Multi-axis speed synchronous control method for ship block attitude adjusting equipment

Abstract

The invention discloses a multi-axis speed synchronous control method for ship block attitude adjusting equipment. The multi-axis speed synchronous control method comprises the steps that S1, a permanent magnet synchronous motor (PMSM) mathematical model is established; s2, establishing a permanent magnet synchronous motor PMSM driver model; s3, constructing an average coupling controller; s4, based on a sliding mode control theory, establishing a speed tracking controller and a speed synchronization controller, and improving the average coupling controller in the S3; and S5, constructing a Lyapunov function to verify the stability of the improved average coupling controller in the S4. On the basis of sliding mode control, tracking errors are used for replacing speed values in a traditional average deviation coupling controller for difference, the multi-motor speed synchronization performance is improved, the anti-interference capacity of a synchronization structure is enhanced, the steady-state precision of the system is guaranteed, the robustness of the system is enhanced, and the system reliability is improved. And the ship block attitude adjusting equipment control system can maintain efficient and stable synchronous operation under various working conditions.

Description

Technical Field

[0001] The invention relates to a multi-axis speed synchronization control method for ship section attitude adjustment equipment, belonging to the technical field of ship attitude adjustment. Background Art

[0002] As the core technology in the operation of ship section attitude adjustment equipment, multi-axis speed synchronization technology has control strategies including master-slave control, which sets a master axis and multiple slave axes, and the slave axis speed will be adjusted synchronously according to the master axis speed; adjacent coupling control, which realizes mutual coupling between axes, and each axis adjusts its own speed synchronously according to the state of the adjacent axis; ring coupling control, which improves overall synchronization by forming a closed-loop system, and each axis is coupled not only with the adjacent axis, but also with other axes in the ring system; average deviation coupling control, which realizes balanced synchronization of all axes based on the average speed and deviation of all axes. In terms of synchronization algorithm, fuzzy control improves the accuracy and robustness of synchronization control by dealing with the uncertainty and fuzziness of the system; neural network control uses the learning ability of artificial neural networks to model and control complex systems, showing strong adaptability; sliding mode control realizes fast and accurate tracking of system status by designing sliding modes, and has excellent anti-interference ability and high-precision synchronization.

[0003] The average coupling control strategy has demonstrated its unique optimization capabilities and high applicability in the field of multi-motor synchronous control. This control method based on the strategy of minimizing correlation not only effectively optimizes the traditional adjacent coupling control, but also simplifies the composition of a single motor controller by focusing on the state feedback of two adjacent axes, including the following error controller and the synchronous error controller of two adjacent axes. Although the increase in the number of motors will not lead to significant complexity of the algorithm of a single controller, it will introduce system control delay problems because the state change of one motor cannot immediately affect non-adjacent motors.

[0004] As the number of motors increases, the problems faced in the field of multi-axis synchronous control gradually increase, including the increase in computational complexity and controller complexity. In order to solve these problems, optimizing the control structure has become the focus of research, with the goal of maintaining synchronization accuracy while reducing system complexity. In particular, with the growing demand for position synchronization, the research focus has shifted from speed synchronization to more complex position synchronization. In terms of control strategy comparison, adjacent cross-coupling and deviation coupling control perform similarly in terms of synchronous control performance. Although the adjacent coupling controller has a simpler structure and stronger scalability, it has a delay in its response to disturbances of non-adjacent axes.

[0005] In summary, the multi-axis speed synchronization control method of ship section attitude adjustment equipment still faces many challenges. China has not yet formed a mature technical system in the field of automated ship section attitude adjustment equipment, and there are problems such as poor multi-motor speed synchronization and weak anti-interference ability of the synchronization structure. Summary of the invention

[0006] Purpose of the invention: In view of the deficiencies in the prior art, the present invention provides a multi-axis speed synchronization control method for ship section attitude adjustment equipment. The present invention adopts an improved average deviation coupling control structure. On the basis of sliding mode control, the tracking error replaces the speed value difference in the traditional average deviation coupling controller, thereby improving the multi-motor speed synchronization performance and enhancing the anti-interference ability of the synchronization structure.

[0007] Technical solution: A method for synchronously controlling multi-axis speed of ship section attitude adjustment equipment, comprising the following steps:

[0008] S1: Establish a mathematical model of the permanent magnet synchronous motor (PMSM) and derive a directional method for controlling the permanent magnet synchronous motor;

[0009] S2: Establish a permanent magnet synchronous motor PMSM drive model according to the permanent magnet synchronous motor mathematical model in S1;

[0010] S3: construct an average coupling controller according to the PMSM drive model established in S2;

[0011] S4: Based on the sliding mode control theory, a speed tracking controller and a speed synchronization controller are established to improve the average coupling controller in S3;

[0012] S5: Construct the Lyapunov function to verify the stability of the improved average coupling controller in S4.

[0013] Preferably, the S1 is specifically:

[0014] The stator and rotor coordinate systems have the following transformation relationship:

[0015]

[0016] Among them, i A 、i B 、i C is the stator three-phase current; C is the coefficient; i o is the zero-sequence current; i d with i q Indicates d-axis and q-axis currents;

[0017] This transformation directly transforms the quantity in the rotor two-phase rotating coordinate system into the stator three-phase stationary coordinate system, thus we can get:

[0018]

[0019] Where: i d with i q represents the d-axis and q-axis currents; i A 、i B 、i C is the stator three-phase current; i o is the zero-sequence current, the induced electromotive force of the stator winding can be regarded as the back electromotive force, the stator applied voltage u and the back electromotive force e and the stator resistance voltage drop R is Phase balance, thus the voltage balance equation of phase A is written as u A :

[0020]

[0021] Where: A is the flux linkage of phase A; R s is the stator phase resistance;

[0022] Substituting the variables in formula (1) into formula (3), we can get:

[0023]

[0024] Where: 0 is the rated magnetic flux; u 0 Stator external rated voltage;

[0025] After sorting, we get:

[0026]

[0027] Where: d With q represents the magnetic flux between the d-axis and the q-axis; R s represents the stator phase resistance;

[0028] The above formula should hold true for any value of the angle θ, so the stator voltage equation can be obtained:

[0029]

[0030] Among them: U d with U q represents the d-axis and q-axis voltages, and:

[0031]

[0032] Where: L d With L q represents the d-axis and q-axis inductance, Ψt is the armature flux;

[0033] The electromagnetic torque formula of the motor is:

[0034] Tem =P n (ψ d i q -ψ q i d ) (8)

[0035] Where: P n is the number of motor pole pairs,

[0036] In summary, the stator voltage equation of the permanent magnet synchronous motor in the rotating coordinate system can be obtained:

[0037]

[0038] Where: P is the differential operator; Ψ r Represents the flux linkage of the permanent magnet fundamental wave excitation magnetic field through the stator winding; ω r is the electronic angular speed;

[0039] Stator flux equation:

[0040]

[0041] Electromagnetic torque equation:

[0042] T em =P n (ψ d i q -ψ q i d )=P n [ψ r i q +(L d -L q )i d i q ] (11)

[0043] Motor motion equation:

[0044]

[0045] Where: T em is the electromagnetic torque; T L is the load torque; B is the viscous friction coefficient; ω is the rotor electrical angular velocity; J is the total moment of inertia,

[0046] Since the stator quadrature-axis current component and the rotor flux determine the motor torque, a rotor flux orientation method is used in the permanent magnet synchronous motor to control the permanent magnet synchronous motor.

[0047] Preferably, S2 is specifically:

[0048] According to the permanent magnet synchronous motor mathematical model established by S1, the electromagnetic torque equation of the permanent magnet synchronous motor can be described as:

[0049]

[0050] Among them, n p is the pole pair number; f is the permanent magnetic flux;

[0051] Electromagnetic dynamics is expressed as:

[0052]

[0053] Where: T e is the electromagnetic torque; T L is the load torque; J is the inertia torque; B is the viscous friction coefficient,

[0054] By using i-based d =0, the dynamic decoupling strategy of vector control can be obtained:

[0055] T e =k p i q (15)

[0056]

[0057] Among them, k p is the magnification;

[0058] Bring (17) into (15)

[0059]

[0060] The motion equation of the i-axis rotor is obtained:

[0061]

[0062] in:

[0063] In order to realize the nominal model of the permanent magnet synchronous motor drive, the nominal values ​​of the parameters must be considered without any disturbances. Therefore, the nominal model of the PMSM drive given by (15) is changed to:

[0064]

[0065] in, They are respectively i With k iIn order to cope with the uncertainty, that is, when the system parameters deviate from the nominal values ​​or the external load is disturbed, these factors must be considered and added to the nominal model of the PMSM real-time drive. Therefore, considering the structured and unstructured uncertainties and unmodeled dynamics of the actual PMSM drive, formula (19) can be expressed as:

[0066]

[0067] d i (t) = △a i ω i (t)+△k i i q(i) (t)+c i T L(i) +d i (twenty one)

[0068] Among them, △a i and △k i Denotes uncertainty, δ i represents the unstructured uncertainty caused by non-ideal current or field-oriented control in transient processes and the unmodeled dynamics in practical applications. In the above equation, L i (t) is called the lumped uncertainty, where it is assumed that for all |L i (t)|<σ, t∈(0,∞), σ is a normal number.

[0069] Preferably, S3 is specifically:

[0070] According to the permanent magnet synchronous motor shown in formula (20), the speed tracking error of the i-th motor is

[0071] e i (t) = ω i (t)-ω*(t) (22)

[0072] Where: i is the actual speed; ω* is the expected speed,

[0073] The speed synchronization error between the i-th motor and the i+1-th motor is:

[0074] e i,i+1 (t) = x i (t)-x i+1 (t) (23)

[0075] Where: X i is the speed of the i-th motor, X i+1 is the speed of the i+1th motor;

[0076] The average speed error of motor i is:

[0077]

[0078] Where x m is the average error of all speeds; n is the total number of motors.

[0079] Preferably, the S4 is specifically:

[0080] S41: Establish a speed tracking controller to obtain the tracking control current of the i-th motor;

[0081] S42: Establish a speed synchronization controller to obtain the synchronous control current of the i-th motor;

[0082] S43: Obtain an improved average coupling controller and obtain the control current of the i-th motor.

[0083] Preferably, the S41 is specifically:

[0084] Substitute equation (20) into equation (23) and take the derivative to obtain

[0085]

[0086] Where: e i is the mechanical speed error change rate; u i (t) is the tracking control input; d i (t) is the uncertainty factor, eωi is the rotor speed error;

[0087] Assume the state variable of the tracking error function is:

[0088]

[0089] Among them, X 1i is the tracking error of the i-th motor; X 2i is the tracking error of the i+1th motor;

[0090] In order to make the speed tracking error converge quickly, a nonlinear function is introduced into the sliding surface, and the global fast sliding surface of the speed tracking controller is defined as:

[0091]

[0092] Where β is the nonlinear part gain; p and q are positive odd numbers, and p>q; h i (t) is the global sliding mode factor for tracking control. The sliding mode factor condition is established: hi(t) needs to satisfy the following conditions at the same time:

[0093] (1)

[0094] (2) When t→+∞, hi(t)→0;

[0095] (3)h i (t) is first-order differentiable,

[0096] To meet the above conditions, we select h i (t) is:

[0097]

[0098] Assume that the sliding mode control law of the motor speed tracking controller is:

[0099]

[0100] By combining equations (26) and (31), we can get the tracking control current i of the i-th motor: qsi for

[0101]

[0102] Among them, H 1i is the global sliding mode factor of motor tracking control; D is the system boundary; η is the boundary layer thickness.

[0103] Preferably, the S42 is specifically:

[0104] Define the global fast sliding surface of the speed synchronization controller and the global sliding factor of the synchronization control:

[0105] Substitute equation (20) into equation (23) and take the derivative of equation (23) to obtain

[0106] e sy (t) = e i (t)-e ix (t) = -a i e i (t)+u syi (t)+d i (t) (33)

[0107]

[0108] Where: u syi (t) is the synchronous control input, e sy To synchronously control the global fast sliding surface; e ix is the synchronization error of the i-th motor;

[0109] Assume the state variable of synchronization error function:

[0110]

[0111] Define the global fast sliding surface of the speed synchronization controller:

[0112]

[0113] Where: x lsyi h is the global sliding mode factor of motor synchronous control; sji To synchronously control the global sliding mode factor;

[0114] h syi (t) is the global sliding mode factor of synchronous control, and its calculation formula is:

[0115]

[0116] Where: h syi is the global sliding mode factor for synchronous control; e syi The global fast sliding surface for synchronous control of the i-th motor;

[0117] The sliding mode control law of the synchronous controller is defined as:

[0118]

[0119] By combining equations (34) and (38), the synchronous control current of the i-th motor can be obtained as:

[0120] Preferably, the S43 is specifically:

[0121] Combining equations (33) and (39), we can get the control current i*qsi of the i-th motor as:

[0122]

[0123] Preferably, the S5 is specifically:

[0124] Construct a Lyapunov function to verify the stability of the improved controller:

[0125]

[0126] The derivative of formula (41) with respect to time is:

[0127]

[0128] Among them, β q is the sliding surface attractor;

[0129] Substituting equations (25) and (33) into equation (42), we can obtain:

[0130]

[0131] Substituting equations (31) and (38) into equation (43), we obtain:

[0132]

[0133] Since p and q are positive odd numbers and 1<p / q<2, β>0, therefore:

[0134]

[0135] When x 2i or x 2syi When it is not zero, V(0) = 0, V(t) is positive definite. From equation (45), we can know that is negative definite, so the control system is globally asymptotically stable, and the equilibrium point is zero.

[0136] When x 2i or x 2syi When is zero, substitute equations (31) and (38) into equations (28) and (35) respectively to obtain

[0137]

[0138] From formula (46), we can see that when S syi >0, x 2syi ≤-η, speed synchronization error e syi Convergence; when S i >0, x 2i ≤-η, speed tracking error e i Convergence; when S i When x < 0, 2i >-η, making the speed tracking error ei diverge; when S syi When x < 0, 2syi ≥-η, speed synchronization error e syi Diverge,

[0139] When x 2i With x 2syi When all are zero, the system is stable, making e i 、e syi Approaches zero,

[0140] When the sliding surface S is equal to zero, equations (29) and (36) can be simplified to obtain

[0141]

[0142] Formula (47) can be rewritten as:

[0143]

[0144] From formula (48), we can see that when x is close to the equilibrium point, -βx determines the convergence speed of the system. When x is far away from the equilibrium point, βh(0)x-k 1 t determines the convergence speed of the system and ensures the globality of the sliding mode.

[0145] In order to reduce the system chattering caused by the switching of the sliding mode control law defined in equations (31) and (38), the function tanh(S / τ) is used to replace the function sgn(S) to reduce the chattering of the control signal. tanh(S / τ) is defined as

[0146]

[0147] In the formula: τ>0 determines the rate of change of the inflection point of the function.

[0148] Beneficial effects: The present invention aims at the problems that the overall section attitude adjustment equipment has poor speed synchronization and weak anti-interference ability of the synchronization structure due to the need for multi-motor coupling control, and preferably adopts the average deviation coupling control structure to solve the multi-axis control problem of the overall section attitude adjustment equipment of the ship; and further proposes an improved average deviation coupling control structure. On the basis of sliding mode control, the tracking error is used instead of the speed value in the traditional average deviation coupling controller as the difference, so as to improve the multi-motor speed synchronization performance and enhance the anti-interference ability of the synchronization structure. The improved average coupling controller not only ensures the steady-state accuracy of the system, but also enhances the robustness of the system, so that the control system of the overall section attitude adjustment equipment of the ship can maintain efficient and stable synchronous operation under various working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0149] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0150] Figure 1 is a flow chart of the method of the present invention;

[0151] Figure 2 This is the average coupling control structure diagram of the improved ship section attitude adjustment equipment of the present invention;

[0152] Figure 3(a) is a traditional average control chart;

[0153] Figure 3(b) is the optimized average control chart;

[0154] Figure 4 This is the running speed extreme difference curve. DETAILED DESCRIPTION

[0155] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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.

[0156] In the description of the present invention, it is necessary to understand that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0157] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0158] like Figure 1 As shown, a method for multi-axis speed synchronization control of ship section attitude adjustment equipment includes the following steps:

[0159] S1: Establish a mathematical model of the permanent magnet synchronous motor (PMSM) and derive a directional method for controlling the permanent magnet synchronous motor;

[0160] The stator and rotor coordinate systems have the following transformation relationship:

[0161]

[0162] This transformation directly transforms the quantity in the rotor two-phase rotating coordinate system into the stator three-phase stationary coordinate system, thus we can get:

[0163]

[0164] Where: i d with i q represents the d-axis and q-axis currents; the induced electromotive force of the stator winding can be regarded as the back electromotive force, the stator applied voltage u and the back electromotive force e and the stator resistance voltage drop R isPhase balance, thus the voltage balance equation of phase A is written as:

[0165]

[0166] Substituting the variables in formula (1) into formula (3), we can get:

[0167]

[0168] After sorting, we get:

[0169]

[0170] Where: d With q represents the magnetic flux between the d-axis and the q-axis; R s represents the stator phase resistance,

[0171] The above formula should hold true for any value of the angle θ, so the stator voltage equation can be obtained:

[0172]

[0173] Among them: U d with U q represents the d-axis and q-axis voltages, and:

[0174]

[0175] Where: L d With L q represents the d-axis and q-axis inductance,

[0176] The electromagnetic torque formula of the motor is:

[0177] T em =P n (ψ d i q -ψ q i d ) (8)

[0178] Where: P n is the number of motor pole pairs,

[0179] In summary, the stator voltage equation of the permanent magnet synchronous motor in the rotating coordinate system can be obtained:

[0180]

[0181] Where: P is the differential operator; Ψ r It indicates the flux linkage of the fundamental wave excitation magnetic field of the permanent magnet passing through the stator winding;

[0182] Stator flux equation:

[0183]

[0184] Electromagnetic torque equation:

[0185] T em =P n (ψ d i q -ψ q i d )=P n [ψ r i q +(L d -L q )i d i q ] (11)

[0186] Motor motion equation:

[0187]

[0188] Where: T em is the electromagnetic torque; T L is the load torque; B is the viscous friction coefficient; ω is the rotor electrical angular velocity; J is the total moment of inertia,

[0189] Since the stator quadrature-axis current component and the rotor flux determine the motor torque, a rotor flux orientation method is used in the permanent magnet synchronous motor to control the permanent magnet synchronous motor.

[0190] S2: Establish a permanent magnet synchronous motor PMSM drive model according to the permanent magnet synchronous motor mathematical model in S1;

[0191] According to the permanent magnet synchronous motor mathematical model established by S1, the electromagnetic torque equation of the permanent magnet synchronous motor can be described as:

[0192]

[0193] Electromagnetic dynamics is expressed as:

[0194]

[0195] Where: T e is the electromagnetic torque; T L is the load torque; J is the inertia torque; B is the viscous friction coefficient,

[0196] By using i-based d =0, the dynamic decoupling strategy of vector control can be obtained:

[0197] T e =k p i q (15)

[0198]

[0199] Bring (17) into (15)

[0200]

[0201] The motion equation of the i-axis rotor is obtained:

[0202]

[0203] in:

[0204] In order to realize the nominal model of the permanent magnet synchronous motor drive, the nominal values ​​of the parameters must be considered without any disturbances. Therefore, the nominal model of the PMSM drive given by (15) is changed to:

[0205]

[0206] in, They are respectively i With k i In order to cope with the uncertainty, that is, when the system parameters deviate from the nominal values ​​or the external load is disturbed, these factors must be considered and added to the nominal model of the PMSM real-time drive. Therefore, considering the structured and unstructured uncertainties and unmodeled dynamics of the actual PMSM drive, formula (19) can be expressed as:

[0207]

[0208] d i (t) = △a i ω i (t)+△k i i q(i) (t)+c i T L(i) +d i (twenty one)

[0209] Among them, △a i and △k i Denotes uncertainty, δ i represents the unstructured uncertainty caused by non-ideal current or field-oriented control in transient processes and the unmodeled dynamics in practical applications. In the above equation, L i (t) is called the lumped uncertainty, where it is assumed that for all |L i (t)|<σ, t∈(0,∞), σ is a normal number.

[0210] S3: construct an average coupling controller according to the PMSM drive model established in S2;

[0211] According to the permanent magnet synchronous motor shown in formula (20), the speed tracking error of the i-th motor is

[0212] e i (t) = ω i (t)-ω*(t) (22)

[0213] Where: i is the actual speed; ω* is the expected speed,

[0214] The speed synchronization error between the i-th motor and the i+1-th motor is:

[0215] e i,i+1 (t) = x i (t)-x i+1 (t) (23)

[0216] The average speed error of motor i is:

[0217]

[0218] The core idea of ​​the multi-motor speed average coupling control structure is to subtract the motor speed tracking error from the average error of all motors to obtain the speed compensation value. This process not only helps the controller to compensate for the tracking error and synchronization error at the same time, but also realizes the coupling of all motor speeds in the system. However, due to the need to average the speed tracking error and the sum of the errors between each motor, the entire system has too many input parameters. A change in one parameter will cause the entire system to oscillate, and the system will be extremely susceptible to disturbances. Therefore, this paper combines the sliding mode control principle to improve the traditional average coupling control structure.

[0219] S4: Based on the sliding mode control theory, a speed tracking controller and a speed synchronization controller are established to improve the average coupling controller in S3;

[0220] S41: Establish a speed tracking controller to obtain the tracking control current of the i-th motor;

[0221] Substitute equation (20) into equation (23) and take the derivative to obtain

[0222]

[0223] Where: e i is the mechanical speed error change rate; u i (t) is the tracking control input; d i (t) is an uncertain factor, and the state variable of the tracking error function is assumed to be:

[0224]

[0225] In order to make the speed tracking error converge quickly, a nonlinear function is introduced into the sliding surface, and the global fast sliding surface of the speed tracking controller is defined as:

[0226]

[0227] Where β is the nonlinear part gain; p and q are positive odd numbers, and p>q; h i (t) is the global sliding mode factor for tracking control. The sliding mode factor condition is established: hi(t) needs to satisfy the following conditions at the same time:

[0228] (1)

[0229] (2) When t→+∞, hi(t)→0;

[0230] (3)h i (t) is first-order differentiable. To meet the above conditions, select h i (t) is:

[0231]

[0232] Assume that the sliding mode control law of the motor speed tracking controller is:

[0233]

[0234] By combining equations (26) and (31), we can get the tracking control current i of the i-th motor: qsi for

[0235]

[0236] S42: Establish a speed synchronization controller to obtain the synchronous control current of the i-th motor;

[0237] Define the global fast sliding surface of the speed synchronization controller and the global sliding factor of the synchronization control:

[0238] Substitute equation (20) into equation (23) and take the derivative of equation (23) to obtain

[0239] e sy (t) = e i (t)-e ix (t) = -a i e i (t)+u syi (t)+d i (t) (33)

[0240]

[0241] Where: u syi (t) is the synchronous control input,

[0242] Assume the state variable of synchronization error function:

[0243]

[0244] Define the global fast sliding surface of the speed synchronization controller:

[0245]

[0246] Where: h syi (t) is the global sliding mode factor of synchronous control, and its calculation formula is:

[0247]

[0248] The sliding mode control law of the synchronous controller is defined as:

[0249]

[0250] By combining equations (34) and (38), the synchronous control current of the i-th motor can be obtained as:

[0251]

[0252] S43: Obtain an improved average coupling controller and obtain the control current of the i-th motor;

[0253] Combining equations (33) and (39), we can get the control current i*qsi of the i-th motor as:

[0254]

[0255] Therefore, the improved average coupling control structure of the ship section attitude adjustment equipment is as follows: Figure 2 shown.

[0256] S5: Construct Lyapunov function to verify the stability of the improved average coupling controller in S4;

[0257] Construct a Lyapunov function to verify the stability of the improved controller:

[0258]

[0259] The derivative of formula (41) with respect to time is:

[0260]

[0261] Substituting equations (25) and (33) into equation (42), we can obtain:

[0262]

[0263] Substituting equations (31) and (38) into equation (43), we obtain:

[0264]

[0265] Since p and q are positive odd numbers and 1<p / q<2, β>0, therefore:

[0266]

[0267] When x 2i or x 2syi When it is not zero, V(0) = 0, V(t) is positive definite. From equation (45), we can know that is negatively definite, so the control system is globally asymptotically stable, and the equilibrium point is zero.

[0268] When x 2i or x 2syi When is zero, substitute equations (31) and (38) into equations (28) and (35) respectively to obtain

[0269]

[0270] From formula (46), we can see that when S syi >0, x 2syi ≤-η, speed synchronization error e syi Convergence; when S i >0, x 2i ≤-η, speed tracking error e i Convergence; when S i When x < 0 2i >-η, making the speed tracking error ei diverge; when S syi When x < 0 2syi ≥-η, speed synchronization error e syi Diverge,

[0271] When x 2i With x 2syi When all are zero, the system is stable, making e i 、e syi Approaches zero,

[0272] When the sliding surface S is equal to zero, equations (29) and (36) can be simplified to obtain

[0273]

[0274] Formula (47) can be rewritten as:

[0275]

[0276] From formula (48), we can see that when x is close to the equilibrium point, -βx determines the convergence speed of the system. When x is far away from the equilibrium point, βh(0)x-k 1 t determines the convergence speed of the system and ensures the globality of the sliding mode.

[0277] In order to reduce the system chattering caused by the switching of the sliding mode control law defined in equations (31) and (38), the function tanh(S / τ) is used to replace the function sgn(S) to reduce the chattering of the control signal. tanh(S / τ) is defined as

[0278]

[0279] In the formula: τ>0 determines the rate of change of the inflection point of the function.

[0280] Multi-axis speed synchronization simulation of posture adjustment equipment:

[0281] Multi-axis motion anti-interference analysis:

[0282] In order to verify the effectiveness and reliability of the multi-axis speed synchronization control method, according to the actual ship section attitude adjustment car, four attitude adjustment car Z-axis direction motors are taken as the controlled objects, and their parameters are shown in Table 1.

[0283] Table 1 Parameters of the posture adjustment car

[0284]

[0285] The Simulink simulation module in MATLAB 2022a is used to simulate and verify the improved average deviation coupling control method without loading. According to the actual parameters of the ship's general section attitude adjustment equipment, the multi-motor speed synchronization control is set when facing sudden interference, as shown in Figure 3 (a) and (b).

[0286] Table 2 Summary of the effects of optimized coupling control structure

[0287]

[0288] As shown in Figure 3(a) and Table 2, during the motor startup phase, the traditional average coupling control structure without the introduction of sliding mode control has a large overshoot, with the maximum overshoot reaching 14.5%. When facing disturbance interference, the maximum disturbance reaches 35rad / s, and the maximum synchronization error is 30rad / s; the time for disturbance recovery is 0.032s. The improved average deviation coupling control based on sliding mode control has only a small overshoot during the motor startup phase, with the maximum overshoot being only 3.5%. At the same time, it has better robustness when facing sudden disturbances, with the disturbance variable being 15rad / s and the maximum synchronization error being only 8rad / s; and the time used to recover the stable state is also shortened to 0.021s, shortened by 34.375%.

[0289] Multi-axis motion speed synchronization analysis:

[0290] First, a multi-axis operation speed synchronization test was conducted, and the motion of the four lifting motors during the translation of the ship's main section was simulated and verified. The simulation environment was set to a multi-axis motion system that ran steadily at a speed of 1500rad / s for 20s, and several random interferences with a step value of 2 were added during the operation to simulate the interference caused by the mechanical vibration of the attitude adjustment equipment when it was working. The speed difference extreme value was extracted for comparison. A total of 5 experiments were conducted to obtain the operation speed extreme difference curve Figure 4 And the statistics are shown in Table 3.

[0291] Table 3 Extreme values ​​of running speed error

[0292]

[0293] From the experimental data, in the process of multi-motor synchronous control of ship section attitude adjustment equipment, except for the master-slave control in terms of running time control, the other mainstream control structures can meet the control requirements of speed error of 20rad / s. Among them, the ring coupling control and adjacent coupling control have similar speed synchronization, and the maximum speed error is about 20rad / s. When the average coupling control is adopted, the speed synchronization is significantly improved, and the maximum speed difference fluctuates around 13rad / s, which is better than other control structures. The improved average coupling control structure further improves the synchronization of the four motors, reduces the maximum speed difference to 9rad / s, and reduces the average speed error by 42.63%, which meets the stability requirements during the translation of the ship section.

[0294] In summary, the improved average coupling control strategy shows superior performance advantages over the traditional average coupling control, especially in improving the synchronization accuracy and dynamic response of the system. The improved average coupling control strategy can reduce the speed tracking error of each motor and the speed synchronization error between motors more quickly, and achieve faster error convergence speed, which is especially important for the control system of the ship's general section attitude adjustment equipment that requires high-precision synchronization. In steady-state operation, the improved average coupling control has no static error, which ensures the high synchronization accuracy of the equipment under long-term operation. In addition, it has better dynamic adjustment ability, can quickly adapt to system state changes, and maintain the stability and synchronization of the system. In the face of sudden interference, the improved average coupling control can effectively limit error fluctuations and show good anti-interference ability. At the same time, the improved control improves the system's response speed to external changes and internal state changes, so that the error can converge to a level close to zero in a shorter time. Therefore, the improved average coupling control strategy not only ensures the steady-state accuracy of the system, but also enhances the robustness of the system, so that the ship's general section attitude adjustment equipment control system can maintain efficient and stable synchronous operation under various working conditions.

[0295] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0296] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for synchronously controlling multi-axis speeds of ship section attitude adjustment equipment, characterized in that: The following steps are involved: S1: Establish a mathematical model of the permanent magnet synchronous motor (PMSM) and derive a directional method for controlling the permanent magnet synchronous motor; S2: Establish a permanent magnet synchronous motor PMSM drive model according to the permanent magnet synchronous motor mathematical model in S1; S3: construct an average coupling controller according to the PMSM drive model established in S2; S4: Based on the sliding mode control theory, a speed tracking controller and a speed synchronization controller are established to improve the average coupling controller in S3; S5: Construct a Lyapunov function to verify the stability of the improved average coupling controller in S4.

2. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 1 is characterized by: The S1 is specifically: The stator and rotor coordinate systems have the following transformation relationship: Among them, i A 、i B 、i C is the stator three-phase current; C is the coefficient; i o is the zero-sequence current; i d with i q Indicates d-axis and q-axis currents; This transformation directly transforms the quantity in the rotor two-phase rotating coordinate system into the stator three-phase stationary coordinate system, thus we can get: Where: i d with i q represents the d-axis and q-axis currents; i A 、i B 、i C is the stator three-phase current; i o is the zero-sequence current, the induced electromotive force of the stator winding can be regarded as the back electromotive force, the stator applied voltage u and the back electromotive force e and the stator resistance voltage drop R is Phase balance, thus the voltage balance equation of phase A is written as u A : Where: A is the flux linkage of phase A; R s is the stator phase resistance; Substituting the variables in formula (1) into formula (3), we can get: Where: Ψ0 is the rated flux; u0 is the rated voltage applied to the stator; After sorting, we get: Where: d With q represents the magnetic flux between the d-axis and the q-axis; R s represents the stator phase resistance; The above formula should hold true for any value of the angle θ, so the stator voltage equation can be obtained: Among them: U d with U q represents the d-axis and q-axis voltages, and: Where: L d With L q represents the d-axis and q-axis inductance, Ψt is the armature flux; The electromagnetic torque formula of the motor is: T em =P n (ψ d I q -ψ q I d ) (8) Where: P n is the number of motor pole pairs, In summary, the stator voltage equation of the permanent magnet synchronous motor in the rotating coordinate system can be obtained: Where: P is the differential operator; Ψ r Represents the flux linkage of the permanent magnet fundamental wave excitation magnetic field through the stator winding; ω r is the electronic angular speed; Stator flux equation: Electromagnetic torque equation: T em =P n (ψ d i q -ψ q i d )=P n [ψ r i q +(L d -L q )i d i q ] (11) Motor motion equation: Where: T em is the electromagnetic torque; T L is the load torque; B is the viscous friction coefficient; ω is the rotor electrical angular velocity; J is the total moment of inertia, Since the stator quadrature-axis current component and the rotor flux determine the motor torque, a rotor flux orientation method is used in the permanent magnet synchronous motor to control the permanent magnet synchronous motor.

3. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 2 is characterized in that: The S2 is specifically: According to the permanent magnet synchronous motor mathematical model established by S1, the electromagnetic torque equation of the permanent magnet synchronous motor can be described as: Among them, n p is the pole pair number; f is the permanent magnetic flux; Electromagnetic dynamics is expressed as: Where: T e is the electromagnetic torque; T L is the load torque; J is the inertia torque; B is the viscous friction coefficient, By using i-based d =0, the dynamic decoupling strategy of vector control can be obtained: T e =k p i q (15) Among them, k p is the magnification; Bring (17) into (15) The motion equation of the i-axis rotor is obtained: in: In order to realize the nominal model of the permanent magnet synchronous motor drive, the nominal values ​​of the parameters must be considered without any disturbances. Therefore, the nominal model of the PMSM drive given by (15) is changed to: in, They are respectively i With k i In order to cope with the uncertainty, that is, when the system parameters deviate from the nominal values ​​or the external load is disturbed, these factors must be considered and added to the nominal model of the PMSM real-time drive. Therefore, considering the structured and unstructured uncertainties and unmodeled dynamics of the actual PMSM drive, formula (19) can be expressed as: Among them, △a i and △k i Denotes uncertainty, δ i represents the unstructured uncertainty caused by non-ideal current or field-oriented control in transient processes and the unmodeled dynamics in practical applications. In the above equation, L i (t) is called the lumped uncertainty, where it is assumed that for all |L i (t)|<σ, t∈(0,∞), σ is a normal number.

4. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 3 is characterized by: The S3 is specifically: According to the permanent magnet synchronous motor shown in formula (20), the speed tracking error of the i-th motor is e i (t)=ω i (t)-ω*(t) (22) Where: i is the actual speed; ω* is the expected speed, The speed synchronization error between the i-th motor and the i+1-th motor is: e i,i+1 (t)=x i (t)-x i+1 (t) (23) Where: X i is the speed of the i-th motor, X i+1 is the speed of the i+1th motor; The average speed error of motor i is: Where x m is the average error of all speeds; n is the total number of motors.

5. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 4 is characterized in that: The S4 is specifically: S41: Establish a speed tracking controller to obtain the tracking control current of the i-th motor; S42: Establish a speed synchronization controller to obtain the synchronous control current of the i-th motor; S43: Obtain an improved average coupling controller and obtain the control current of the i-th motor.

6. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 5 is characterized by: The S41 is specifically: Substitute equation (20) into equation (23) and take the derivative to obtain Where: e i is the mechanical speed error change rate; u i (t) is the tracking control input; d i (t) is the uncertainty factor, eωi is the rotor speed error; Assume the state variable of the tracking error function is: Among them, X 1i is the tracking error of the i-th motor; X 2i is the tracking error of the i+1th motor; In order to make the speed tracking error converge quickly, a nonlinear function is introduced into the sliding surface, and the global fast sliding surface of the speed tracking controller is defined as: Where β is the nonlinear part gain; p and q are positive odd numbers, and p>q; h i (t) is the global sliding mode factor of tracking control, Sliding factor condition establishment: hi(t) needs to satisfy the following conditions at the same time: (1) (2) When t→+∞, hi(t)→0; (3)h i (t) is first-order differentiable, To meet the above conditions, we select h i (t) is: Assume that the sliding mode control law of the motor speed tracking controller is: By combining equations (26) and (31), we can get the tracking control current i of the i-th motor: qsi for Among them, H 1i is the global sliding mode factor of motor tracking control; D is the system boundary; η is the boundary layer thickness.

7. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 6 is characterized by: The S42 is specifically: Define the global fast sliding surface of the speed synchronization controller and the global sliding factor of the synchronization control: Substitute equation (20) into equation (23) and take the derivative of equation (23) to obtain e sy (t)=e i (t)-e ix (t)=-a i e i (t)+u syi (t)+d i (t) (33) Where: u syi (t) is the synchronous control input, e sy To synchronously control the global fast sliding surface; e ix is the synchronization error of the i-th motor; Assume the state variable of synchronization error function: Define the global fast sliding surface of the speed synchronization controller: Where: x lsyi h is the global sliding mode factor of motor synchronous control; sji To synchronously control the global sliding mode factor; h syi (t) is the global sliding mode factor of synchronous control, and its calculation formula is: Where: h syi is the global sliding mode factor for synchronous control; e syi The global fast sliding surface for synchronous control of the i-th motor; The sliding mode control law of the synchronous controller is defined as: By combining equations (34) and (38), the synchronous control current of the i-th motor can be obtained as: 。 8. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 7 is characterized by: The S43 is specifically: Combining equations (33) and (39), we can get the control current i*qsi of the i-th motor as: 。 9. The multi-axis speed synchronization control method for ship section attitude adjustment equipment according to claim 8 is characterized in that: The S5 is specifically: Construct a Lyapunov function to verify the stability of the improved controller: The derivative of formula (41) with respect to time is: Among them, β q is the sliding surface attractor; Substituting equations (25) and (33) into equation (42), we can obtain: Substituting equations (31) and (38) into equation (43), we obtain: Since p and q are positive odd numbers and 1<p / q<2, β>0, therefore: When x2i or x 2syi When it is not zero, V(0) = 0, V(t) is positive definite. From equation (45), we can know that is negatively definite, so the control system is globally asymptotically stable, and the equilibrium point is zero. When x 2i or x 2syi When is zero, substitute equations (31) and (38) into equations (28) and (35) respectively to obtain From formula (46), we can see that when S syi >0, x 2syi ≤-η, speed synchronization error e syi Convergence; when S i >0, x 2i ≤-η, speed tracking error e i Convergence; when S i When x < 0 2i >-η, making the speed tracking error ei diverge; when S syi When x < 0 2syi ≥-η, speed synchronization error e syi Diverge, When x 2i With x 2syi When all are zero, the system is stable, making e i 、e syi Approaches zero, When the sliding surface S is equal to zero, equations (29) and (36) can be simplified to obtain Formula (47) can be rewritten as: It can be seen from formula (48) that when x is close to the equilibrium point, -βx determines the convergence speed of the system, and when x is far away from the equilibrium point, βh(0)x-k1t determines the convergence speed of the system, which ensures the globality of the sliding mode. In order to reduce the system chattering caused by the switching of the sliding mode control law defined in equations (31) and (38), the function tanh(S / τ) is used to replace the function sgn(S) to reduce the chattering of the control signal. tanh(S / τ) is defined as In the formula: τ>0 determines the rate of change of the inflection point of the function.

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