CN113300644B - Nacelle propulsion motor sliding mode control method based on compact-format dynamic linearization - Google Patents

Abstract

The invention discloses a sliding mode control method for a pod propulsion motor based on tight-format dynamic linearization, which is suitable for the control of the pod propulsion motor. The steps include: establishing a dynamic model of the pod propulsion motor; establishing a compact dynamic linearization data model of the dynamic model of the pod propulsion motor based on pseudo partial derivatives; designing a sliding mode control method control law and an estimation law; The disturbance term of , designed an extended state observer to estimate the load disturbance and unknown disturbance in the control system; for the influence of the unmodeled dynamics on the performance of the control system, a sliding mode control scheme with a series compact dynamic linearization model was designed to improve the system control performance. The invention combines the advantages of the compact dynamic linearization method and the sliding mode control, and effectively improves the dynamic performance and steady-state performance of the pod propulsion motor control system.

Description

A sliding mode control method for podded propulsion motor based on compact dynamic linearization

technical field

The invention belongs to the technical field of ship electric thruster control, and uses a data-driven idea to design a sliding mode control scheme for a pod propulsion motor based on compact dynamic linearization.

Background technique

Semi-submersible ship is a ship specializing in the transportation of indivisible super-large integral equipment and extra-heavy cargo. When diving and surfacing operations, it needs to rely on the dynamic positioning system to accurately locate and complete underwater operations. high performance requirements. The podded electric propulsion is the most advanced marine electric propulsion system. The podded propulsion in the system improves the hydrodynamic performance of the ship and optimizes the hull structure and the design of the pod. Permanent magnet synchronous motor (PMSM) has the characteristics of small size and high efficiency. It is used as a propulsion motor in a pod electric propulsion system, which not only improves the efficiency of the propeller, but also has higher reliability and stability. Therefore, the research on the control performance of the permanent magnet synchronous propulsion motor has also become the focus of the current research on the ship positioning control system.

At present, many advanced algorithms are used to improve the control performance of permanent magnet synchronous motors and reduce the impact of disturbances, such as model-based adaptive control, variable structure sliding mode control, and model predictive control. Kong Xiaobing et al. proposed a nonlinear model predictive control method for the speed control of permanent magnet motors, decoupling into a new linear system through the input-output feedback linearization strategy, and using an iterative quadratic programming method to deal with input- The nonlinear constraints generated by the output feedback linearization can effectively reduce the amount of calculation and improve the dynamic control performance. In the traditional PI control, Li Zheng et al. designed a load torque observer based on the principle of the Lomborg linear observer, and fed the observation value to the design of the sliding mode controller, which improved the performance of the system against load disturbance and enhanced the system stability. SIRA-RAMIREZ H introduces an active disturbance rejection control scheme suitable for large disturbance and uncertain permanent magnet synchronous motor angular velocity trajectory tracking task, and uses high gain extended observer to improve disturbance observation accuracy. Zhang Xiaoguang et al. took the load torque as the expansion state and the motor speed and load torque as the observation objects, and proposed a feedforward compensation sliding mode control to effectively weaken the system buffeting. The controllers of the above control systems are mostly designed based on mathematical models. Under the premise of known accurate mathematical models, designing appropriate controller parameters can improve the control performance of permanent magnet synchronous motors to a certain extent, but PMSM is a multi-variable, It is a complex object with strong coupling and nonlinearity, and the working environment of the pod propulsion motor of the semi-submersible ship is harsh, especially it is easily affected by the load disturbance of the propeller. When the system is affected by factors such as internal parameter changes or external disturbances, the conventional model-based control strategies have the problems of unmodeled dynamics and inability to establish accurate models, so they cannot meet the requirements of high-performance control of pod propulsion motors.

SUMMARY OF THE INVENTION

The invention aims to improve the speed control performance of the pod propulsion motor of the semi-submersible ship and reduce the influence of disturbance on the control system of the pod propulsion motor of the ship; A sliding mode control scheme based on compact dynamic linearization; at the same time, an expanded state observer is introduced to add the observed value to the control rate to compensate the disturbance of the control system; finally, a series of pods based on compact dynamic linearization is designed. Propulsion motor sliding mode control scheme.

In order to realize the above-mentioned purpose of the invention, the present invention adopts the following design scheme:

(1) Establish a dynamic model of the pod propulsion motor and discretize it:

1) Considering the high requirements on the torque performance of the pod propulsion motor, the permanent magnet synchronous motor rotor magnetic field oriented control method with _idw = 0 ( _idw is the current value set by the d-axis) is used, which is convenient to calculate and does not exist. The demagnetization problem of the pivot reaction motor, the torque equation of the propulsion motor of the permanent magnet synchronous motor in the dq coordinate system is:

为永磁体与定子交链磁链，i_q为q轴电流；Among them, T _e is the electromagnetic torque, p is the number of motor pole pairs,

is the flux linkage between the permanent magnet and the stator, i _q is the q-axis current;

The equation of motion of the permanent magnet synchronous motor is:

Among them, ω propulsion motor rotor angular speed, ω=2πn/60, n is the output speed of the propulsion motor, T _L is the load torque, J is the moment of inertia, F is the friction coefficient of the pod propulsion motor, K _Q is the torque coefficient , ρ is the density of water, D is the diameter of the propeller, and f _ld (k) is defined as the unknown disturbance that affects the speed of the propulsion motor at time k;

2) According to the equation of motion, the discrete speed system equation of the pod propulsion motor is established as follows:

Among them, n(k+1) is the output speed of the propulsion motor at time k+1, n(k) is the output speed of the propulsion motor at time k, i _q (k) is the q-axis current at time k, and h is the sampling time;

(2) Using the concept of pseudo-partial derivatives combined with the discrete speed system equation of the pod propulsion motor to establish its compact-format dynamic linearization data model:

1) The pod propulsion motor is a nonlinear system, which can be expressed as:

n(k+1)=f(n(k),n(k-1),…,n(kl _y ),i _q (k),i _q (k-1),…,i _q (kl _u ))+f _AL (k)

Among them, f _AL (k) represents the total disturbance signal of the system, including load disturbance and unknown disturbance f _ld ( _k ), f ( ) is a nonlinear function, _ly , lu ∈ R is the unknown order of the system, let:

n _m (k+1)=f(n(k),n(k-1),…,n(kl _y ),i _q (k),i _q (k-1),…,i _q (kl _u ))

Then the pod propulsion motor system can be rewritten as:

n(k+1)=n _m (k+1)+f _AL (k)

For the pod propulsion motor system, when |Δi _q (k)|≠0, there must be a quantity φ(k) called the partial derivative, such that:

Δn _m (k+1)=φ(k)Δi _q (k)

but:

Δn(k+1)=φ(k)Δi _q (k)+Δf _AL (k)

Among them, φ(k) is the pseudo-partial derivative of the velocity loop control law, Δf _AL (k)=f _AL (k)-f _AL (k-1) is the variation of the total disturbance signal of the system from time k-1 to time k ;

2) The pod propulsion motor system can use the following parameter estimation algorithm to obtain the estimated value of the pseudo-partial derivative of the speed loop control law, considering the following criterion function:

可得速度环伪偏导数估计律：by solving

The estimation law of the pseudo-partial derivative of the velocity loop can be obtained:

或|Δi_q(k-1)|≤α，

when

or |Δi _q (k-1)|≤α,

Among them, η∈(0,1] is the step factor of the speed loop control law, which makes the algorithm more general, and α is a constant greater than 0;

(3) Design of sliding mode controller in sliding mode control method of pod propulsion motor based on compact dynamic linearization:

1) Define the sliding mode plane function as:

s(k)=e(k)+ce(k-1)

Among them, c is a constant greater than 0, so the error polynomial formed is a stable polynomial, and e(k) is the speed tracking error, which is defined as follows:

e(k)= _nw (k)-n(k)

Among them, n _w (k) is the expected output speed of the propulsion motor at time k, and the reaching law is adopted as follows:

s(k+1)=(1-d)s(k)-εsgn(s(k))

Among them, d and ε are constants greater than 0;

The equivalent control looks like this:

s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k)

2) Combining the mathematical model of the compact dynamic linearization of the podded propulsion motor with the sliding mode control, the sliding mode control scheme of the podded propulsion motor based on the compact dynamic linearization can be obtained as follows:

为k-1时刻到k时刻系统总扰动信号估计值的变化量，sgn(·)为符号函数；Among them, σ>0 is a weight coefficient, n _w (k+1) is the expected output speed of the propulsion motor at time k+1, i _qw (k) is the expected current of the q-axis at time k,

is the variation of the estimated value of the total disturbance signal of the system from time k-1 to time k, and sgn( ) is the sign function;

(4) Design an extended state observer to estimate the total disturbance signal f _AL (k) in the sliding mode control scheme of podded propulsion motor based on compact dynamic linearization:

make:

吊舱推进电机一阶系统可扩张为：Among them, x ₂ (k) is the expansion state variable, namely

The first-order system of the pod propulsion motor can be expanded to:

Defining e _l (k) as the output speed error of the propulsion motor in the observer, the second-order extended state observer can be constructed as:

z₂(k)为扩张状态观测器中总扰动信号估计值

arsh(·)为反双曲正弦函数；Among them, β ₁ , β ₂ , β ₃ are the parameters of the expanded state observer in the system and are all greater than 0, and z ₁ (k) is the estimated value of the output speed of the propulsion motor in the expanded state observer

z ₂ (k) is the estimated value of the total disturbance signal in the extended state observer

arsh( ) is the inverse hyperbolic sine function;

(5) Design the sliding mode control method of the podded propulsion motor based on the compact dynamic linearization model in series:

The inner current loop is used as the secondary loop of the propulsion motor speed system, and the podded propulsion motor sliding mode controller based on the compact dynamic linearization model is used to replace the original current PI controller for secondary adjustment. The dynamic linearized sliding mode control method of the pod propulsion motor forms a cascade control structure with the speed loop. The difference between the inner current loop control method and the outer speed loop is that the quadrature axis current is used as the output and u _q (k) is used as the input. , and remove the disturbance term. The design of this controller can refer to the design of the previous speed loop controller. The secondary control loop also adopts a data-driven control method to reduce the influence of unmodeled dynamics on the system and improve the speed of the propulsion motor system. Control performance, the control scheme is as follows:

为内电流环控制律的伪偏导数估计值，e₁(k)为q轴电流跟踪误差，定义为e₁(k)＝i_qw(k)-i_q(k)，u_qw(k)为q轴期望电压，u_q(k-1)为k-1时刻的q轴电压，Δu_q(k-1)＝u_q(k-1)-u_q(k-2)。Among them, η ₁ ∈(0,1] is the step factor of the inner current loop control law, μ ₁ >0 is the weight factor of the inner current loop control law, σ ₁ >0 is a weight coefficient to limit the q-axis voltage Variation, α ₁ , d ₁ , ε ₁ are all constants greater than 0,

is the estimated value of the pseudo-partial derivative of the inner current loop control law, e ₁ (k) is the q-axis current tracking error, defined as e ₁ (k)=i _qw (k)-i _q (k), u _qw (k) is the expected q-axis voltage, u _q (k-1) is the q-axis voltage at time k-1, Δu _q (k-1)=u _q (k-1)-u _q (k-2).

Further, step (2) unifies the internal disturbance and the external disturbance into a total system disturbance signal f _AL (k) when the system disturbance is processed in the solution of the present invention, which is fed back to the control system. The total disturbance signal f _AL (k) includes load disturbance and unknown disturbance f _ld (k), where the load torque is expressed as:

T _L =K _Q ρD ⁵ n ²

It can be seen that the load torque changes with the speed of the propulsion motor, and the disturbance caused by the load change and the unknown disturbance are superimposed to form a nonlinear disturbance. It is a reasonable approach to treat the two as the total disturbance. 4) The constructed extended state observer observes the total disturbance and adds the observation results to the control law, which not only considers the comprehensiveness of the real pod propulsion motor system, but also reduces the complexity of formula derivation and calculation.

Further, the device for determining the internal state variables of the system according to the observation of the external variables in step (4) is a state observer, that is, a device for determining all the internal state information of the system according to the measured control amount and the function of some state variables or state variables. , using the undisturbed current i _q to enter the pod propulsion motor model, the motor speed of the system without internal disturbance and external load disturbance can be obtained, as well as the expansion state observation value, and the disturbance estimation value is used to perform disturbance compensation for the system. Disturbance compensation before generation can increase system stability.

Further, in step (5), the inner loop of the inner current loop adopts a method based on data-driven control, that is, a sliding mode control method for the pod propulsion motor based on tight-format dynamic linearization:

1) The input and output of the pod propulsion motor system are observable and controllable. For a given bounded expected output signal i _qw (k+1), there is always a bounded input signal that enables the system to control the input signal. The output under driving is equal to the expected output i _qw (k+1) of the system, and the partial derivative of f(·) with respect to the control input signal u _q (k) exists and is continuous. The moment and |Δu _q (k)|≠0 have:

Δi _q (k+1)=φ ₁ (k)Δu _q (k)

2) The following parameter estimation algorithm is used to obtain the estimated value of the pseudo-partial derivative of the inner current loop control law:

或|Δu_q(k-1)|≤α₁，

when

or |Δu _q (k-1)|≤α ₁ ,

为内电流环控制律的伪偏导数估计值，η₁∈(0,1]是内电流环控制律的步长因子，α₁是大于0的常数；in,

is the estimated value of the pseudo partial derivative of the inner current loop control law, η ₁ ∈(0,1] is the step factor of the inner current loop control law, and α ₁ is a constant greater than 0;

3) The inner current loop also adopts a data-driven control method. Combining the above estimation law and step (3), the inner current loop control scheme can be obtained as follows:

Beneficial effects:

1. Aiming at the problem that the pod propulsion motor has a complex working environment and is easily affected by disturbances, resulting in poor system dynamic and steady-state performance, a control strategy that integrates data-driven control and sliding-mode variable structure control is proposed, using only I/O data. For system control, the advantages of compact dynamic linearization that do not require precise mathematical models are combined with the advantages of sliding mode control's strong robustness to disturbances.

2. In order to solve the contradiction between strong robustness and chattering in sliding mode control, an extended state observer is constructed, which takes the disturbance as the extended state variable, and the estimated value is added to the dynamic linearization based compact scheme. In the sliding mode control scheme of the pod propulsion motor, the buffeting of the system is effectively reduced.

3. Comparing the speed and torque changes of the podded propulsion motor sliding mode control scheme and PI control scheme based on the compact dynamic linearization in the constant speed and variable speed operation of the podded propulsion motor, in the same simulation environment, based on the tight The sliding mode control scheme of the podded propulsion motor with dynamic linearization has faster speed response and smaller overshoot, and the torque pulse is significantly reduced. Therefore, the scheme effectively improves the dynamic performance and steady-state performance of the system, and reduces the influence of disturbance.

Description of drawings

Fig. 1 is the flow chart of the sliding mode control scheme of pod propulsion motor based on compact dynamic linearization;

Fig. 2 is the structure diagram of the expansion observer proposed by the present invention;

Fig. 3 is the structure diagram of the speed regulation system of the pod propulsion motor of the semi-submersible ship proposed by the present invention;

Fig. 4 is the structure diagram of the PI speed regulation system of the pod propulsion motor of the semi-submersible ship in the prior art;

FIG. 5 is a comparison diagram with or without an expanded state observer under the control strategy proposed by the present invention;

FIG. 6 is a comparison diagram of the speed and torque of the propulsion motor under the control strategy proposed by the present invention and the PI vector control.

Detailed ways

As mentioned above, the podded propulsion motor of the semi-submersible ship is easily affected by unknown factors such as waves and sea wind when it works at sea. Influence, the present invention designs a sliding mode control scheme of pod propulsion motor based on compact dynamic linearization. The present invention will be described in more detail below with reference to the accompanying drawings.

Referring to Fig. 1, the control scheme for the pod propulsion motor of the semi-submersible ship in this embodiment specifically includes the following steps:

Step S1: Establish a dynamic model of the pod propulsion motor and discretize it:

1) When designing the control strategy for the podded propulsion motor, in order to meet the high torque performance requirements of the podded propulsion motor, the permanent magnet synchronous motor rotor magnetic field oriented control method with i _dw = 0 is adopted. The torque equation of the propulsion motor in the coordinate system is:

为永磁体与定子交链磁链，i_q为q轴电流；Among them, T _e is the electromagnetic torque, p is the number of motor pole pairs,

is the flux linkage between the permanent magnet and the stator, i _q is the q-axis current;

The permanent magnet synchronous motor is a nonlinear system with multiple variables and time-varying parameters. The equation of motion after considering the unknown disturbance is as follows:

Among them, ω is the rotor angular speed of the propulsion motor, ω=2πn/60, n is the output speed of the propulsion motor, T _L is the load torque, J is the moment of inertia, F is the friction coefficient of the pod propulsion motor, and K _Q is the torque coefficient, ρ is the density of water, D is the diameter of the propeller, and f _ld (k) is defined as the unknown disturbance that affects the speed of the propulsion motor at time k;

2) Perform linear dynamic processing on the permanent magnet synchronous motor, and combine the equations (1) and (2) to discretize the motion equation of the permanent magnet synchronous motor. The discrete motion equation is as follows:

Among them, n(k+1) is the output speed of the propulsion motor at time k+1, i _q (k) is the q-axis current at time k, and h is the sampling time;

Step S2: Using the concept of pseudo-partial derivatives combined with the discrete speed system equation of the pod propulsion motor to establish its compact dynamic linearization data model:

1) The pod propulsion motor is a nonlinear system, which can be expressed as:

n(k+1)=f(n(k),n(k-1),…,n(kl _y ),i _q (k),i _q (k-1),…,i _q (kl _u ))+f _AL (k)(4)

Among them, f _AL (k) represents the total disturbance signal of the system, including load disturbance and unknown disturbance f _ld ( _k ), f( ) is an unknown nonlinear function, _ly , lu ∈ R is the unknown order of the system; let:

n _m (k+1)=f(n(k),n(k-1),…,n(kl _y ),i _q (k),i _q (k-1),…,i _q (kl _u )) (5)

Then the pod propulsion motor system can be rewritten as:

n(k+1)=n _m (k+1)+f _AL (k) (6)

Assumption 1: The input and output of the pod propulsion motor system are observable and controllable. For a given bounded expected propulsion motor output speed n _w (k+1), there is always a bounded input signal that makes the propulsion motor here The output driven by the control input signal is equal to the expected output speed n _w (k+1) of the propulsion motor;

Assumption 2: The partial derivative of f(·) with respect to the q-axis current i _q (k) exists and is continuous;

Assumption 3: The system is generalized Lipschitz, that is, it satisfies for any k time and |Δi _q (k)|≠0:

Δn _m (k+1)=φ(k)Δi _q (k) (7)

but:

Δn(k+1)=φ(k)Δi _q (k)+Δf _AL (k) (8)

Among them, Δn(k+1)=n(k+1)-n(k) is the output speed change of the propulsion motor from time k to time k+1, Δi _q (k)=i _q (k)-i _q (k-1) is the variation of the q-axis current from time k to time k+1;

Assumption 4: The changes of the load disturbance and the unknown disturbance in the system at two adjacent times are bounded and satisfy the generalized Lipschitz condition:

|Δf _AL (k+1)|≤b|Δi _q (k)| (9)

where b is a positive constant;

Assumption 5: The podded propulsion motor nonlinear system has a globally asymptotically stable zero dynamics. From a practical application point of view, the above assumptions are reasonable and acceptable. Among them, Assumption 1 is a basic assumption of the controlled system, if it is not satisfied, the system is uncontrollable. Assumption 2 is a typical condition for many control laws, which is satisfied by the podded propulsion motor nonlinear system. Assumption 3 is a limit to the output change of the system, the size of the speed change will not be infinite, it is limited by the size of the torque, the torque change is affected by the input current, and the current change per unit time is limited . Assumption 4 The total disturbance should have a limited effect on the system. Assumption 5 is an assumption about the internal dynamics of the system.

Theorem: For the pod propulsion motor system, the assumptions 1 to 5 are satisfied. When |Δi _q (t)|≠0, there must be a quantity φ(k) called the partial derivative, such that:

Δn(k+1)=Δn _m (k+1)+Δf _AL (k) (10)

Among them, φ(k) is the pseudo-partial derivative of the velocity loop control law;

Combined with formula (7), formula (10) can be rewritten as:

Δn(k+1)=φ(k)Δi _q (k)+Δf _AL (k) (11)

2) The pod propulsion motor system can use the following parameter estimation algorithm to obtain the estimated value of the pseudo partial derivative of equation (11):

可得速度环控制律的伪偏导数估计值：by solving

The pseudo-partial derivative estimates of the velocity loop control law can be obtained:

或|Δi_q(k-1)|≤α，

when

or |Δi _q (k-1)|≤α,

Step S3: Design a sliding mode control law scheme for the pod propulsion motor based on compact dynamic linearization:

1) Define the sliding mode plane function as:

s(k)=e(k)+ce(k-1) (14)

Among them, c is a constant greater than 0, so the error polynomial formed is a stable polynomial, and e(k) is the speed tracking error, which is defined as follows:

e(k)= _nw (k)-n(k) (15)

Among them, n _w (k) is the expected output speed of the propulsion motor at time k, and the reaching law is adopted as follows:

s(k+1)=(1-d)s(k)-εsgn(s(k)) (16)

Among them, d and ε are constants greater than 0;

The equivalent control can be obtained by the equation shown in Eq. (16):

s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k) (17)

Combining formulas (14) to (17), we can get:

e(k+1)=(1-d)s(k)-εsgn(s(k))-ce(k) (18)

which is:

Then the sliding mode control law of the pod propulsion motor based on the compact dynamic linearization is as follows:

2) Combined with the estimated value of the pseudo-partial derivative of the velocity loop control law obtained by equation (13), the sliding mode control scheme of the pod propulsion motor based on the compact dynamic linearization can be obtained as follows:

In formula (20), the speed tracking can be gradually approached to zero. However, when the pod propulsion motor is working, due to the unmodeled dynamics, unknown disturbances, load disturbances and other uncertain factors brought about by disturbances, it is easy to cause chattering in the system, and sliding mode control has always had strong robustness. If the disturbance can be estimated, compensation at the control input will reduce the problem of system chattering. Step S4 is a solution to this problem.

Step S4: Design an expanded state observer, the structure of which is shown in Figure 2:

An extended state observer is designed to estimate the total disturbance signal f _AL (k) in the sliding mode control scheme of the podded propulsion motor based on compact dynamic linearization:

make:

吊舱推进电机一阶系统可扩张为：Among them, x ₂ (k) is the expansion state variable,

The first-order system of the pod propulsion motor can be expanded to:

Defining e _l (k) as the observed velocity error, the second-order extended state observer can be constructed as:

z₂(k)为扩张状态观测器中总扰动信号估计值

arsh(·)为反双曲正弦函数。Among them, β ₁ , β ₂ , β ₃ are the parameters of the expansion state observer in the system and are all greater than 0, e _l (k) is the output speed error of the propulsion motor in the observer, and z ₁ (k) is the expansion state observation The estimated value of the output speed of the propulsion motor in the

z ₂ (k) is the estimated value of the total disturbance signal in the extended state observer

arsh(·) is the inverse hyperbolic sine function.

Step S5: Design the sliding mode control scheme of the pod propulsion motor based on the compact dynamic linearization in series:

1) The input and output of the pod propulsion motor system are observable and controllable, and the partial derivative of f(·) with respect to the expected q-axis voltage u _q (k) exists and is continuous, so the system is generalized Lipschitz, that is, it satisfies Any k time and |Δu _q (k)|≠0 have:

i _q (k+1)=φ ₁ (k)Δu _q (k) (26)

2) The following parameter estimation algorithm is used to obtain the estimated value of the pseudo-partial derivative of the inner current loop control law:

可得：by solving

Available:

或|Δu_q(k-1)|≤α₁，

when

or |Δu _q (k-1)|≤α ₁ ,

3) The inner current loop is used as the secondary loop of the propulsion motor speed system, and the podded propulsion motor sliding mode controller based on the compact dynamic linearization model is used to replace the original current PI controller for secondary adjustment. The sliding mode control method of the pod propulsion motor with compact dynamic linearization is different from the speed loop to form a cascade control structure. The inner current loop control method is different from the speed outer loop. Here, the quadrature axis current is used as the output, and u _q (k) is used as Input and remove the disturbance term. The design of this controller can refer to the design of the previous speed loop controller. The sub control loop also adopts a data-driven control method to reduce the influence of unmodeled dynamics on the system and improve the speed of the propulsion motor system. The control performance of , the control scheme is as follows:

为内电流环控制律的伪偏导数估计值，e₁(k)为q轴电流跟踪误差，定义为e₁(k)＝i_qw(k)-i_q(k)，u_qw(k)为q轴期望电压，u_q(k-1)为k-1时刻q轴电压，Δu_q(k-1)＝u_q(k-1)-u_q(k-2)。Among them, η ₁ ∈(0,1] is the step factor of the inner current loop control law, μ ₁ >0 is the weight factor of the inner current loop control law, σ ₁ >0 is a weight coefficient, used to limit the q-axis voltage Variation, α ₁ , d ₁ , ε ₁ are all constants greater than 0,

is the estimated value of the pseudo-partial derivative of the inner current loop control law, e ₁ (k) is the q-axis current tracking error, defined as e ₁ (k)=i _qw (k)-i _q (k), u _qw (k) is the expected q-axis voltage, u _q (k-1) is the q-axis voltage at time k-1, Δu _q (k-1)=u _q (k-1)-u _q (k-2).

Referring to Fig. 3, use MATLAB/Simulink to establish the structure model of the speed regulation system of the semi-submersible pod propulsion motor of the control scheme of the present invention and simulate it. It is composed of SVPWM, expansion state observer and permanent magnet synchronous motor. The parameters of the semi-submersible pod propulsion motor refer to the "Taiankou" semi-submersible ship propulsion motor. The specific parameters are: rated voltage of 660V; rated power of 4700kW; rotor permanent magnet The flux linkage is 2.6458Wb; the resistance is 0.00164Ω; the number of motor pole pairs is 8; the d-axis inductance is 0.0085H; the q-axis inductance is 0.0085H. According to the debugging situation of the actual system, the parameters of the speed loop controller and the inner current loop controller are designed, and the output signals _ud and u _q of the inner current loop controller are subjected to Park transformation to obtain the voltage u _α in the two-phase static coordinate system After , u _β , the control signal of the inverter is obtained through the space vector pulse width modulation algorithm SVPWM, and the corresponding three-phase voltage signal is output by the inverter, which is applied to the stator winding of the permanent magnet synchronous motor, and the permanent magnet synchronous motor is carried out. Speed regulation.

Referring to Fig. 4, the PI control scheme is used to establish a structure model of the speed regulation system of the semi-submersible pod propulsion motor by using MATLAB/Simulink for simulation comparison with the control scheme proposed by the present invention. The parameters of the semi-submersible ship pod propulsion motor are the same as above.

Referring to Figure 5, in order to illustrate the effectiveness of the expanded state observer, the system uses the control scheme of the present invention to compare the speed and torque response curves with and without the state observer. It can be seen that the state observer can track the change of the disturbance very well. After the state observer compensates the disturbance, the overshoot of the speed of the propulsion motor is reduced, and it stabilizes faster after reaching the set value. At the same time, the torque pulse of the propulsion motor is reduced, and the dynamic performance of the system is improved.

Referring to Fig. 6, in order to illustrate the effectiveness of the constant speed operation of the semi-submersible pod propulsion motor under the control scheme of the present invention, the speed and torque response curves of the propulsion motor under the two control schemes are compared. The simulation results are shown in Figure 6. In Figure 6, the speed of the propulsion motor reaches the desired speed at 0.045s under the control scheme of the present invention, the maximum speed fluctuates 14rpm, and reaches a stable state at 0.074s, and the continuous fluctuation is small. Compared with the PI control The time to reach the desired speed for the first time is reduced by 25%, the time for the system to reach a stable state is reduced by 45%, the maximum speed fluctuation is reduced by 4.5rpm, and the torque reaches a stable state earlier by 0.12s. Relatively speaking, the control scheme of the present invention can well suppress the transient speed fluctuation and torque ripple caused by the load change, reduce the damage to the motor, and maintain the system stability even when there is an unknown disturbance in the system, effectively weakening the system. Chattering, showing better response speed and anti-interference performance.

This embodiment proposes a sliding mode control method for a pod propulsion motor based on compact dynamic linearization, which is used for the control of the pod propulsion motor of a semi-submersible ship. The dynamic performance and steady-state performance of the propulsion motor under the scheme of the present invention and the existing PI vector control scheme are compared under the MATLAB/Simulink simulation environment. The method can improve the speed and torque control accuracy of the propulsion motor, reduce the damage of the torque ripple to the motor, and has strong robustness to the uncertainty and unknown disturbance of the internal parameters of the pod propulsion motor, which is a good tool for the dynamic positioning of semi-submersible ships. The system provides an effective control method.

The above-mentioned specific description further describes the purpose, technical solutions and beneficial effects of the invention in further detail. It should be understood that the embodiments are only used to explain the invention, and are not used to limit the protection scope of the invention. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention should be based on the scope defined by the claims.

Claims (3)

1. a pod propulsion motor sliding mode control (CFDL-SMC) method based on tight format dynamic linearization, is characterized in that: described method comprises the following steps: (1) Discretization of the dynamic equation of the pod propulsion motor: 1) Establish the dynamic model of the pod propulsion motor, and the motion equation of the permanent magnet synchronous motor is as follows:

Among them, T _e is the electromagnetic torque, p is the number of motor pole pairs,

is the flux linkage between the permanent magnet and the stator, i _q is the q-axis current, ω is the rotor angular velocity of the propulsion motor, ω=2πn/60, n is the output speed of the propulsion motor, T _L is the load torque, J is the moment of inertia, F is the friction coefficient of the pod propulsion motor, K _Q is the torque coefficient, ρ is the density of water, D is the diameter of the propeller, and f _ld (k) is defined as the unknown disturbance that affects the speed of the propulsion motor at time k; 2) The discrete speed system equation of the pod propulsion motor is established as follows:

Among them, n(k+1) is the output speed of the propulsion motor at time k+1, n(k) is the output speed of the propulsion motor at time k, i _q (k) is the q-axis current at time k, and h is the sampling time; (2) Establish a compact dynamic linearization data model of the pod propulsion motor: 1) Using the concept of pseudo-partial derivatives combined with the discrete speed system equation of the pod propulsion motor to establish its compact-format dynamic linearization data model as follows: Δn(k+1)=φ(k)Δi _q (k)+Δf _AL (k) Among them, Δn(k+1)=n(k+1)-n(k) is the output speed change of the propulsion motor from time k to time k+1, Δi _q (k)=i _q (k)-i _q (k-1) is the variation of the q-axis current from time k-1 to time k, φ(k) is the pseudo-partial derivative of the speed loop control law, Δf _AL (k)=f _AL (k)-f _AL (k- 1) is the variation of the total disturbance signal of the system from time k-1 to time k; 2) The pod propulsion motor system can use the following parameter estimation algorithm to obtain the estimated value of the pseudo-partial derivative of the speed loop control law:

in,

is the estimated value of the pseudo-partial derivative of the velocity loop control law, Δi _q (k-1)=i _q (k-1)-i _q (k-2),

is the variation of the estimated value of the total disturbance signal of the system from time k-2 to time k-1, η∈(0,1] is the step size factor of the speed loop control law, μ>0 is the weight factor of the speed loop control law; (3) Design a sliding mode control method for podded propulsion motor based on compact dynamic linearization: The sliding mode plane function is defined as: s(k)=e(k)+ce(k-1) Among them, c is a constant greater than 0, so the error polynomial formed is a stable polynomial, and e(k) is the speed tracking error, which is defined as follows: e(k)= _nw (k)-n(k) Among them, n _w (k) is the expected output speed of the propulsion motor at time k, and the reaching law is adopted as follows: s(k+1)=(1-d)s(k)-εsgn(s(k)) Among them, d and ε are constants greater than 0; The equivalent control looks like this: s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k) Data model Δn(k+1)=φ(k)Δi _q (k)+Δf _AL (k) after dynamic linearization of pod propulsion motor, and estimated value of pseudo partial derivative

Combined with the above formula, the sliding mode control method of the pod propulsion motor based on the compact dynamic linearization can be obtained as follows:

Among them, σ>0 is a weight coefficient used to limit the amount of q-axis current change, d, c, ε are all constants greater than 0, e(k) is the speed tracking error of the propulsion motor, defined as e(k)= n _w (k)-n(k), n _w (k+1) is the expected output speed of the propulsion motor at time k+1, i _qw (k) is the expected current of the q-axis at time k, and sgn( ) is the sign function ; (4) Design an expanded state observer: To estimate the total disturbance f _AL (k) in the sliding mode control method of podded propulsion motor based on compact dynamic linearization, the expanded state observer is designed as follows: The first-order system of the pod propulsion motor is expressed as follows:

make:

Among them, x ₂ (k) is the expansion state variable,

Then the first-order system of the pod propulsion motor can be expanded as:

Defining e _l (k) as the observed velocity error, the second-order extended state observer can be constructed as:

Among them, β ₁ , β ₂ , and β ₃ are the parameters of the expansion state observer in the system and are all greater than 0, e _l (k) is the output speed error of the propulsion motor in the expansion state observer, and z ₁ (k) is the expansion state observer. Estimated output speed of the propulsion motor in the state observer

z ₂ (k) is the estimated value of the total disturbance signal in the extended state observer

arsh( ) is the inverse hyperbolic sine function; (5) Design the sliding mode control method of the podded propulsion motor based on the compact dynamic linearization model in series:

Among them, η ₁ ∈(0,1] is the step factor of the inner current loop control law, μ ₁ >0 is the weight factor of the inner current loop control law, σ ₁ >0 is a weight coefficient, used to limit the q-axis voltage Variation, α ₁ , d ₁ , ε ₁ are all constants greater than 0,

is the estimated value of the pseudo-partial derivative of the inner current loop control law, e ₁ (k) is the q-axis current tracking error, defined as e ₁ (k)=i _qw (k)-i _q (k), u _qw (k) is the expected q-axis voltage, u _q (k-1) is the q-axis voltage at time k-1, Δu _q (k-1)=u _q (k-1)-u _q (k-2). 2. method according to claim 1 is characterized in that: when step (2) is to system disturbance processing, internal disturbance and external disturbance are unified into system total disturbance signal f _AL (k) is fed back to the dynamic linearization based on compact format. In the sliding mode control system of the pod propulsion motor, the specific design is as follows: The first-order system of the pod propulsion motor can be expressed as follows:

In the first-order system, the load disturbance part is -30pT _L (k)/πJ, and the unknown disturbance part is 30pf _ld (k)/πJ, so the total disturbance signal can be expressed as:

3. method according to claim 1, is characterized in that: step (5) inner current loop adopts the sliding mode control method of pod propulsion motor based on tight format dynamic linearization, forms cascade control structure with speed loop, inner current The difference between the loop control method and the speed outer loop is that the quadrature axis current is used as the output, u _q (k) is used as the input, and the disturbance term is removed. The specific design is as follows: 1) The input and output of the pod propulsion motor system are observable and controllable. For a given bounded expected output signal i _qw (k+1), there is always a bounded input signal that enables the system to control the input signal. The output under driving is equal to the expected output i _qw (k+1) of the system, and the partial derivative of f(·) with respect to the control input signal u _q (k) exists and is continuous. The moment and |Δu _q (k)|≠0 have: Δi _q (k+1)=φ ₁ (k)Δu _q (k) 2) The following parameter estimation algorithm is used to obtain the estimated value of the pseudo-partial derivative of the inner current loop control law:

when

or |Δu _q (k-1)|≤α ₁ ,

in,

is the estimated value of the pseudo partial derivative of the inner current loop control law, η ₁ ∈(0,1] is the step factor of the inner current loop control law, and α ₁ is a constant greater than 0; 3) The data-driven control method for the inner current loop can reduce the influence of unmodeled dynamics. Referring to the design of the control scheme in step (3), the inner current loop control scheme can be obtained as follows:

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