the hydraulic oil temperature and bulk modulus of elasticity are both constants;

[0168] Assumption 4: The internal and external leaks of the hydraulic cylinder are both laminar flows;

[0169] Considering the oil compressibility during the disassembly operation of the lifting arm hydraulic system, the pressure-flow dynamic equations for the rodless chamber and the rod chamber of the hydraulic cylinder are shown in equation (9):

[0170]

[0171] Among them, β e is the elastic modulus of the hydraulic oil, C t is the internal leakage coefficient of the hydraulic cylinder, Δ 1 and Δ 2 are the defined parameter uncertainties and modeling errors of the rodless chamber and the rod chamber, V 1 and V 2 are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, and their calculation process is shown in formula (10):

[0172]

[0173] Among them, V 01 and V 02 are the initial volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, A 1 and A 2 are the cross-sectional areas of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, and y is the displacement of the piston rod of the hydraulic cylinder;

[0174] (4) State-space equation of the lifting arm hydraulic system

[0175] Define the system state variables According to the load dynamics equation (1) of the hydraulic cylinder, the flow calculation equations (8) of the rodless chamber and the rod chamber of the hydraulic cylinder, the pressure-flow dynamic equations (9) of the rodless chamber and the rod chamber of the hydraulic cylinder, and the defined state variable x, the state-space equation of the lifting arm hydraulic system is obtained, as shown in formula (36):

[0176]

[0177] Among them, f(x) represents the correlation coefficient of the lifting arm hydraulic system, and d(t) represents the lumped uncertainty caused by the external wind, wave and flow interference and the system nonlinearity of the lifting arm hydraulic system. The derivation results of the specific parameters in the state equation of the lifting arm hydraulic system are shown in formula (12):

[0178]

[0179] In the expression of d(t), under the stable working condition of the system, the changes of Δ 1 and Δ 2 are small, the areas of the rodless chamber and the rod chamber are close, so the value of the nonlinear term (A 1 Δ 1 -A 2 Δ 2 ) / m is also small, and the interference expression term d(t) can be mainly regarded as the force change rate of the system caused by various internal and external uncertainties per unit mass, that is, the change degree of the internal and external forces when the lifting arm hydraulic system works;

[0180] Considering system uncertainties, rewrite Equation (12) as

[0181]

[0182] where represents the nominal value of f(x), and Δf(x) represents the perturbation of f(x), represents the nominal value of g, and Δg represents the perturbation of g.

[0183] Step 2: Construct a fuzzy adaptive sliding mode controller based on a high-gain observer;

[0184] Construct a high-gain observer to estimate the unmeasurable system states in the hydraulic system and improve the observation accuracy and response speed capabilities.

[0185] Step 2-1: Construct a high-gain state observer based on the established mathematical model;

[0186] Define the extended state x 4 = w, where w = Δf(x)+Δbu + d represents the total perturbation of the system, and this term is bounded;

[0187] Define the system state X = (x 1 , x 2 , x 3 x 4 ), the observed value of the system state The system output y = x 1 represents the displacement vector of the hydraulic cylinder rod;

[0188] Design a high-gain observer as shown in Equation (40):

[0189]

[0190] where represents the estimation error of the extended state observer, and α i (i = 1, 2, 3, 4) and σ are positive constants;

[0191] Define the sensing error of the high-gain observer as:

[0192]

[0193] Then the dynamic equation of the observation error between the actual perturbation and the estimated perturbation is as shown in Equation (42):

[0194]

[0195] Further arranging it gives:

[0196]

[0197] Among them, If A satisfies the Hurwitz criterion, its eigenvalues are negative. At this time, the observation error is stable. Therefore, it is necessary to select an appropriate α i (i = 1, 2, 3, 4) satisfies the Hurwitz criterion;

[0198] λ(s) = |sI - A| = λ 4 +α 1 λ 3 +α 2 λ 2 +α 3 λ + α 4 = 0 (45)

[0199] Select α 1 = 6, α 2 = 11, α 3 = 6, α 4 = 6. At this time, the eigenvalues are λ 1 = -2.8805 + 0.8099i, λ 2 = -2.8805 - 0.8099i, λ 3 = -0.1195 + 0.8099i, λ 4 = -0.1195 - 0.8099i;

[0200] For any given symmetric positive definite matrix Q, there exists a symmetric positive definite matrix P that satisfies the following Lyapunov equation:

[0201] A T P + PA + Q = 0 (46)

[0202] Define the Lyapunov function of the observer as:

[0203] V o = εη T Pη (47)

[0204] Taking the derivative gives

[0205]

[0206] And

[0207]

[0208] Among them, λ min (Q) is the minimum eigenvalue of Q, and L is the upper bound;

[0209] From it can be obtained that the convergence condition of the observer is

[0210]

[0211] By analyzing the characteristics of the observer, it can be obtained that for the system measurement error and the system modeling uncertainty caused by external wind, waves and currents, a high-gain observer can be used to overcome them. When a sufficiently large observation gain is selected, the system observation error can converge to an arbitrarily small value, but the selection of its parameter values also needs to be balanced between maintaining the system robustness and accelerating the response rate of the controller.

[0212] Step 2-2: Construct a sliding mode controller using the system state estimated by the high-gain state observer; define the desired position of the hydraulic cylinder piston rod as x d , then the error is defined as

[0213]

[0214] Define the sliding mode surface as

[0215] s = λ 2 e 1 + 2λe 2 + e 3 (24)

[0216] Taking the derivative, we get

[0217]

[0218] where

[0219]

[0220] Design

[0221]

[0222] where

[0223]

[0224] To prove the stability of the control system, define the Lyapunov function Taking the derivative, we get

[0225]

[0226] Define

[0227]

[0228] Then

[0229]

[0230] Define The upper bound of is Δ max , which represents the total error of the extended state observer and is transformed into

[0231]

[0232] Furthermore, it can be obtained that

[0233]

[0234] Take Then

[0235]

[0236] Since V s ≥ 0, when t → ∞, The convergence speed depends on the control gain k and the observer parameter ε;

[0237] Considering the closed-loop system composed of the observer and the controller comprehensively, the Lyapunov function is V = V s + V o Then

[0238]

[0239] Taking a sufficiently large k and a sufficiently small ε can ensure that Thus, when t → ∞, s → 0, e → 0, The convergence speed depends on the control gain k and the observer parameter ε.

[0240] Compared with the conventional control method, the sliding mode control can make the control input of the system change continuously with the sign function, that is, it has discontinuous control characteristics. This control characteristic enables the system to have a sliding mode, and under certain conditions, it can make the system tracking error jitter slightly and frequently up and down along the designed sliding mode surface.

[0241] Step 3: Use the constructed high-gain state observer and sliding mode controller to control the lifting arm hydraulic system to disassemble the jacket offshore platform integrally.

[0242] Combined with the above embodiments, the following specific examples are proposed. It can be understood that the following specific examples only exemplarily elaborate on the specific implementation of the above embodiments, and do not limit the technical solutions of the above embodiments.

[0243] 1. Simulation module construction and parameter setting

[0244] Aiming at the problem that the system state is unmeasurable under strong interference conditions, a high-gain state observer is applied to accurately and quickly estimate the system state. During the simulation process, the controller parameters are set as shown in Table 1.

[0245] Table 1 Parameter setting of the fuzzy adaptive sliding mode controller based on the high-gain observer

[0246]

[0247] Set the desired trajectories representing low-speed lifting and high-speed lifting:

[0248]

[0249] 2. Control performance of multiple control algorithms under different sea condition scenarios

[0250] Taking the low-speed lifting desired trajectory 1 as a benchmark, analyze the control performance of multiple control algorithms under different sea condition scenarios, and introduce multiple simulated sea conditions as shown in Table 2.

[0251] Table 2 Multiple sea condition interference signals with variable force rates

[0252]

[0253] Apply real-time interference under different simulated sea conditions to the lifting arm hydraulic system, and obtain the comparison of the experimental results of the control algorithm in this paper and the control algorithms in the previous two chapters as Figures 3 - 6 shown.

[0254] By analyzing the experimental results, it can be known that:

[0255] In terms of control accuracy, under simulated sea condition 1, the steady-state error of the sliding mode controller is 1.14 mm, and the steady-state error of the robust controller is 1.05 mm. The overall steady-state control accuracy of the sliding mode controller and the robust controller is not much different; under simulated sea condition 2, the steady-state error of the sliding mode controller is 3.5 mm, and the steady-state error of the neural network controller is 1.51 mm. The control accuracy of the sliding mode controller is weaker than that of the neural network controller; under simulated sea condition 3, the sliding mode controller fluctuates at 0.4 s, with a maximum error of 5.2 mm and a steady-state error of 1.51 mm. The neural network controller fluctuates at 0.5 s, with a maximum error of 17.5 mm and a steady-state error of 1.65 mm. The sliding mode controller can achieve better control accuracy compared with the neural network controller; under simulated sea condition 4, the sliding mode controller has a large steady-state error of 7.1 mm, and the steady-state error of the neural network controller is 1.2 mm. The performance of the sliding mode controller is poor compared with the neural network controller.

[0256] In terms of response speed, compared with the robust controller and the neural network controller, the sliding mode controller can achieve a rapid response of the error in the initial stage.

[0257] In summary, the sliding mode controller can achieve high-precision steady-state control of the lifting arm hydraulic system under high-amplitude and high-frequency extreme sea conditions, and has the advantages of simple structure, small computational load, and fast response speed.

[0258] So far in the embodiments of the present invention, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A sliding mode control method for the hydraulic system of the integrated disassembly lifting arm of a jacket offshore platform, characterized in that: The steps include: Step 1: mathematically model the hydraulic system of the integrated disassembly lifting arm of the jacket offshore platform; Step 2: construct a fuzzy adaptive sliding mode controller based on a high-gain observer, wherein the controller includes a high-gain state observer and a sliding mode controller; Step 3, using the constructed high-gain state observer and sliding mode controller to control the lifting arm hydraulic system to dismantle the jacket offshore platform integration; The mathematical modeling of the hydraulic system of the jacket offshore platform integrated disassembly lifting arm described in step 1 includes: Step 1-1, simplifying the lifting arm hydraulic system based on the idea of ​​reducing the complexity of the hydraulic system, and obtaining the lifting arm valve-controlled asymmetric hydraulic cylinder system, wherein the idea of ​​reducing the complexity of the hydraulic system is to regard the hydraulic pump as the output unit of the controller, establish a lifting arm hydraulic system mathematical model around the hydraulic cylinder and its associated hydraulic valve, classify the influencing factors of the hydraulic cylinder and the hydraulic valve and other components into the modeling uncertainty, and make unified processing and compensation for the complex modeling uncertainty combined with external interference in the controller; Step 1-2, based on the lift arm valve-controlled asymmetric hydraulic cylinder system structure, establish the hydraulic cylinder load dynamics equation, the flow calculation equation of the rodless chamber and the rod chamber of the hydraulic cylinder, and the pressure flow dynamic equation of the rodless chamber and the rod chamber of the hydraulic cylinder in the lift arm hydraulic system, and combine these three equations to establish the state space equation of the lift arm hydraulic system; Step 2 constructs a fuzzy adaptive sliding mode controller based on a high-gain observer, including: Step 2-1, constructing a high-gain state observer based on the established mathematical model; Step 2-2: Construct a sliding mode controller using the system state estimated by a high-gain state observer.

2. The sliding mode control method for the hydraulic system of the integrated dismantling lifting arm of the jacket offshore platform according to claim 1 is characterized in that: The specific process of steps 1-2 is as follows: For the lift arm valve-controlled asymmetric hydraulic cylinder system, the extension direction of the hydraulic cylinder piston rod is taken as the positive direction, and the hydraulic cylinder load dynamics equation is established according to Newton's second law, as shown in the formula As shown: in, For a single lifting arm lifting weight, and are the cross-sectional areas of the rodless and rod-bearing chambers of the hydraulic cylinder, and are the pressures in the rodless and rod chambers of the hydraulic cylinder, respectively. is the control gain of the lifting arm hydraulic system, is the viscous damping coefficient of the hydraulic cylinder, is the piston rod speed of the hydraulic cylinder, is the unknown disturbance force on the hydraulic cylinder, is the coupling force on the hydraulic cylinder; The flow equation of the hydraulic cylinder proportional servo valve is established to establish a correlation with the dynamic equation. In order to simplify the modeling process, the following assumptions need to be met: Assumption 1: The proportional servo valve used in the lifting arm hydraulic system should be a four-way slide valve with an ideal zero-opening structure, and the four throttling windows should be fully matched and symmetrical; Assumption 2: The flow characteristics of the liquid at the throttling window are turbulent flow, and the density change of the hydraulic oil is small, and the compressibility of the hydraulic oil inside the valve is negligible; Assumption 3: The oil supply pressure of the lifting arm hydraulic system is constant, the oil supply pipeline loss and pipeline dynamic characteristics are ignored, the return oil pressure is zero, and the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder meets , ,in is the tank supply pressure, is the system supply pressure; When the hydraulic cylinder piston rod is extended, the flow rate of the rodless chamber and the rod chamber of the hydraulic cylinder is calculated as follows: As shown: in, and are the flow rates of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, is the throttle flow coefficient of the proportional servo valve, is the orifice area gradient, is the hydraulic oil density, is the valve core displacement of the proportional servo valve; Similarly, when the hydraulic cylinder retracts, the flow rate flowing into the rodless chamber and the rod chamber of the hydraulic cylinder through the proportional servo valve is calculated as follows: As shown: In order to facilitate the expression of the proportional servo valve flow equation, the proportional servo valve flow gain coefficient is defined as As the formula As shown: Comprehensive formula - It can be obtained that the comprehensive calculation of the flow rate flowing into the rodless chamber and the rod chamber of the hydraulic cylinder through the proportional servo valve is as follows: As shown: In the formula, represents a semi-symbolic function, specifically: Since the response speed of the proportional servo valve is much higher than the bandwidth of the lifting arm hydraulic system, the expansion and contraction process of the proportional servo valve core displacement can be approximated as a proportional process during the control process. With control input The approximate expression of As shown: in, is the voltage-spool displacement gain of the proportional servo valve; Finally, the flow calculation equations for the rodless chamber and the rod chamber of the hydraulic cylinder with control input are as follows: As shown: in, Relative to the control input Total flow gain; According to the calculated flow of the rodless chamber and the rod chamber of the hydraulic cylinder and , the dynamic equations of pressure and flow of the rodless and rod chambers of the hydraulic cylinder can be further established. According to the sealing and internal liquid characteristics of the hydraulic cylinder, the following assumptions must be met when establishing the dynamic equations of pressure and flow of the rodless and rod chambers of the hydraulic cylinder: Assumption 3: The pressure in each working chamber of the hydraulic cylinder is equal, and the hydraulic oil temperature and bulk elastic modulus are constants; Assumption 4: The internal and external leakage of the hydraulic cylinder are both laminar flows; Considering the oil compressibility of the lifting arm hydraulic system during disassembly operations, the dynamic equations of pressure and flow in the rodless and rod chambers of the hydraulic cylinder are as follows: As shown: in, is the elastic modulus of hydraulic oil, is the leakage coefficient in the hydraulic cylinder, and The uncertainty of the parameters and modeling errors of the defined rodless and rod-containing cavities are: and is the volume of the rodless chamber and the rod chamber of the hydraulic cylinder. The calculation process is as follows: As shown: in, and are the initial volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, and are the cross-sectional areas of the rodless and rod-bearing chambers of the hydraulic cylinder, is the displacement of the hydraulic cylinder piston rod; Define system state variables , according to the hydraulic cylinder load dynamics equation , Flow calculation equations for the rodless and rod chambers of hydraulic cylinders , Dynamic equations of pressure and flow in the rodless and rod chambers of hydraulic cylinders And the defined state variables , the state space equation of the lifting arm hydraulic system is obtained, as shown in the formula As shown: in, Indicates the correlation coefficient of the lifting arm hydraulic system, It represents the lumped uncertainty of the lifting arm hydraulic system caused by the external wind, wave and current interference and the nonlinearity of the system. The derivation results of the specific parameters in the lifting arm hydraulic system state equation are as follows: As shown: exist In the expression of and The change of is small, the area of ​​the rodless cavity and the rod cavity is close, so the nonlinear term The value of is also small, interfering with the expression term It can be mainly regarded as the force variation rate caused by various internal and external uncertainties under unit mass, that is, the degree of variation of internal and external forces when the lifting arm hydraulic system is working; Considering the system uncertainty, Rewrite as in, express The nominal value of express The disturbance, express The nominal value of express of disturbance.

3. The sliding mode control method for the hydraulic system of the integrated dismantling lifting arm of the jacket offshore platform according to claim 2 is characterized in that: The specific process of step 2-1 is as follows: Defining extended states ,in represents the total disturbance of the system, which is bounded; Defining system status , system state observation value , system output represents the displacement vector of the hydraulic cylinder rod; Design a high-gain observer as shown in Eq. As shown: in, represents the estimation error of the extended state observer, and is a positive constant; The perception error of the high-gain observer is defined as: The dynamic equation for the observed error between the actual disturbance and the estimated disturbance is as follows: As shown: Further arranging it yields: in, , ,like If the Hurwitz criterion is satisfied, the eigenvalue is negative and the observation error is stable. Therefore, it is necessary to choose a suitable Satisfy the Hurwitz criterion; choose , , , , then the eigenvalue is , , , ; For any given symmetric positive definite matrix , there exists a symmetric positive definite matrix Satisfies the following Lyapunov equation: The Lyapunov function of the observer is defined as: Derivation and in, for The minimum eigenvalue of for upper bound; Depend on The convergence condition of the observer is 4. The sliding mode control method for the hydraulic system of the integrated dismantling lifting arm of the jacket offshore platform according to claim 3 is characterized in that: The specific process of step 2-2 is as follows: Define the desired position of the hydraulic cylinder piston rod as , then the error is defined as (23) The sliding surface is defined as (24) Derivation (25) in (26) design (27) in (28) (29) To prove the stability of the control system, define the Lyapunov function , and we can get (30) definition (31) but (32) definition The upper bound of , which represents the total error of the extended state observer, is converted to (33) Then we can get (34) Pick ,but (35) because , so hour, , the convergence speed depends on the control gain and observer parameters ; Considering the closed-loop system composed of the observer and the controller, the Lyapunov function is ,but (36) Take a large enough and small enough , which can be guaranteed ,thereby hour, , , , the convergence speed depends on the control gain and observer parameters .

Images