A Rotary Column Cooperative Stabilization Control System Applicable to Marine Mobile Observation Platforms

Abstract

The present invention is a column-rotor cooperative stabilization control system applicable to marine mobile observation platforms, belonging to the field of motion control systems for marine mobile observation platforms, and aims to improve the operation stability of marine mobile observation platforms. The specific steps are as follows: Establish a column-rotor lift force model and a non-linear rolling model of the marine mobile observation platform to provide a theoretical basis for column-rotor cooperative stabilization control; Design a sliding mode torque controller based on an RBF neural network, receive the total anti-rolling torque, predict the rolling model and generate a control law to ensure that the output tracks the expectation; Establish a cooperative allocation controller based on the sequential quadratic programming method, obtain the column-rotor state in real time and allocate weights, optimize the allocation of anti-rolling torque, and achieve optimal control; Adopt a motor follow-up system to quickly respond to the expected speed and adjust the working state of the column-rotor. The present invention not only has a good stabilization effect, but also takes into account the driving power consumption and dynamic performance of each actuator, and is more conducive to the stable operation and long-distance navigation of marine mobile observation platforms.

Description

Technical Field

[0001] The present invention relates to the field of ocean engineering equipment, especially to the field of motion control systems for ocean mobile observation platforms, and specifically to a column-rotor collaborative stabilization control system applicable to ocean mobile observation platforms. Background Art

[0002] With the increasing emphasis on ocean development at home and abroad, the research and manufacturing of ocean engineering equipment have developed rapidly. Among them, ocean mobile observation platforms represented by polar icebreakers, semi-submersible transport ships, and scientific research ships have become increasingly significant in ocean field observations.

[0003] However, due to the complex and changeable ocean environment, an ocean mobile observation platform in operation is prone to violent shaking, which will, at the least, affect the observation efficiency and, at the worst, cause safety accidents. Considering that stability is of great significance for the smooth progress of observation tasks and the accuracy of data, anti-rolling equipment is generally installed on ocean mobile observation platforms to maintain stability. As a new type of anti-rolling device, the column-rotor anti-rolling device has excellent anti-rolling performance, low power consumption, and less occupied space. Currently, most control studies on column-rotor anti-rolling devices mainly focus on single pairs of column-rotor anti-rolling devices, and generally use simple and effective PID controllers to achieve stability. However, when an ocean mobile observation platform conducts long-term observations, it will inevitably encounter complex sea conditions, and the anti-rolling effect of the PID controller is not ideal for nonlinear complex sea conditions. Therefore, it is very important to design a control system for nonlinear complex sea conditions to improve the stability of ocean mobile observation platforms.

[0004] Considering that an ocean mobile observation platform will encounter special sea conditions during observation operations, the anti-rolling device faces a huge test. Relying solely on a pair of column-rotor anti-rolling devices cannot meet the stability requirements, or when some columns suddenly fail, it will lead to the lack of a stability mechanism for the ocean mobile observation platform. Therefore, installing multiple pairs of column-rotor anti-rolling devices can not only increase the stability performance of the ocean mobile observation platform but also overcome the difficulties brought by partial column failures through column-rotor collaborative stabilization. Currently, the research on the collaborative control of multiple pairs of column-rotor anti-rolling devices is still insufficient. Therefore, it is very important to carry out research on the collaborative control of multiple pairs of column-rotor anti-rolling devices.

[0005] (1) The paper "Design and Characteristic Analysis of Anti-rolling Tanks for Polar Scientific Research Ships" designed an improved anti-rolling tank for polar scientific research ships working in harsh environments, effectively reducing the rolling motion of polar scientific research ships and ensuring their ability to continuously operate at sea. However, there are the following problems: ① The anti-rolling tank occupies a large space; ② The anti-rolling tank can only function when its natural rolling frequency is greater than the rolling frequency, which has certain limitations.

[0006] (2) The papers "Research on the Design and Control Characteristics of Magnus Rotary Stabilizer" and "Research on the Hydrodynamic Performance of Marine Magnus" both use the PID control system for simulation and obtain good anti-rolling effects by comparing before and after anti-rolling. However, the following problems exist: ① It ignores that the swinging column has almost no anti-rolling effect during a specific period, increasing the driving energy consumption; ② Using an ideal linear ship rolling model does not consider the actual environment. If a non-linear ship rolling model is used, the anti-rolling effect of the PID controller is not ideal.

[0007] (3) The paper "Research on Control Allocation Technology for Overactuated Surface Vehicles" uses the generalized inverse allocation strategy to solve the possible singularity in the thrust allocation process, optimize the thruster system configuration, improve the system performance and fault tolerance ability, so as to ensure the stable operation and high efficiency of the surface vehicle. However, the following problems exist: ① The allocation method based on the generalized inverse cannot take into account the physical constraints of each actuator; ② It requires all actuators to participate in the allocation, reducing the flexibility of the control allocation of redundant actuators.

[0008] (4) The paper "Performance Analysis and Experimental Research on Ship Stabilizer Based on Magnus Effect" aims at surface ships equipped with two pairs of column stabilizers, analyzes the lift performance of the stabilizer at zero speed, low speed and above the critical speed, and explores the anti-rolling effect of the anti-rolling system when some column stabilizers do not work. However, the following problems exist: ① It ignores the interference of the external environment on the lift performance of the column; ② It does not solve the problem of low anti-rolling efficiency when some columns do not work. Summary of the Invention

[0009] Based on the above existing problems, the present invention designs a column cooperative stabilization control system suitable for marine mobile observation platforms through optimization theory and control theory, solves the problem of poor anti-rolling effect in a short period, reduces the driving loss of the column stabilizer, improves the anti-rolling efficiency when some columns do not work, and ensures the observation quality and navigation stability for marine mobile observation platforms encountering special sea conditions.

[0010] To achieve the above object, the technical solution adopted by the present invention is as follows: Design a column cooperative stabilization control system suitable for marine mobile observation platforms, including a sliding mode torque controller based on RBF neural network, a cooperative allocation controller based on sequential quadratic programming method, a motor follow-up system, a column stabilizer composed of four columns, a marine mobile observation platform model, a lift feedback mechanism and an angle sensor.

[0011] S1: Establish a mathematical model of the lift of a single column and a non-linear rolling model of a marine mobile observation platform equipped with two pairs of columns, providing a theoretical basis for the subsequent establishment of a column cooperative stabilization control system. The process is as follows:

[0012] S1.1: Set the radius of the fixed end of a single variable-diameter cylinder as r1, the diameter ratio as λ, introduce the Kutta-Joukowski theorem, and set the correction parameters K and B related to the rotational speed and the ship speed to correct the deviation between the theory and the actual situation. Divide the ship speed conditions by taking 3 kn as the boundary through integrating the literature and simulation data. Then the lift force F of a single variable-diameter cylinder L i is:

[0013]

[0014] In the formula: ρ is the fluid density (kg / m 3 ), ω i is the angular velocity of self-rotation of a single variable-diameter cylinder (rad / s), is the angular velocity of swing of a single variable-diameter cylinder, L is the length of the span of a single variable-diameter cylinder (m), r1 is the radius of the fixed end of a single variable-diameter cylinder (m), λ is the diameter ratio of a single variable-diameter cylinder, V is the oncoming flow velocity (m / s), θ i is the swing angle of a single variable-diameter cylinder (rad);

[0015] S1.2: Define the ship speed V as the relative oncoming flow velocity between the marine mobile observation platform and the sea water. F i ′ is the actual lift force generated by the i-th rotating cylinder, r rw is the anti-rolling force arm of the rotating cylinder anti-rolling device, r M is the distance between the lift center of the rotating cylinder anti-rolling device and the center of gravity of the ship's hull. ε is the angle between the rolling arm of the rotating cylinder anti-rolling device and the sea level line. Then the anti-rolling force arm r rw and the total anti-rolling moment generated are:

[0016] r rw = r M cosε (2)

[0017]

[0018] Combining formula (2) and formula (3), the nonlinear rolling model of the marine mobile observation platform equipped with two pairs of rotating cylinder anti-rolling devices is:

[0019]

[0020] In the formula: I x and ΔI x are the moment of inertia and the added inertia of the marine mobile observation platform (kg·m 2 ), φ is the rolling angle (rad), B1, B2, C2, C3 are the relevant parameters of the marine mobile observation platform, D is the displacement (t), h is the transverse metacentric height of the marine mobile observation platform (m), α f is the effective wave inclination angle (rad), K cis the total anti-rolling moment (N·m) generated by the rotary column anti-rolling device.

[0021] S2: Establish a sliding mode torque controller based on the RBF neural network. It is used to receive the input total anti-rolling moment, introduce the RBF neural network to predict the unknown rolling model of the ship, and design the anti-rolling moment control law based on the sliding mode control algorithm, so that the output of the system can always track the desired output of the system. The process is as follows:

[0022] S2.1: The state-space expression of the nonlinear rolling motion model of the marine mobile observation platform is:

[0023]

[0024] In the formula: The parameters of the marine mobile observation platform model are mainly concentrated in f(x), so it can be regarded as the marine mobile observation platform model, and d(t) = a7α f , K T is the control output of the torque controller, representing the total anti-rolling moment;

[0025] Set the sliding mode surface as According to formula (7), the ideal control law of the sliding mode torque controller is:

[0026]

[0027] In the formula: c is the control gain, η is the switching gain, and e is the error between the desired output and the actual output;

[0028] S2.2: Introduce the RBF neural network to predict the unknown rolling model of the marine mobile observation platform and improve the accuracy of the control law. Among them, the activation function of the neural network is the Gaussian basis function h(x), and the output of the Gaussian basis function is h = [h1, h2,..., h n T . To make the error e and the parameter error of the RBF network as small as possible, the neural network should approximate the controlled model in real time and dynamically. Therefore, the parameter variation law of the neural network can be designed as:

[0029]

[0030] In the formula: is the actual network weight, γ is the adaptive change parameter of the neural network, then the following formula holds:

[0031]

[0032] In the formula: is the rolling model of the marine mobile observation platform predicted by the RBF neural network, ε is the approximation error between the predicted rolling model and the ideal model, then the sliding mode torque control law based on the RBF neural network is:​

[0033]

[0034] where: c is the control gain, and η is the switching gain.

[0035] S3: Establish a cooperative allocation controller based on the sequential quadratic programming method. It is used to obtain the actual working state of each rotating column in real time and assign allocation weights, and then establish a multi-objective optimization function to calculate the total anti-rolling moment K required for the ocean mobile observation platform to counteract rolling by the sliding mode torque controller T Substitute into the formula, and finally seek the optimal distribution of the anti-rolling moment among the three indicators of anti-rolling effect, energy consumption economy, and system stability through the sequential quadratic programming method. The process is as follows:

[0036] S3.1: Considering the interference of the external environment on the rotating column, the system introduces a lift feedback mechanism. By taking into account the internal and external states of each rotating column, the cooperative allocator can more reasonably distribute the anti-rolling moment according to the actual working state of the anti-rolling device of each rotating column, calculate the control signal, so that they cooperate with each other;

[0037] S3.2: Balancing the three indicators of anti-rolling effect, energy consumption economy, and system stability involves a complex optimization problem, and a unified multi-objective optimization function needs to be constructed. Let the following multi-objective optimization function be set:

[0038]

[0039] where: n d = [n d1 , n d2 , n d3 , n d4 is the desired rotational speed of each rotating column, that is, the control signal output by the cooperative allocator, Δn d is the change in the desired rotational speed of the rotating column anti-rolling device, i is the number of indicators, t is the simulation step size, p i is the weight of each performance indicator, J i (k) is each indicator of the multi-objective optimization function;

[0040] (1) Setting of the anti-rolling effect index:

[0041]

[0042] where: K i (k) is the theoretical anti-rolling moment generated by each rotating column at the k-th moment. Combining equations (1) and (3), its expression can be obtained as:

[0043]

[0044] where: n di (k), θi (k) and is the internal state of the i-th rotating column at the k-th moment, representing the expected rotational speed, swing angle and swing angular velocity of the rotating column respectively, δ i (k) is the external efficiency factor generated by each rotating column in its respective working environment at the k-th moment;

[0045] (2) Setting of energy consumption economy index:

[0046]

[0047] (3) Setting of stability index:

[0048]

[0049] S3.3: For solving the nonlinear programming problem of the multi-objective optimization function, the sequential quadratic programming method can be used to solve it. First, the nonlinear programming problem is transformed into the following quadratic programming sub-problem by Taylor expansion at the n-th step:

[0050]

[0051] In the formula: d n is the optimal solution of the quadratic programming sub-problem and also the advancing direction of the current iteration point, g i (·) and c j (·) are the general expression forms of inequality constraints and equality constraints respectively, and are the Jacobian matrices of inequality constraints and equality constraints respectively, H n is the Hessian matrix of the Lagrangian function;

[0052] The BFGS method, i.e., the quasi-Newton method, is used to approximately solve the Hessian matrix of the Lagrangian function, and its expression is:

[0053]

[0054] S4: Use the motor follow-up system to transmit the expected rotational speed of each rotating column calculated by the cooperative distributor to the drive motors of each rotating column in the form of electrical signals, so that they can respond quickly, adjust the existing working state, rotate at the expected rotational speed, and act the generated anti-rolling torque on the marine mobile observation platform model to resist the rolling caused by wave interference. Finally, the rolling situation of the marine mobile observation platform is fed back to the controller through the angle sensor.

[0055] The present invention has the following beneficial effects:

[0056] (1) Compared with other anti-rolling devices, the rotating column anti-rolling device has the advantages of small driving power, small occupied space, low cost, and continuous provision of stable torque. Moreover, the anti-rolling torque can be increased by adding the number of rotating columns, and it is applicable in sea conditions at full speed.

[0057] (2) A cooperative stability strategy is designed for the stability system with two pairs of rotating column anti-rolling devices. Each rotating column is independently controlled to make them work together synergistically, taking into account the internal and external states of the rotating column anti-rolling device, interacting with the environment in real time, facilitating the flexible adjustment of lift, and optimizing the problem of poor anti-rolling effect in a short period. Considering three indicators of anti-rolling performance, energy consumption economy, and stability, the optimal distribution of the anti-rolling torque of each rotating column anti-rolling device is completed, achieving the best anti-rolling effect, energy consumption economy, and stability, and ensuring the observation quality and navigation stability for the marine mobile observation platform encountering special sea conditions.

[0058] (3) Compared with the PID stability control system of the conventional stability strategy, this cooperative stability control system has excellent anti-rolling performance when facing the wave interference in high sea conditions. The anti-rolling efficiency is 85.8%, which is better than 72.3% of the PID stability control system, and the stability effect is improved by 13.5%. In the case of the failure of some rotating column anti-rolling devices, its anti-rolling efficiency remains unchanged, while the anti-rolling efficiency of the PID stability control system drops to 63.4% respectively, verifying the feasibility of the theory and reflecting the superiority of this cooperative stability control system. Description of the Drawings

[0059] Figure 1 is a structural block diagram of a rotating column cooperative stability control system applicable to a marine mobile observation platform;

[0060] Figure 2 is a schematic diagram for the analysis of a variable-diameter cylinder model;

[0061] Figure 3 is a schematic diagram of the stability mechanism of a marine mobile observation platform;

[0062] Figure 4 is a calculation flow chart of the external efficiency factor;

[0063] Figure 5 is a flow chart of the sequential quadratic programming algorithm;

[0064] Figure 6 are the simulation results of the roll angle and rotational speed at a speed of 1 kn and 10 kn in high sea conditions;

[0065] Figure 7 are the simulation results of the roll angle and rotational speed of the cooperative stability control system and the PID stability control system at a speed of 1 kn in high sea conditions. Detailed Implementation Manner

[0066] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0067] Embodiment: As Figure 1 shown, Figure 1 Fig. is a structural block diagram of a rotary column cooperative stabilization control system applicable to a marine mobile observation platform, including: a sliding mode torque controller based on an RBF neural network, a cooperative allocation controller based on the sequential quadratic programming method, a motor follow-up system, a rotary column anti-rolling device composed of four rotary columns, a marine mobile observation platform model, a lift feedback mechanism, and an angle sensor. The specific steps are as follows:

[0068] S1: Establish a mathematical model of the lift of a single rotary column and a nonlinear rolling model of a marine mobile observation platform equipped with two pairs of rotary column anti-rolling devices, which provides a theoretical basis for the subsequent establishment of a rotary column cooperative stabilization control system. The process is as follows:

[0069] S1.1: Considering that the shapes of rotary columns are diverse and the lift model of a conventional cylindrical column cannot achieve full coverage, a variable-diameter cylindrical column with a regularly changing shape is selected as the research object to achieve full coverage of the rotary column lift model. As Figure 2 shown, set the fixed-end radius of a single variable-diameter cylindrical column as r1, the diameter ratio (the ratio of the radius of the swinging end to the radius of the fixed end) as λ, introduce the Kutta-Joukowski theorem, and set the correction parameters K and B related to the rotational speed and the ship speed to correct the deviation between the theory and the actual situation. The ship speed conditions are divided by 3 kn by integrating literature and simulation data. Then the lift F of a single variable-diameter cylindrical column L i is:

[0070]

[0071] In the formula: ρ is the fluid density (kg / m 3 ), ω i is the angular velocity of self-rotation of a single variable-diameter cylindrical column (rad / s), is the angular velocity of swinging of a single variable-diameter cylindrical column, L is the length of a single variable-diameter cylindrical column (m), r1 is the fixed-end radius of a single variable-diameter cylindrical column (m), λ is the diameter ratio of a single variable-diameter cylindrical column, V is the oncoming flow velocity (m / s), θ i is the swinging angle of a single variable-diameter cylindrical column (rad);

[0072] S1.2: As Figure 3As shown in the figure, assume that an ocean mobile observation platform is sailing along a fixed direction, and two pairs of fin stabilizers are symmetrically installed on both sides of it. The rolling direction of the hull is defined as from the port side to the starboard side of the ship, the sailing speed V is the relative incoming flow velocity between the ocean mobile observation platform and the sea water, and F i ′ is the actual lift generated by the i-th fin, and r rw is the anti-rolling arm of the fin stabilizer, and r M represents the distance between the lift center of the fin stabilizer and the center of gravity of the ship's hull. ε is the angle between the rolling arm of the fin stabilizer and the sea level line, then the anti-rolling arm r rw and the total anti-rolling moment generated are:

[0073] r rw = r M cosε (2)

[0074]

[0075] Combining Equation (2) and Equation (3), the nonlinear rolling model of the ocean mobile observation platform equipped with two pairs of fin stabilizers is:

[0076]

[0077] Where: I x and ΔI x are the moment of inertia and added inertia of the ocean mobile observation platform (kg·m 2 ), φ is the rolling angle (rad), B1, B2, C2, C3 are the relevant parameters of the ocean mobile observation platform, D is the displacement (t), h is the metacentric height of the ocean mobile observation platform (m), α f is the effective wave inclination angle (rad), and K c is the total anti-rolling moment generated by the fin stabilizer (N·m).

[0078] S2: Establish a sliding mode torque controller based on the RBF neural network. It is used to receive the input total anti-rolling moment K T , introduce the RBF neural network to predict the unknown rolling model of the ship and design the anti-rolling torque control law based on the sliding mode control algorithm, so that the output y (the rolling angle φ of the ocean mobile observation platform) of the system can always track the expected output y d (the expected rolling angle φ d = 0) of the ocean mobile observation platform. The process is as follows:

[0079] S2.1: Let y = φ = x1, and assume that the total anti-rolling moment K T is directly used as the input of the controlled model. From Equation (4), the state space expression of the nonlinear rolling motion model of the ocean mobile observation platform is:

[0080]

[0081] Where: a f is the effective wave tilt angle of the ocean wave, and a1 to a7 are the coefficients generated during the formula transformation;

[0082] Since the ocean mobile observation platform is affected by many disturbances and unknown factors when sailing in high sea conditions with strong winds and waves, the structure of the ocean mobile observation platform is prone to uncertain parameter changes under this influence. Therefore, the formula needs to be sorted out as:

[0083]

[0084] Where: The parameters of the ocean mobile observation platform model are mainly concentrated in f(x), so it can be regarded as the ocean mobile observation platform model. And d(t) = a7α f , K T is the control output of the torque controller, representing the total anti-rolling torque;

[0085] According to Equation (6), the error e between the expected output and the actual output is defined as:

[0086] e = y d -y = -x1 (7)

[0087] Set the sliding mode surface as According to Equation (7), the ideal control law of the sliding mode torque controller is:

[0088]

[0089] Where: c is the control gain, and η is the switching gain;

[0090] S2.2: Considering that the structure of the real ocean mobile observation platform will change unknownly during navigation, an RBF neural network is introduced to predict the unknown rolling model of the ocean mobile observation platform to improve the accuracy of the control law. Among them, the activation function of the neural network is the Gaussian basis function h(x), and the output of the Gaussian basis function is h = [h1, h2,..., h n T , x is the state variable in Equation (6) and is used as the input of the neural network at the same time. Then the output of the jth neuron node in the hidden layer is:

[0091]

[0092] Where: c ij is the center vector of the jth neuron corresponding to the ith network input, and b j is the basis width of the jth neuron;

[0093] ​To minimize the error e and the parameter error of the RBF network as much as possible, the neural network should approximate the controlled model in real time and dynamically. Therefore, the parameter variation law of the neural network can be designed as follows:

[0094]

[0095] In the formula: is the actual network weight, γ is the adaptive change parameter of the neural network, then the following formula holds:

[0096]

[0097] In the formula: is the roll model of the ocean mobile observation platform predicted by the RBF neural network, and ε is the approximation error between the predicted roll model and the ideal model;

[0098] According to the function approximation theory of the RBF neural network, when there are enough neurons, the approximation error ε of the network approaches 0, that is, the predicted roll model of the ocean mobile observation platform approaches the ideal roll model. Introduce the saturation function sat(s) to replace the sign function sgn(s) and combine with formula (8) to obtain the sliding mode torque control law based on the RBF neural network as follows:

[0099]

[0100] In the formula: The control gain c and the switching gain η should reasonably select the parameter values and should not be too large.

[0101] S3: Establish a cooperative allocation controller based on the sequential quadratic programming method. It is used to obtain the actual working state of each rotating column in real time and assign allocation weights, and then establish a multi-objective optimization function to calculate the total anti-roll torque K required for the ocean mobile observation platform to resist roll by the sliding mode torque controller T Substitute it into the formula, and finally seek the optimal distribution of the anti-roll torque among the three indexes of anti-roll effect, energy consumption economy and system stability through the sequential quadratic programming method. The process is as follows:

[0102] S3.1: Considering the interference of the outside world on the rotating column, the system introduces a lift feedback mechanism. By taking into account the internal and external states of each rotating column, the cooperative allocator can more reasonably distribute the anti-roll torque according to the actual working state of each rotating column, calculate the control signal, so that they cooperate with each other, as Figure 4 shown, where is the theoretical anti-roll lift of each rotating column. And n di , θ i and are the internal states of the i-th rotating column, representing the expected rotational speed, swing angle and swing angular velocity of the rotating column respectively, n i is the actual rotational speed of the i-th rotating column, F iL′(k) is the actual anti-rolling lift detected by the lift feedback mechanism of the i-th rotating column at the k-th moment. N is the detection period of the lift feedback mechanism, and δ i (k) is the external efficiency factor generated by each rotating column in its respective working environment at the k-th moment, which is used to feedback the working performance of the rotating column and the fluid interference it receives. It represents the lift generation efficiency of the rotating column under the interference of the external environment, and its initial state is 1, that is, δ i (1) = 1;

[0103] S3.2: Balancing the three indicators of anti-rolling effect, energy consumption economy and system stability involves a complex optimization problem. It is necessary to construct a unified multi-objective optimization function and comprehensively consider these three performance indicators to comprehensively improve the anti-rolling performance of the system. Therefore, the following multi-objective optimization function is set:

[0104]

[0105] In the formula: n d = [n d1 , n d2 , n d3 , n d4 is the expected rotational speed of each rotating column, that is, the control signal output by the cooperative distributor. Δn d is the change in the expected rotational speed of the rotating column anti-rolling device. i is the number of indicators, t is the simulation step size, and p i is the weight of each performance indicator. Here, they are taken as 5, 2, and 130 respectively. J i (k) are the various indicators of the multi-objective optimization function, specifically as follows:

[0106] (1) Anti-rolling effect indicator, that is, the cooperative distributor reasonably distributes the maximum total control torque K T calculated by the anti-rolling torque controller in the upper layer to the four rotating columns. The difference between the total torque generated by each rotating column and K T . The smaller the difference, the better the anti-rolling effect. Therefore, it can be set as:

[0107]

[0108] In the formula: K i (k) is the theoretical anti-rolling torque generated by each rotating column at the k-th moment. Combining formula (1) and formula (3), its expression can be obtained as:

[0109]

[0110] In the formula: n di (k), θ i (k) and are the internal states of the i-th rotating column at the k-th moment, representing the expected rotational speed, swing angle, and swing angular velocity of the rotating column respectively, and δi (k) is the external efficiency factor generated by each rotary column under its respective working environment at the k-th moment;

[0111] (2) Energy consumption economy index, that is, the energy consumption of the rotary column anti-rolling device during navigation, is mainly related to the rotational speeds of the drive motors of each rotary column. Therefore, it can be set that:

[0112]

[0113] (3) Stability index, that is, to avoid large-scale adjustment of the rotational speed of the drive motor in a short time, and ensure the rationality of the distribution effect of the cooperative distributor and the stability of the anti-rolling control system. Therefore, it can be set that:

[0114]

[0115] S3.3: For solving the nonlinear programming problem of the multi-objective optimization function, the sequential quadratic programming method can be used to solve this problem. Its core idea is: first determine the initial point of iteration, then expand the original problem into the form of a quadratic programming sub-problem at the iteration point, and then determine the next iteration direction by solving the quadratic programming problem, and re-convert the iterated original problem into a quadratic programming sub-problem at the next iteration point, and so on, until the solution that meets the nonlinear programming problem is found, as Figure 5 shown. Therefore, the iterative result n d (n) at the n-th step can be defined as:

[0116] n d (n) = n d (n - 1) + α n ×d n-1 (18)

[0117] In the formula: α n is the step size factor, and d n-1 is the iteration step size;

[0118] The nonlinear programming problem is transformed into the following quadratic programming sub-problem at the n-th step through the Taylor expansion formula:

[0119]

[0120] In the formula: d n is the optimal solution of the quadratic programming sub-problem and also the forward direction of the current iteration point, g i () and c j () are the general expression forms of the inequality constraint and the equality constraint respectively, and are the Jacobian matrices of the inequality constraint and the equality constraint respectively, and H n is the Hessian matrix of the Lagrangian function. The Lagrangian function is:

[0121] L(n d , μ, λ) = J(n d ) - μ × g i (k) - λ × c j (k) (20)

[0122] Where: μ and λ are the Lagrange multiplier vectors of the inequality constraint and the equality constraint respectively, and i and j are the numbers of the inequality constraint and the equality constraint respectively;

[0123] Since calculating H n will generate a huge amount of computation during the iteration process, the BFGS method, i.e., the quasi-Newton method, will be used to approximately solve the Hessian matrix of the Lagrangian function, and its expression is:

[0124]

[0125] Where: γ n The expression of is:

[0126]

[0127] S4: Use the motor follow-up system to transmit the expected rotational speeds of each rotating column calculated by the cooperative distributor to the drive motors of each rotating column in the form of electrical signals, so that they can respond quickly, adjust the existing working state, rotate at the expected rotational speed, and act the generated anti-rolling torque on the marine mobile observation platform model to resist the rolling caused by the wave interference. Finally, the rolling situation of the marine mobile observation platform is fed back to the controller through the angle sensor, and the process is as follows:

[0128] S4.1: To improve the reliability of the control system, select the PID control system commonly used in traditional anti-rolling systems to control the drive motor to track the control signal output by the cooperative distributor in real time. The transfer function of the PID controller is:

[0129]

[0130] Where: K P is the proportional coefficient, K I is the integral coefficient, K D is the differential coefficient;

[0131] S4.2: Since the lift force of the rotating column anti-rolling device is generated by the high-speed rotation of the drive motor, compared with the electro-hydraulic drive system of traditional anti-rolling fins, the all-motor drive method is adopted, which greatly reduces the occupied space of the rotating column anti-rolling device. The transfer function of the DC drive motor used here is:

[0132]

[0133] where: K is the motor gain, T m is the mechanical time constant.

[0134] The offline simulation verification of the column-cylinder cooperative stabilization control system applicable to the marine mobile observation platform according to the present invention is given below. Figure 6 The simulation results of the roll angle and rotational speed at the high sea state with the ship speeds of 1 kn and 10 kn are shown. In the face of the interference of the high sea state, the marine mobile observation platform generates a roll motion of about 7 deg at the ship speeds of 1 kn and 10 kn. After the cooperative stabilization control system works, each column-cylinder anti-rolling device alternately exerts the best anti-rolling performance. The maximum roll angles after anti-rolling are maintained at about 1.5 deg and 0.5 deg respectively, and the maximum rotational speeds of the column-cylinder anti-rolling devices are 1786 r / min and 1218 r / min respectively. The anti-rolling effect is very obvious. Figure 7 The simulation results of the roll angle and rotational speed of the cooperative stabilization control system and the PID stabilization control system at the high sea state with the ship speed of 1 kn are shown. It is assumed that at 20 s, the No. 2 column-cylinder located in the front of the starboard suddenly has a mechanical failure, and the lift generated by it drops to 20% of the previous value. The anti-rolling efficiency of the marine mobile observation platform at the ship speed of 1 kn is 85.8%, which is better than 72.3% of the PID stabilization control system, and the stability effect is improved by 13.5%. After the failure occurs, the anti-rolling efficiency of the cooperative stabilization control system remains basically unchanged, and the anti-rolling efficiency of the PID stabilization control system drops to 63.4%. The maximum rotational speeds of both increase, but the rotational speed of the No. 2 column-cylinder in the cooperative stabilization control system decreases compared with the other column-cylinders. This is because after the cooperative distributor detects the abnormal operation of the No. 2 column-cylinder, it redistributes the anti-rolling lift it is responsible for to the other column-cylinders, playing a role of cooperative work. While the PID stabilization control system based on the traditional stabilization control strategy can only increase the rotational speeds of all column-cylinders simultaneously to maintain the hull stability, which wastes unnecessary energy and will also exacerbate the failure of the No. 2 column-cylinder. The cooperative stabilization control system designed by the present invention effectively reduces the energy consumption, increases the stability effect, and is more conducive to the long-term navigation of the marine mobile observation platform.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit. Although the technical solutions of the present invention have been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present invention, and they should all be covered by the protection scope of the present invention.

Claims

1. A rotary column cooperative stabilization control system applicable to marine mobile observation platforms, comprising: Sliding mode torque controller based on RBF neural network, cooperative allocation controller based on sequential quadratic programming method, motor servo system, rolling column anti-rolling device composed of four rolling columns, marine mobile observation platform model, lift feedback mechanism and angle sensor; S1: Establish the mathematical model of the lift of a single rolling column and the nonlinear rolling model of the marine mobile observation platform equipped with two pairs of rolling columns. The process is as follows: S1.1: Set the lift force F of a single stepped cylinder L i as follows: Where: ρ is the fluid density (kg / m 3 ), ω i is the angular velocity of self-rotation of a single variable-diameter cylinder (rad / s), is the angular velocity of oscillation of a single variable-diameter cylinder, L is the extended length of a single variable-diameter cylinder (m), r1 is the radius of the fixed end of a single variable-diameter cylinder (m), λ is the diameter ratio of a single variable-diameter cylinder, V is the oncoming flow velocity (m / s), θ i is the oscillation angle of a single variable-diameter cylinder (rad); S1.2: The nonlinear rolling model of the marine mobile observation platform equipped with two pairs of rolling column anti-rolling devices is: Where: I x and ΔI x are the moment of inertia and added inertia of the marine mobile observation platform (kg·m 2 ), φ is the roll angle (rad), B1, B2, C2, C3 are the relevant parameters of the marine mobile observation platform, D is the displacement (t), h is the metacentric height of the marine mobile observation platform (m), α f is the effective wave tilt angle (rad), K c is the total anti-rolling moment generated by the rotary column anti-rolling device (N·m); S2: Establish a sliding mode torque controller based on RBF neural network, which is used to receive the total anti-rolling torque input. Introduce the RBF neural network to predict the unknown rolling model of the marine mobile observation platform and design the anti-rolling torque control law based on the sliding mode control algorithm, so that the output of the system can always track the expected output of the system. The process is as follows: S2.1: Let \(x1 = \varphi\), K T = K c , and the state - space expression of the nonlinear rolling motion model of the ocean mobile observation platform is: Where: x1 is the roll angle of the marine mobile observation platform, x2 is the roll angular velocity of the marine mobile observation platform, f(x) is regarded as the marine mobile observation platform model, and d(t) = a7α f , K T is the control output of the torque controller, representing the total anti-rolling torque; Set the sliding mode surface as According to Equation (3), the ideal control law of the sliding mode torque controller is as follows: Where: c is the control gain, η is the switching gain, and e is the error between the expected output and the actual output; S2.2: Set the activation function of the neural network as the Gaussian function h(x), and the output of the Gaussian function is h = [h1, h2,..., h n T , then the parameter variation law of the neural network is designed as:​ In the formula: is the actual network weight, and γ is the adaptive change parameter of the neural network. Then the following formula holds: In the formula: is the hull rolling model predicted by the RBF neural network, ε is the approximation error between the predicted rolling model and the ideal model, then the sliding mode torque control law based on the RBF neural network is: Where: c is the control gain, η is the switching gain; S3: Establish a cooperative allocation controller based on the sequential quadratic programming method, which is used to obtain the actual working state of each rolling column in real time and assign allocation weights. Then establish a multi-objective optimization function and substitute the total anti-rolling torque required for the marine mobile observation platform to resist rolling calculated by the sliding mode torque controller into the formula. Finally, seek the optimal allocation of the anti-rolling torque through the sequential quadratic programming method among the three indicators of anti-rolling effect, energy consumption economy and system stability. The process is as follows: S3.1: Considering the interference of the outside world on the rolling columns, the system introduces a lift feedback mechanism. By taking into account the internal and external states of each rolling column, the cooperative allocator can more reasonably allocate the anti-rolling torque according to the actual working state of each rolling column, calculate the control signal, so that they cooperate with each other; S3.2: Set the following multi-objective optimization function: Where: n d = [n d1 , n d2 , n d3 , n d4 is the expected rotational speed of each rotating column, that is, the control signal output by the cooperative distributor, Δn d is the change in the expected rotational speed of the rotating column, i is the number of indicators, t is the simulation step size, p i is the weight of each performance index, J i (k) are the various indicators of the multi-objective optimization function; (1) Setting of anti-rolling effect index: where: K i (k) is the theoretical anti-rolling moment generated by each rotating column at the k-th moment. Combining with Equation (1), its expression can be obtained as follows: where: n di (k), θ i (k) and is the internal state of the i-th spinning column at the k-th moment, representing the expected rotational speed, swing angle, and swing angular velocity of the spinning column respectively, δ i (k) is the external efficiency factor generated by each spinning column in its respective working environment at the k-th moment, r rw is the anti-rolling lever arm of the spinning column; (2) Setting of energy consumption economy index: (3) Setting of stability index: S3.3: Use the sequential quadratic programming method to solve the multi-objective optimization function to solve the nonlinear programming problem. First, transform the nonlinear programming problem into the following quadratic programming sub-problem through the Taylor expansion formula at the nth step: where: d n is the optimal solution of the quadratic programming sub-problem and also the forward direction of the current iteration point, g i (·) and c j (·) are the general expression forms of inequality constraints and equality constraints respectively, and are the Jacobian matrices of inequality constraints and equality constraints respectively, H n is the Hessian matrix of the Lagrangian function, and the Lagrangian function is: L(n d , μ, λ) = J(n d ) - μ × g i (k) - λ × c j (k) (14) Where: μ and λ are the Lagrange multiplier vectors of the inequality constraint and the equality constraint respectively, and i and j are the numbers of the inequality constraint and the equality constraint respectively; Use the BFGS method, that is, the quasi-Newton method, to approximately solve the Hessian matrix of the Lagrangian function, and its expression is: where: γ n is an intermediate variable, and its expression is: S4: Use the motor servo system to transmit the expected rotation speed of each rolling column calculated by the cooperative allocator to the drive motors of each rolling column in the form of electrical signals, rotate at the expected rotation speed, and apply the generated anti-rolling torque to the marine mobile observation platform model to resist the rolling caused by the sea wave interference. Finally, feedback the rolling situation of the marine mobile observation platform to the controller through the angle sensor, and the controller adjusts the output again according to the rolling situation until the marine mobile observation platform tends to be stable.

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