USV rotary column stabilization control system considering complex disturbance and motor dynamic characteristics

Abstract

The invention discloses a USV rotary column stabilization control system considering complex disturbance and motor dynamic characteristics, belongs to the field of motion control systems of ocean mobile observation platforms, and aims to improve the stability and control efficiency of USV navigation. The method comprises the following specific steps: firstly, establishing a rotary column stabilizer lift model, a USV nonlinear rolling model and a servo motor dynamic model; then designing a Backstepping controller based on a differential item disturbance observer, estimating and compensating disturbance caused by external and model uncertainty in real time, then adjusting expected control input in real time, and ensuring that the output rolling angle tracks the expected rolling angle. The MPC controller based on servo motor state feedback is designed, the state quantity of the motor is fed back to the controller for prediction and adjustment, the problems of response lag and output overload of the servo motor in complex sea conditions are effectively solved, rolling angle error minimization and effective control over energy consumption are further achieved, and the service life of the servo motor is prolonged. And the purpose of multi-objective optimization is achieved.

Description

Technical Field

[0001] The invention relates to the field of motion control systems for marine mobile observation platforms, and in particular to a USV rotary column anti-roll control system that takes complex disturbances and motor dynamic characteristics into consideration. Background Art

[0002] In the marine environment, some USVs are often used as marine mobile observation platforms to monitor the marine environment and ship dynamics. Therefore, they often face the challenges of complex sea conditions, especially in terms of nonlinear roll motion, which is not only strongly affected by the external environment, such as waves, wind and currents, but also disturbed by the uncertainty of the internal model, which greatly increases the difficulty of USV roll reduction. At present, the method of using neural networks to approximate the internal model to design an ideal controller has theoretical potential, but has encountered many limitations in practical applications. Among them, the quality of training data, the complexity of the network architecture and the lack of generalization ability have become key factors restricting the performance of the controller.

[0003] In order to solve these problems, researchers began to explore simpler and more efficient control strategies. Among them, the Backstepping control strategy has gradually attracted attention due to its unique advantages. By decomposing the nonlinear system into multiple simple subsystems and designing control laws at each step to stabilize the current subsystem, the Backstepping controller can gradually solve the nonlinear problems of the system through feedback connections and achieve global stability. However, in practical applications, the disturbances caused by external and internal model uncertainties are still a problem that cannot be ignored.

[0004] On the other hand, servo motors have broad application prospects in USV anti-roll control systems due to their high precision, stability and fast response characteristics. However, servo motors also face problems such as output response lag and output overload when responding to control signals. These problems are particularly prominent in complex sea conditions, seriously affecting the stability and safety of USVs.

[0005] Therefore, in order to solve the problem of USV roll control in complex sea conditions, it is necessary to design a control system that can effectively deal with nonlinear roll motion and make full use of the performance advantages of servo motors. In this context, this patent proposes a rotating column roll control system based on a double-layer controller. The system uses a Magnus rotating column stabilizer as a new type of roll reduction device, and combines a Backstepping controller based on the differential disturbance observer and an MPC controller based on servo motor state feedback. Through the coordinated work of the inner and outer loop controllers, the system can control the roll angle to about ±0.5deg under complex disturbances, so that the motor can respond quickly and its output is controlled within the constraint range. Their power consumption is also reduced by about 28%, achieving effective and stable control of USV roll motion, and significantly improving the stability and safety of USV in wind and waves. The design of this control system not only solves the limitations of existing control methods in the face of complex disturbances, but also makes full use of the performance advantages of servo motors, providing a new solution for USV's rotating column roll control.

[0006] (1) In order to deal with the problem of continuous parameter changes in the roll model caused by external disturbances, the paper "Lift analysis and anti-rolling control system design of Magnus rotating roll stabilizer at full speed range" adopts RBF neural network for real-time approximation and designs a sliding mode anti-roll control system based on RBF neural network, which ensures that the ship can maintain good stability under various complex conditions. However, there are the following problems: ① The performance of the neural network depends on the selection of training data and network structure, and there may be a problem of insufficient generalization ability; ② The sliding mode control has good robustness, but the combination with RBF neural network will reduce the system's resistance to external disturbances; ③ The dynamic characteristics of the motor are not taken into account. When the control signal input by the controller does not match the actual demand of the motor, this will affect the control accuracy of the motor and thus affect the stability of the system.

[0007] (2) The paper "Simulation and analysis of Magnus rotating roll stabilizer at low speed" designs a PID anti-roll control system to reduce the rolling of ships at low speeds. The results show that at low speeds, the system can effectively reduce the rolling amplitude of the ship and improve the stability of the ship. However, there are the following problems: ① The response of the PID controller is limited by fixed parameter settings, and for nonlinear models, the traditional PID anti-roll control system may have poor control effects; ② The PID controller is not effective in dealing with disturbances caused by external environment and internal model uncertainties; ③ The dynamic characteristics of the motor are not taken into account. When the control signal input by the controller does not match the actual needs of the motor, this will affect the control accuracy of the motor and thus affect the stability of the system.

[0008] (3) "Study on AGV Control System Design and Speed ​​Control System Based on μC_OS_Ⅲ" designed a speed control system for the DC motor of AGV by integrating PID control algorithm and Kalman filter technology. The system can accurately predict the motor state and effectively suppress noise, thereby optimizing the speed control performance and improving the stability and efficiency of motor control. However, there are the following problems: ① Kalman filter needs to be designed based on the state space model of the system, so it has a certain dependence on the accuracy of the motor model. If the model changes due to the external environment, the performance of Kalman filter may be affected; ② The design of PID controller is relatively simple, mainly relying on empirical formulas and debugging process. If the performance of Kalman filter is not good, the parameters of PID controller may be difficult to adjust, resulting in poor control performance; ③ The dynamic characteristics of the motor are not taken into account. When the control signal input by the controller does not match the actual needs of the motor, this will affect the accuracy and stability of the speed control system. Summary of the invention

[0009] Based on the above problems, the present invention designs a USV rotating column anti-roll control system that is suitable for considering complex disturbances and motor dynamic characteristics through control theory and optimization theory, which solves the problems of poor anti-roll effect and system response lag caused by the complex disturbances and motor dynamic characteristics that often affect the USV during navigation. The system can not only estimate and compensate for external disturbances and model uncertainties in real time, ensuring that the roll angle can accurately track the reference input, but also avoid motor overload and significantly improve the motor response speed, providing strong support for the stable operation and long-distance navigation of the USV.

[0010] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is as follows: a USV rotary column anti-roll control system considering complex disturbances and motor dynamic characteristics is designed, including: a Backstepping controller based on a differential disturbance observer, an MPC controller based on servo motor state feedback, a servo motor dynamic model, a D / A converter, an amplifier, a rotary column stabilizer, a USV controlled object, a travel meter and an angular velocity gyroscope.

[0011] S1: Establish the lift model of the rotating column stabilizer, the nonlinear roll model of the USV and the dynamic model of the servo motor to provide a theoretical basis for the anti-roll control system. The process is as follows:

[0012] S1.1: The rotor stabilizer is a cylindrical rotor blade installed on both sides of the hull. Its working principle is based on the Magnus effect, such as Figure 2 According to the Kutta-Joukowski theorem, under ideal conditions, the Magnus effect force F exerted on the spin column stabilizer in water is:

[0013] F=ρvlΓ (1)

[0014] Where: ρ is the fluid density, v is the incoming flow velocity, l is the length of the swirl stabilizer, and Γ is the circulation intensity;

[0015] And Γ=2πr 2 ω, ω = 2πn, substituting it into formula (1) we get:

[0016] F=4ρπ 2 r 2 lvn (2)

[0017] Where: ρ is the fluid density, r is the radius of the swirl stabilizer, v is the incoming flow velocity, and n is the rotation speed of the swirl stabilizer;

[0018] S1.2: Assume that a USV is sailing in a fixed direction, and two pairs of rotating column stabilizers are installed symmetrically on both sides. Figure 3 As shown in the figure, the speed v is the relative flow speed between the USV and the seawater, F i is the lift generated by the ith spin column stabilizer, then the total anti-roll moment actually generated by the two pairs of spin column stabilizers is:

[0019]

[0020] Where: K i is the anti-roll moment generated by the ith swivel stabilizer, F i is the lift generated by the i-th spin stabilizer, r rw It is the anti-roll arm of the swivel stabilizer;

[0021] Combining formula (3), the nonlinear roll model of USV is:

[0022]

[0023] Where: I x and ΔI x is the moment of inertia and additional inertia of USV, φ is the roll angle, B1, B2, C2, C3 are hull related parameters, D is the displacement, h is the transverse metacentric height of USV, α f is the effective wave inclination angle;

[0024] S1.3: The servo motor has high precision and high response speed, is suitable for complex control tasks, and has closed-loop control capabilities, which can ensure stable and precise control. Its dynamic model can be described as a second-order differential equation from input voltage u to output speed n, which consists of an electrical part model and a mechanical part model. The electrical part model is:

[0025]

[0026] Where: u is the motor input voltage, i is the motor current, L a is the armature inductance, R a is the armature resistance, ω is the angular velocity of the motor output, K e The back-EMF constant describes the relationship between the angular velocity ω and the back-EMF;

[0027] The mechanical part model is:

[0028]

[0029] Where: I is the moment of inertia of the motor, B is the friction coefficient of the motor, K t is the torque constant of the motor, describing the relationship between current i and torque;

[0030] Combining equations (5) and (6), we establish the relationship between input voltage u and output speed, and obtain:

[0031]

[0032] The speed Damping ratio Natural frequency Substitute it into the above formula and simplify it, and finally get the complete servo motor dynamic model:

[0033]

[0034] Where: n is the output speed of the motor.

[0035] S2: Design a Backstepping controller based on a disturbance observer to estimate and compensate for disturbances caused by external and model uncertainties in real time, and then adjust the input of the anti-roll moment in real time to ensure that the output roll angle tracks the reference input. The process is as follows:

[0036] S2.1: Since the torque output by the Backstepping controller is not the actual anti-roll torque acting on the USV, the expected anti-roll torque K is introduced d Substitute into equation (4), transform equation (4) into state space form, and let x1 = φ, u c =K d , the state space expression of the USV nonlinear rolling motion model is obtained:

[0037]

[0038] Where: d t =Dhα f is the sum of disturbances encountered by the USV during navigation,

[0039] Introduce the desired roll angle φ d and its first-order derivative and the second derivative Considering the actual situation, it is difficult to control the roll angle to zero and keep it unchanged, so let the desired roll angle φ d The changing curve of is an arbitrary continuous function floating at zero point. Define the tracking error e1 of the roll angle:

[0040] e1=x 1d -x1 (10)

[0041] Taking the derivative of e1, we get:

[0042]

[0043] Define the Lyapunov function V1:

[0044]

[0045] Taking the derivative of V1, we get:

[0046]

[0047] If V1 is negative definite, then the expected value of x2 can be x 2d for:

[0048]

[0049] Where: k1 is an adjustable real number;

[0050] Define the tracking error e2 of the rolling angular velocity:

[0051] e2=x 2d -x2 (15)

[0052] Combining equation (10) and equation (12), we get:

[0053]

[0054] Taking the derivative of e2, we get:

[0055]

[0056] Define the Lyapunov function V2:

[0057]

[0058] Taking the derivative of V2 and substituting equation (9) into it, we can obtain:

[0059]

[0060] If V2 is negatively determined, we can set:

[0061]

[0062] Combining equations (9), (11), (14) and (17), we get the control law:

[0063]

[0064] S2.2: According to equation (9), the Backstepping controller will be affected by disturbances during the output torque process, which will lead to poor tracking effect of the desired roll angle. Therefore, a disturbance observer is designed to estimate the disturbance so as to achieve the ideal tracking effect. g1(x)=b,g2(x)=1, then the disturbance estimate

[0065]

[0066] Where: L(x) is the observation gain function of the disturbance observer, is the estimated value of the disturbance, then the estimated error of the disturbance is:

[0067]

[0068] Assume that in the actual process, d t The change of disturbance is slower than the change of system state, so we can set d t The derivative of is zero, then the estimated error of the disturbance can be expressed as:

[0069]

[0070] Equation (24) shows that by choosing an appropriate observation gain function, the system can be guaranteed to be asymptotically stable, and the designed observer can well observe the disturbance of the system. The above observer should be improved. Subtract the two pairs of equations (22) at the same time. And simplify it to get:

[0071]

[0072] eliminate Then integrate both sides of equation (22) to obtain:

[0073]

[0074] Where: Introducing intermediate variables Substitute it into formula (26) and derive it again to obtain:

[0075]

[0076] Where: z is the internal state of the observer, p(x) is the function that the observer needs to design;

[0077] In summary, the modified disturbance observer is as follows:

[0078]

[0079] Combining equation (21) and equation (28), the Backstepping control law based on nonlinear disturbance observer is obtained as follows:

[0080]

[0081] S3: Design an MPC controller that takes into account the dynamic characteristics of the servo motor. This controller predicts the future behavior of the motor by feeding back the motor's state quantity to the controller and performs optimal control accordingly. It also solves the delay and saturation problems of the motor and effectively optimizes the roll angle error and energy consumption according to the control objectives and constraints, ensuring the feasibility and efficiency of the control effect. The process is as follows:

[0082] S3.1: To facilitate the design of the controller, the differential equation form of equation (8) is transformed into the state space form:

[0083]

[0084] Where:

[0085] Therefore, the dynamic model of the servo motor equipped with two pairs of rotating column stabilizers is:

[0086]

[0087] Where: state vector Control vector u = [u1u2 u3 u4] T , output vector n = [n1 n2n3 n4] T , A=diag{A1 A2 A3 A4}, B=diag{B1 B2 B3 B4}, C=[1 0 1 0 1 0 1 0] T ;

[0088] S3.2: Since the MPC controller is operated in the discrete time domain, the model in equation (31) must also be converted into the discrete time domain form;

[0089]

[0090] Assuming the prediction step length is N, define the N-step prediction state vector at the kth moment: Input vector U k and the error vector E k They are:

[0091]

[0092] Design the following cost function:

[0093]

[0094] Where: coefficient a = 4ρπ 2 r 2 lv,u c is the desired torque output by the Backstepping controller and also the reference input of the MPC controller, and u is the control input vector of the MPC controller;

[0095] Solve the quadratic programming problem for the above cost function. Combining equations (33) and (34), according to the model in equation (32), we can obtain the predicted state vector at the kth moment N steps: With the input vector U k The algebraic relationship between:

[0096]

[0097] Where: is the initial measured state quantity, and the matrices M and C are:

[0098]

[0099] make U c =[u c ,u c ,…,u c ] T Combining equations (33), (34) and (35), the cost function can be simplified as follows:

[0100]

[0101] Continue to simplify formula (40) to obtain:

[0102]

[0103] In the formula,

[0104] Finally, the standard form for solving the quadratic programming problem is:

[0105]

[0106] The result obtained from the above formula is a set of control sequences that minimize the cost function. This control sequence will be used as the control input of the servo motor dynamic model so that the optimal speed sequence is distributed to the four rotary column stabilizers. In this case, both the anti-roll effect and the energy consumption problem are taken into account, and it can respond quickly without exceeding the output limit, which is in line with the actual operating conditions.

[0107] The present invention has the following beneficial effects:

[0108] (1) The control method designed in this patent combines the advantages of the Backstepping controller in handling nonlinear systems with the improved disturbance observer's characteristics of disturbance estimation and noise resistance. The Backstepping controller based on the differential term elimination disturbance observer takes into account the sensitivity of the observer's differential term to noise, and eliminates the differential term by introducing intermediate variables, thereby improving the accuracy of disturbance observation. Then, the disturbances caused by external and internal model uncertainties are estimated in real time, and these disturbances are introduced into the Backstepping control law through feedforward compensation, ultimately achieving global stability of the system. Compared with the PID control method that controls the roll angle to about ±4.5deg, the control method designed in this patent can control the roll angle to about ±0.5deg, significantly improving the stability of the system and achieving precise control of the USV roll motion under complex disturbances.

[0109] (2) This patent uses a servo motor as the actuator of the rotary column stabilizer, and combines it with an MPC controller to significantly improve the dynamic performance of the servo motor and effectively solve the response lag and output overload problems of the servo motor in complex sea conditions. Among them, the MPC controller feeds back the state quantity of the servo motor to the controller and predicts the future state, and adjusts the control strategy in real time according to the prediction results, thereby significantly improving the response speed, reducing the delay, and ensuring the efficient operation of the system. At the same time, the controller effectively avoids motor output overload during the control process by setting reasonable constraints, and controls the output speed within the constraint range of ±20r / s. In contrast, without considering the dynamic characteristics of the motor, the speed output of the motor not only responds slowly, but also exceeds the speed output limit at some times, and its maximum value reaches 25r / s. Therefore, the smooth operation of the system is effectively protected and the service life of the servo motor is extended.

[0110] (3) In addition, the MPC controller designed in this patent is designed for the MIMO motor system, and a weight matrix is ​​designed to optimize the control distribution. The weight matrix is ​​to adjust the speed obtained by each rotary column stabilizer according to its own operating state. Finally, the system achieves effective control of minimizing the roll angle error, and the power consumption is reduced by about 28%, further improving the performance and efficiency of the entire system. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 This is a structural block diagram of a USV swivel column anti-roll control system that is suitable for considering complex disturbances and motor dynamic characteristics;

[0112] Figure 2 This is a schematic diagram of the Magnus effect;

[0113] Figure 3 Schematic diagram of the ship rolling model with two pairs of rotating column stabilizers installed;

[0114] Figure 4 The simulation results are compared for the anti-rolling effect under the disturbance of sea wave white noise and sine superimposed wave;

[0115] Figure 5 The simulation results of disturbance observation under the disturbance of ocean wave white noise and sine superposition wave;

[0116] Figure 6 The simulation results of roll angle tracking under the disturbance of sea wave white noise and sine superposition wave;

[0117] Figure 7 The simulation results are compared for the output speed of each motor with and without considering the dynamic characteristics of the motor. DETAILED DESCRIPTION

[0118] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0119] Example: Figure 1 As shown, Figure 1 This is a structural block diagram of a USV rotary column anti-roll control system that takes into account complex disturbances and motor dynamic characteristics, including: Backstepping controller based on differential disturbance observer elimination, MPC controller based on servo motor state feedback, servo motor dynamic model, D / A converter, amplifier, rotary column stabilizer, USV controlled object, travel meter and angular velocity gyroscope. The specific steps are as follows:

[0120] S1: Establish the lift model of the rotating column stabilizer, the nonlinear roll model of the USV and the dynamic model of the servo motor to provide a theoretical basis for the anti-roll control system. The process is as follows:

[0121] S1.1: The rotor stabilizer is a cylindrical rotor blade installed on both sides of the hull. Its working principle is based on the Magnus effect, such as Figure 2 According to the Kutta-Joukowski theorem, under ideal conditions, the Magnus effect force F exerted on the spin column stabilizer in water is:

[0122] F=ρvlΓ (1)

[0123] Where: ρ is the fluid density, v is the incoming flow velocity, l is the length of the swirl stabilizer, and Γ is the circulation intensity;

[0124] And Γ=2πr 2 ω, ω = 2πn, substituting it into formula (1) we get:

[0125] F=4ρπ 2 r 2 lvn (2)

[0126] Where: ρ is the fluid density, r is the radius of the swirl stabilizer, v is the incoming flow velocity, and n is the rotation speed of the swirl stabilizer;

[0127] S1.2: Assume that a USV is sailing in a fixed direction, and two pairs of rotating column stabilizers are installed symmetrically on both sides. Figure 3 As shown in the figure, the speed v is the relative flow speed between the USV and the seawater, F i is the lift generated by the ith spin column stabilizer, then the total anti-roll moment actually generated by the two pairs of spin column stabilizers is:

[0128]

[0129] Where: K i is the anti-roll moment generated by the ith swivel stabilizer, F i is the lift generated by the i-th spin stabilizer, r rw It is the anti-roll arm of the swivel stabilizer;

[0130] Combining formula (3), the nonlinear roll model of USV is:

[0131]

[0132] Where: I x and ΔI x is the moment of inertia and additional inertia of USV, φ is the roll angle, B1, B2, C2, C3 are hull related parameters, D is the displacement, h is the transverse metacentric height of USV, α f is the effective wave inclination angle;

[0133] S1.3: Since the dynamic characteristics of the motor will affect the performance and stability of the control system, it should be taken into account in the control scope. The servo motor has high precision and high response speed, is suitable for complex control tasks, and has closed-loop control capabilities, which can ensure stable and precise control. Therefore, a servo motor is used to drive the rotary column stabilizer for anti-roll work. The dynamic model of the servo motor can be described as a second-order differential equation from the input voltage u to the output speed n, which consists of an electrical part model and a mechanical part model. The electrical part model is:

[0134]

[0135] Where: u is the motor input voltage, i is the motor current, L a is the armature inductance, R a is the armature resistance, ω is the angular velocity of the motor output, K e The back-EMF constant describes the relationship between the angular velocity ω and the back-EMF;

[0136] The mechanical part model is:

[0137]

[0138] Where: I is the moment of inertia of the motor, B is the friction coefficient of the motor, K t is the torque constant of the motor, describing the relationship between current i and torque;

[0139] Combining equations (5) and (6), we establish the relationship between input voltage u and output speed, and obtain:

[0140]

[0141] The speed Damping ratio Natural frequency Substitute it into the above formula and simplify it, and finally get the complete servo motor dynamic model:

[0142]

[0143] Where: n is the output speed of the motor.

[0144] S2: In view of the nonlinear roll and disturbance problems caused by external environment and internal model uncertainty that USVs often face during navigation, a Backstepping controller is designed to deal with the nonlinear roll problem. The state of the nonlinear system is decomposed into multiple simple subsystems, and a control law is designed in each step to stabilize the current subsystem, and connected to the next step through feedback. The dynamic characteristics of the system are gradually solved at each stage to ultimately achieve global stability; a disturbance observer that eliminates the differential term is designed to eliminate the sensitivity of the differential term to noise, and then the disturbance caused by external and model uncertainties is estimated in real time, and finally introduced into the Backstepping control law through feedforward compensation to adjust the input of the anti-roll torque to ensure that the output roll angle tracks the reference input. The process is as follows:

[0145] S2.1: Since the torque output by the Backstepping controller is not the actual anti-roll torque acting on the USV, the expected anti-roll torque K is introduced d Substitute into equation (4), transform equation (4) into state space form, and let x1 = φ, u c =K d , the state space expression of the USV nonlinear rolling motion model is obtained:

[0146]

[0147] Where: d t =Dhα f is the sum of disturbances encountered by the USV during navigation,

[0148] Introduce the desired roll angle φ d and its first-order derivative and the second derivative Considering the actual situation, it is difficult to control the roll angle to zero and keep it unchanged, so let the desired roll angle φ d The changing curve of is an arbitrary differentiable function floating at zero point. Define the tracking error e1 of the roll angle:

[0149] e1=x 1d-x1 (10)

[0150] Taking the derivative of e1, we get:

[0151]

[0152] Define the Lyapunov function V1:

[0153]

[0154] Taking the derivative of V1, we get:

[0155]

[0156] If V1 is negative definite, then the expected value of x2 can be x 2d for:

[0157]

[0158] Where: k1 is an adjustable real number;

[0159] Define the tracking error e2 of the rolling angular velocity:

[0160] e2=x 2d -x2 (15)

[0161] Combining equation (13) and equation (15), we get:

[0162]

[0163] Taking the derivative of e2, we get:

[0164]

[0165] Define the Lyapunov function V2:

[0166]

[0167] Taking the derivative of V2 and substituting equation (12) into it, we can obtain:

[0168]

[0169] If V2 is negatively determined, we can set:

[0170]

[0171] Combining equations (9), (11), (14) and (17), we get the control law:

[0172]

[0173] S2.2: According to equation (9), the Backstepping controller will be affected by disturbances during the output torque process, which will lead to poor tracking effect of the desired roll angle. Therefore, a disturbance observer is designed to estimate the disturbance so as to achieve the ideal tracking effect. g1(x)=b,g2(x)=1, then the disturbance estimate

[0174]

[0175] Where: L(x) is the observation gain function of the disturbance observer, is the estimated value of the disturbance, then the estimated error of the disturbance is:

[0176]

[0177] Assume that in the actual process, d t The change of disturbance is slower than the change of system state, so we can set d t The derivative of is zero, then the estimated error of the disturbance can be expressed as:

[0178]

[0179] Equation (24) shows that by selecting an appropriate observation gain function, the asymptotic stability of the system can be guaranteed, and the designed observer can observe the disturbance of the system well. However, in actual systems, noise usually has high-frequency components, and the differential operation will amplify the rate of change of the input signal, and also amplify the high-frequency noise. In the case of large noise, it is difficult for the observer to distinguish between actual disturbances and noise, which affects the accuracy of disturbance estimation. This will cause the observer output to fluctuate violently and affect the overall performance of the control system. Even if the noise amplitude is small, the differential operation may cause the observer output to be unstable or produce large errors, thereby reducing the robustness of the system. For this reason, the above observer should be improved, and the two pairs of equations (22) should be subtracted at the same time. And simplify it to get:

[0180]

[0181] eliminate Then integrate both sides of equation (22) to obtain:

[0182]

[0183] Where: Introducing intermediate variables Substitute it into formula (26) and derive it again to obtain:

[0184]

[0185] Where: z is the internal state of the observer, p(x) is the function that the observer needs to design;

[0186] In summary, the modified disturbance observer is as follows:

[0187]

[0188] Combining equation (21) and equation (28), the Backstepping control law based on the improved disturbance observer is obtained as follows:

[0189]

[0190] S3: When responding to control signals, servo motors may be affected by factors such as mechanical inertia and electrical delay, causing their output response to lag behind the expected value. This delay characteristic limits the dynamic performance of servo motors, making it difficult to meet the requirements in applications with high-frequency control or fast response requirements. In addition, servo motors also have saturation characteristics, that is, there are physical limitations on their control input and output. When the control signal exceeds these limits, the servo motor may generate shock and vibration, which will affect the smooth operation and life of the system. In order to improve the dynamic performance of the servo motor, an MPC controller based on servo motor state feedback is designed. By feeding back the state quantity of the servo motor to the controller, the state in the future is predicted, and the control strategy is adjusted in real time according to the prediction results to improve the response speed and reduce delay; in the prediction process, MPC also considers the saturation characteristics of the servo motor, that is, the control input cannot exceed a preset maximum or minimum value. By setting constraints in the solution process, MPC can achieve the best control effect of the servo motor under the premise of meeting the constraints, thereby ensuring that the servo motor operates within a safe and stable range. In addition, the roll angle error and energy consumption can be optimized through control allocation to achieve the purpose of multi-objective optimization. The process is as follows:

[0191] S3.1: To facilitate the design of the controller, the differential equation form of equation (8) is transformed into the state space form:

[0192]

[0193] Where:

[0194] Therefore, the dynamic model of the servo motor equipped with two pairs of rotating column stabilizers is:

[0195]

[0196] Where: state vector Control vector u = [u1u2 u3 u4] T , output vector n = [n1 n2n3 n4] T, A=diag{A1 A2 A3 A4}, B=diag{B1 B2 B3 B4}, C=[1 0 1 0 1 0 1 0] T ;

[0197] S3.2: Since the MPC controller is operated in the discrete time domain, the model in equation (31) must also be converted into the discrete time domain form;

[0198]

[0199] Assuming the prediction step length is N, define the N-step prediction state vector at the kth moment: Input vector U k and the error vector E k They are:

[0200]

[0201] Design the following cost function:

[0202]

[0203] Where: coefficient a = 4ρπ 2 r 2 lv,u c is the desired torque output by the Backstepping controller and also the reference input of the MPC controller, and u is the control input vector of the MPC controller;

[0204] Solve the quadratic programming problem for the above cost function. Combining equations (33) and (34), according to the model in equation (32), we can obtain the predicted state vector at the kth moment N steps: With the input vector U k The algebraic relationship between:

[0205]

[0206] Where: is the initial measured state quantity, and the matrices M and C are:

[0207]

[0208]

[0209] make U c =[u c ,u c ,…,u c ] T Combining equations (30), (31) and (32), the cost function can be simplified as follows:

[0210]

[0211] Continue to simplify formula (40) to obtain:

[0212]

[0213] Where:

[0214]

[0215] Finally, the standard form for solving the quadratic programming problem is:

[0216]

[0217] The result obtained from the above formula is a set of control sequences that minimize the cost function. This control sequence will be used as the control input of the servo motor dynamic model so that the optimal speed sequence is distributed to the four rotary column stabilizers. In this case, both the anti-roll effect and the energy consumption problem are taken into account, and it can respond quickly without exceeding the output limit, which is in line with the actual operating conditions.

[0218] S4: This patent takes the Cloud borne series USV of Ocean Alpha USV as an example. The ship parameters are as follows: length 46.8 meters, transverse metacentric height 2.8 meters, displacement of about 500 tons, length between verticals 44.9 meters, width 9.3 meters, draft 2.6 meters, depth 3.8 meters, maximum speed 25 knots; according to Quantum's description of the matching size of the rotating column stabilizer and the hull, the size parameters of the rotating column stabilizer selected in this patent are as follows: diameter 0.34 meters, span 2.5 meters; the parameters involved in the control system are as follows: observation gain L = 10, control gain k1 = 1, k2 = 50, prediction time domain N = 5, weight matrix Q = 10, R = diag{1,1,0.8,0.8}, F = 10, ζ = 0.5, ω n =15, K t =10,L a =10, I = 100, and the preset speed range is -20r / s≤n≤20r / s. In order to reflect the beneficial effects of the patented control system, simulation experiments were conducted on its roll reduction effect, disturbance observation, roll angle tracking and servo motor output under different disturbances.

[0219] Figure 4 The simulation results of the roll reduction effect under the disturbance of sea wave white noise and sine superimposed wave are shown. It can be seen that compared with the traditional PID control method that controls the roll angle at about ±4.5deg, the control method designed by this patent can control the roll angle at about ±0.5deg, which significantly improves the stability of the system. Figure 5The disturbance observation simulation results under the disturbance of sea wave white noise and sinusoidal superposition wave are shown. It can be seen that the disturbance observer designed in this patent has excellent observation performance, can accurately and quickly capture various disturbance information in the system, and provides strong support for the stable control of the system. Figure 6 The simulation results of roll angle tracking under the disturbance of white noise of sea waves and superimposed sinusoidal waves are demonstrated, which verifies the effectiveness and robustness of the patented control method and ensures the stable operation of the USV in complex sea conditions. Figure 7 The simulation results of the output speed of each motor with and without considering the dynamic characteristics of the servo motor are shown. Due to the constant change of the rolling motion, the system can make the motor output the corresponding speed faster according to the anti-roll demand when the dynamic characteristics of the motor are considered, and the output speed is controlled within the constraint range of ±20r / s. In contrast, when the dynamic characteristics of the motor are not considered, the speed of the motor output not only responds slowly, but also exceeds the speed output limit at some times, and its maximum value reaches 25r / s. Since the speed is the main parameter that determines the power consumption of the motor, it can be found that when the dynamic characteristics of the motor are considered, the power consumption of the motor is reduced to a certain extent, by about 28%.

[0220] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to be limiting. Although the technical solutions of the present invention have been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the present invention, and all of them should be included in the protection scope of the present invention.

Claims

1. A USV swivel column anti-roll control system considering complex disturbances and motor dynamic characteristics, characterized by: Backstepping controller based on observer for eliminating differential disturbance, MPC controller based on servo motor state feedback, servo motor dynamic model, D / A converter, amplifier, swivel stabilizer, USV controlled object, travel meter and angular velocity gyroscope; S1: Establish the lift model of the rotating column stabilizer, the nonlinear roll model of the USV and the dynamic model of the servo motor to provide a theoretical basis for the anti-roll control system. The process is as follows: S1.1: The swirl stabilizer is a cylindrical rotor blade installed on both sides of the hull. Its working principle is based on the Magnus effect. According to the Kutta-Joukowski theorem, under ideal conditions, the Magnus effect force F exerted on the swirl stabilizer in water is: F=4ρπ 2 r 2 lvn (1) Where: ρ is the fluid density, r is the radius of the swirl stabilizer, l is the length of the swirl stabilizer, v is the incoming flow velocity, and n is the rotation speed of the swirl stabilizer; S1.2: Assume that a USV is sailing in a fixed direction, with two pairs of swivel stabilizers symmetrically installed on both sides. The speed v is the relative flow speed between the USV and the seawater, F i is the lift generated by the ith spin column stabilizer, then the total anti-roll moment actually generated by the two pairs of spin column stabilizers is: Where: K i is the anti-roll moment generated by the ith swivel stabilizer, F i is the lift generated by the i-th spin stabilizer, r rw It is the anti-roll arm of the swivel stabilizer; Combining formula (2), the nonlinear rolling model of USV is: Where: I x and ΔI x is the moment of inertia and additional inertia of USV, φ is the roll angle, B1, B2, C2, C3 are hull related parameters, D is the displacement, h is the transverse metacentric height of USV, α f is the effective wave inclination angle; S1.3: The servo motor has high precision and high response speed, is suitable for complex control tasks, and has closed-loop control capabilities to ensure stable and precise control. Its dynamic model can be described as: Where: ζ is the damping ratio, ω n is the natural frequency, L a is the armature inductance, K t is the torque constant of the motor, I is the moment of inertia of the motor; S2: Design a backstepping controller based on a differential disturbance observer to estimate and compensate for disturbances caused by external and model uncertainties in real time, and then adjust the input of the anti-roll moment in real time to ensure that the output roll angle tracks the reference input. The process is as follows: S2.1: Since the torque output by the Backstepping controller is not the actual anti-roll torque acting on the USV, the expected anti-roll torque K is introduced d , then the state space expression of the USV nonlinear rolling motion model is: Where: d t =Dhα f is the sum of disturbances encountered by the USV during navigation, Introduce the desired roll angle φ d and its first-order derivative and the second derivative The tracking errors of roll angle and roll angular velocity are defined as: e1=x 1d -x1 (6) e2=x 2d -x2 (7) According to the principle of Backstepping controller, the final control law is: S2.2: The Backstepping controller will be affected by disturbances during the output torque process, which will lead to poor tracking of the desired roll angle. Therefore, a disturbance observer is designed to estimate the disturbance so as to achieve the ideal tracking effect. g1(x)=b,g2(x)=1, then the disturbance estimate Where: L(x) is the observation gain function of the disturbance observer, is the estimated value of the disturbance; make Introducing intermediate variables The improved disturbance observer is as follows: Where: z is the internal state of the observer, p(x) is the function that the observer needs to design; Combining equations (8) and (10), the Backstepping control law based on the improved disturbance observer is obtained as follows: S3: Design an MPC controller based on servo motor state feedback. By feeding the motor state into the controller for prediction and adjustment, the control system can operate stably, accurately and efficiently under various operating conditions while complying with the physical constraints of the servo motor. The process is as follows: S3.1: The state space form of the servo motor dynamic model is: Where: Therefore, the dynamic model of the servo motor equipped with two pairs of rotating column stabilizers is: Where: state vector Control vector u = [u1u2 u3 u4] T , output vector n = [n1 n2 n3n4] T , A=diag{A1 A2 A3 A4}, B=diag{B1 B2 B3 B4}, C＝[1 0 1 0 1 0 1 0] T ； S3.2: Since the MPC controller is implemented in discrete time domain, the dynamic model of the servo motor must also be converted into discrete time domain form; Assuming the prediction step length is N, define the N-step prediction state vector at the kth moment: Input vector U k and the error vector E k They are: YOU k =[u(k|k),u(k+1|k),···,u(k+N-1|k)] T (16) Design the following cost function: Where: coefficient a = 4ρπ 2 r 2 lv,u c is the desired torque output by the Backstepping controller and also the reference input of the MPC controller, and u is the control input vector of the MPC controller; According to the recursive principle of the MPC controller, the standard form for solving the quadratic programming problem is finally obtained: The result obtained from the above formula is a set of control sequences that minimize the cost function. This control sequence will be used as the control input of the servo motor dynamic model so that the optimal speed sequence is distributed to the four rotary column stabilizers. In this case, both the anti-roll effect and the energy consumption problem are taken into account, and it can respond quickly without exceeding the output limit, which is in line with the actual operating conditions.

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