CN113300644B - Nacelle propulsion motor sliding mode control method based on compact-format dynamic linearization - Google Patents
Nacelle propulsion motor sliding mode control method based on compact-format dynamic linearization Download PDFInfo
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- H—ELECTRICITY
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Abstract
本发明公开了一种基于紧格式动态线性化的吊舱推进电机滑模控制方法,适用于吊舱推进电机控制。其步骤包括:建立吊舱推进电机动力学模型;基于伪偏导数建立吊舱推进电机动力学模型的紧格式动态线性化数据模型;滑模控制方法控制律和估计律设计;针对估计控制律中的扰动项,设计扩张状态观测器对控制系统中的负载扰动和未知扰动进行估计;针对未建模动态对控制系统性能的影响,设计串联紧格式动态线性化模型的滑模控制方案改善系统控制性能。本发明结合紧格式动态线性化方法和滑模控制的优点,有效提高吊舱推进电机控制系统动态性能及稳态性能。
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
技术领域technical field
本发明属于船舶电力推进器控制技术领域,利用数据驱动的思想设计一种基于紧格式动态线性化的吊舱推进电机滑模控制方案。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.
背景技术Background technique
半潜船是专门从事无法分割的超大型整体设备、特重大件运输的船舶,在进行下潜和上浮作业时,需要依靠动力定位系统精确定位完成水下作业,因此对吊舱推进器有着较高的性能要求。吊舱式电力推进是现在最先进的船舶电力推进系统,系统中的吊舱推进器提高了船舶的水动力性能、优化了船体结构和吊舱的设计。永磁同步电机(permanentmagnet synchronous motor,PMSM)具有体积小、效率高的特点,作为推进电机使用在吊舱式电力推进系统中,不仅提高了螺旋桨的效率,而且具有更高的可靠性和稳定性,所以对永磁同步推进电机控制性能的研究也成为了当下船舶定位控制系统研究的热点。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.
目前许多先进算法用于提高永磁同步电机的控制性能,减少扰动带来的影响,如基于模型自适应控制、变结构滑模控制、模型预测控制等。孔小兵等人针对永磁电机的转速控制提出了非线性模型预测控制方法,通过输入-输出反馈线性化策略解耦成为新的线性系统,并利用一种迭代二次规划方法来处理由输入-输出反馈线性化产生的非线性约束,有效降低计算量,提高动态控制性能。李政等人在传统PI控制中,依据龙伯格线性观测器的原理设计了负载转矩观测器,将观测值反馈到滑模控制器的设计中,提高了系统抗负载扰动的性能,增强了系统的稳定性。SIRA-RAMIREZ H介绍了一种适用于大扰动、不确定永磁同步电动机角速度轨迹跟踪任务的自抗扰控制方案,利用高增益扩展观测器提高扰动观测精度。张晓光等人以负载转矩作为扩展状态,以电机转速和负载转矩作为观测对象,提出的前馈补偿滑模控制有效削弱系统抖振。以上控制系统的控制器多是基于数学模型设计,在已知精确数学模型的前提下,设计合适的控制器参数可以在一定程度上提高永磁同步电机的控制性能,但PMSM是一个多变量、强耦合、非线性的复杂对象,而且半潜船的吊舱推进电机工作环境恶劣,尤其是易受到螺旋桨负载扰动的影响。当系统受到内部参数变化或外界扰动等因素影响时,常规基于模型的控制策略存在未建模动态和无法建立精确模型的问题,因此并不能满足吊舱推进电机高性能控制的要求。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.
发明内容SUMMARY OF THE INVENTION
本发明旨在提高半潜船吊舱推进电机的转速控制性能,减小扰动对船舶吊舱推进电机控制系统的影响;将紧格式动态线性化方法和滑模变结构控制方法相融合,提出了一种基于紧格式动态线性化的滑模控制方案;同时引入扩张状态观测器,将观察值添加到控制率中,对控制系统进行扰动补偿;最后设计了串联基于紧格式动态线性化的吊舱推进电机滑模控制方案。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.
为了实现上述发明目的,本发明采取如下设计方案:In order to realize the above-mentioned purpose of the invention, the present invention adopts the following design scheme:
(1)建立吊舱推进电机动力学模型并且离散化:(1) Establish a dynamic model of the pod propulsion motor and discretize it:
1)考虑到吊舱推进电机转对矩性能要求较高,采用idw=0(idw为d轴设定的电流值)的永磁同步电机转子磁场定向控制方法,计算方便且不存在电枢反应电动机的去磁问题,永磁同步电机在d-q坐标系下的推进电机转矩方程为: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:
其中,Te为电磁转矩,p为电机极对数,为永磁体与定子交链磁链,iq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;
永磁同步电机运动方程为:The equation of motion of the permanent magnet synchronous motor is:
其中,ω推进电机转子角速度,ω=2πn/60,n为推进电机的输出转速,TL为负载转矩,J为转动惯量,F为吊舱推进电机的摩擦系数,KQ为转矩系数,ρ为水的密度,D为螺旋桨直径,fld(k)定义为k时刻影响推进电机转速的未知扰动;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)根据运动方程建立吊舱推进电机的离散转速系统方程如下:2) According to the equation of motion, the discrete speed system equation of the pod propulsion motor is established as follows:
其中,n(k+1)为k+1时刻推进电机的输出转速,n(k)为k时刻推进电机的输出转速,iq(k)为k时刻q轴电流,h为采样时间;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)利用伪偏导数的概念结合吊舱推进电机的离散转速系统方程建立其紧格式动态线性化数据模型:(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)吊舱推进电机是一个非线性系统,可表示为:1) The pod propulsion motor is a nonlinear system, which can be expressed as:
n(k+1)=f(n(k),n(k-1),…,n(k-ly),iq(k),iq(k-1),…,iq(k-lu))+fAL(k)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)
其中,fAL(k)表示系统总扰动信号,包括负载扰动和未知扰动fld(k),f(·)是非线性函数,ly,lu∈R为系统未知阶数,令: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:
nm(k+1)=f(n(k),n(k-1),…,n(k-ly),iq(k),iq(k-1),…,iq(k-lu))n m (k+1)=f(n(k),n(k-1),…,n(kl y ),i q (k),i q (k-1),…,i q (kl u ))
则吊舱推进电机系统可改写为:Then the pod propulsion motor system can be rewritten as:
n(k+1)=nm(k+1)+fAL(k)n(k+1)=n m (k+1)+f AL (k)
对于吊舱推进电机系统,当|Δiq(k)|≠0时,一定存在一个被称为偏导数的量φ(k),使得:For the pod propulsion motor system, when |Δi q (k)|≠0, there must be a quantity φ(k) called the partial derivative, such that:
Δnm(k+1)=φ(k)Δiq(k)Δn m (k+1)=φ(k)Δi q (k)
则:but:
Δn(k+1)=φ(k)Δiq(k)+ΔfAL(k)Δn(k+1)=φ(k)Δi q (k)+Δf AL (k)
其中,φ(k)为速度环控制律的伪偏导数,ΔfAL(k)=fAL(k)-fAL(k-1)为k-1时刻到k时刻系统总扰动信号的变化量;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)吊舱推进电机系统可采用如下参数估计算法来求取速度环控制律的伪偏导数的估计值,考虑如下准则函数: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:
通过求解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:
当或|Δiq(k-1)|≤α, when or |Δi q (k-1)|≤α,
其中,η∈(0,1]是速度环控制律的步长因子,使算法更具有一般性,α为大于0的常数;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)基于紧格式动态线性化的吊舱推进电机滑模控制方法中滑模控制器设计:(3) Design of sliding mode controller in sliding mode control method of pod propulsion motor based on compact dynamic linearization:
1)定义滑模平面函数为:1) Define the sliding mode plane function as:
s(k)=e(k)+ce(k-1)s(k)=e(k)+ce(k-1)
其中,c为大于0的常数,因此构成的误差多项式为稳定多项式,e(k)为转速跟踪误差,定义如下: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)e(k)= nw (k)-n(k)
其中,nw(k)为k时刻推进电机的期望输出转速,采用趋近律如下: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))s(k+1)=(1-d)s(k)-εsgn(s(k))
其中,d、ε为大于0的常数;Among them, d and ε are constants greater than 0;
等效控制如下所示:The equivalent control looks like this:
s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k)s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k)
2)将吊舱推进电机紧格式动态线性化后的数学模型与滑模控制相结合可得到则基于紧格式动态线性化的吊舱推进电机滑模控制方案如下: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:
其中,σ>0是一个权重系数,nw(k+1)为k+1时刻推进电机的期望输出转速,iqw(k)为k时刻q轴期望电流,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)设计扩张状态观测器,对基于紧格式动态线性化的吊舱推进电机滑模控制方案中的总扰动信号fAL(k)进行估计:(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:
令:make:
其中,x2(k)为扩张状态变量,即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:
定义el(k)为观测器中推进电机的输出转速误差,可构造二阶扩张状态观测器为: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:
其中,β1、β2、β3为本系统中扩张状态观测器的参数且均大于0,z1(k)为扩张状态观测器中推进电机的输出转速估计值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)设计串联基于紧格式动态线性化模型的吊舱推进电机滑模控制方法:(5) Design the sliding mode control method of the podded propulsion motor based on the compact dynamic linearization model in series:
内电流环作为推进电机转速系统的副回路,采用基于紧格式动态线性化模型的吊舱推进电机滑模控制器替代原有的电流PI控制器,进行二次调节,内电流环采取基于紧格式动态线性化的吊舱推进电机滑模控制方法,与速度环构成串级控制结构,内电流环控制方法与速度外环不同的是,这里将交轴电流作为输出,uq(k)作为输入,并且去除扰动项,该控制器的设计可参考前面转速环控制器的设计,副控制回路同样采取基于数据驱动控制的方法,减少未建模动态对系统的影响,提高了推进电机转速系统的控制性能,控制方案如下: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:
其中,η1∈(0,1]是内电流环控制律的步长因子,μ1>0是内电流环控制律的权重因子,σ1>0是一个权重系数,用于限制q轴电压变化量,α1、d1、ε1均为大于0的常数,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)=iqw(k)-iq(k),uqw(k)为q轴期望电压,uq(k-1)为k-1时刻的q轴电压,Δuq(k-1)=uq(k-1)-uq(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).
进一步的,步骤(2)在本发明方案中对系统扰动处理时将内部扰动和外部扰动统一成系统总扰动信号fAL(k)反馈到控制系统中。总扰动信号fAL(k)包括负载扰动和未知扰动fld(k),其中负载转矩表达式为: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:
TL=KQρD5n2 T L =K Q ρD 5 n 2
可知负载转矩随着推进电机的转速变化改变,负载变化造成的扰动和未知扰动叠加后是一种的非线性变化的扰动,将二者作为总扰动处理是一种合理的做法,结合步骤(4)构造的扩张状态观测器对总扰动进行观测,并将观测结果添加到控制律中,既考虑到了真实吊舱推进电机系统的全面性,又减少了公式推导计算的复杂性。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.
进一步的,步骤(4)根据外部变量的观测来确定系统内部状态变量的装置为状态观测器,即根据测量到的控制量和部分状态变量或状态变量的函数来确定系统所有内部状态信息的装置,利用未受扰动的电流iq输入吊舱推进电机模型,可以得到系统未受内部扰动和外部负载扰动的电机转速,以及扩张状态观测量,利用扰动估计值对系统进行扰动补偿,在扰动影响产生前进行扰动补偿能够增加系统稳定性。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.
进一步的,步骤(5)内电流环内环采取基于数据驱动控制的方法,即基于紧格式动态线性化的吊舱推进电机滑模控制方法: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)吊舱推进电机系统输入输出是可观测且可控的,对于给出的有界期望输出信号iqw(k+1),总存在一有界的输入信号使系统在此控制输入信号的驱动下输出等于系统的期望输出iqw(k+1),f(·)关于控制输入信号uq(k)的偏导数是存在且连续的,系统是满足广义Lipschitz的,即满足对任意k时刻和|Δuq(k)|≠0有: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:
Δiq(k+1)=φ1(k)Δuq(k)Δi q (k+1)=φ 1 (k)Δu q (k)
2)采用如下参数估计算法来求取内电流环控制律的伪偏导数估计值: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:
当或|Δuq(k-1)|≤α1, when or |Δu q (k-1)|≤α 1 ,
其中,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)内电流环同样采取基于数据驱动控制的方法,结合以上估计律及步骤(3)可得内电流环控制方案如下: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:
有益效果:Beneficial effects:
1、针对吊舱推进电机工作环境复杂,容易受到扰动影响导致系统动态和稳态性能差的问题,提出了一种融合数据驱动控制和滑模变结构控制的控制策略,仅利用I/O数据进行系统控制,将紧格式动态线性化不需要精确数学模型的优点和滑模控制对扰动强鲁棒性的优点相结合。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、为了解决滑模控制中的强鲁棒性与产生系统抖振的矛盾问题,构造了一种扩张状态观测器,将扰动作为扩张状态变量,得到估计值添加到基于紧格式动态线性化的吊舱推进电机滑模控制方案中,有效减小系统抖振。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、对比基于紧格式动态线性化的吊舱推进电机滑模控制控制方案和PI控制方案在吊舱推进电机恒速和变速作业时的转速、转矩变化,在相同的仿真环境下,基于紧格式动态线性化的吊舱推进电机滑模控制方案转速响应更快超调更小,且转矩脉冲明显降低。因此该方案有效的提高了系统的动态性能和稳态性能,降低了扰动带来的影响。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.
附图说明Description of drawings
图1为基于紧格式动态线性化的吊舱推进电机滑模控制控制方案的流程图;Fig. 1 is the flow chart of the sliding mode control scheme of pod propulsion motor based on compact dynamic linearization;
图2是本发明提出的扩张观测器结构图;Fig. 2 is the structure diagram of the expansion observer proposed by the present invention;
图3是本发明提出半潜船吊舱推进电机调速系统结构图;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;
图4是现有技术中半潜船吊舱推进电机PI调速系统结构图;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;
图5是在本发明提出的控制策略下有无扩张状态观测器对比图;FIG. 5 is a comparison diagram with or without an expanded state observer under the control strategy proposed by the present invention;
图6是本发明提出的控制策略与PI矢量控制下推进电机转速、转矩对比图。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.
具体实施方式Detailed ways
如上所述,半潜船吊舱推进电机工作在海上工作时容易受到海浪、海风等未知因素的影响,为了提高吊舱推进电机的动态性能和稳态性能,减少负载扰动和未知扰动对系统的影响,本发明设计了一种基于紧格式动态线性化的吊舱推进电机滑模控制方案。以下将结合附图,对本发明进行更为详细的描述。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.
参见图1所示,本实施例半潜船吊舱推进电机控制方案,具体包括以下步骤: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:
步骤S1:建立吊舱推进电机动力学模型并且离散化:Step S1: Establish a dynamic model of the pod propulsion motor and discretize it:
1)针对吊舱推进电机进行控制策略设计时,为了满足吊舱推进电机转矩性能要求较高的要求,采用idw=0的永磁同步电机转子磁场定向控制方法,永磁同步电机在d-q坐标系下的推进电机转矩方程为: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:
其中,Te为电磁转矩,p为电机极对数,为永磁体与定子交链磁链,iq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;
永磁同步电机个具有多变量、参数时变的非线性系统,考虑到未知扰动后的运动方程为如下: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:
其中,ω为推进电机转子角速度,ω=2πn/60,n为推进电机的输出转速,TL为负载转矩,J为转动惯量,F为吊舱推进电机的摩擦系数,KQ为转矩系数,ρ为水的密度,D为螺旋桨直径,fld(k)定义为k时刻影响推进电机转速的未知扰动;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)对永磁同步电机进行线性动态化处理,结合式(1)和式(2)将永磁同步电机的运动方程离散化处理,离散运动方程如下: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:
其中,n(k+1)为k+1时刻推进电机的输出转速,iq(k)为k时刻q轴电流,h为采样时间;Among them, n(k+1) is the output speed of the propulsion motor at
步骤S2:利用伪偏导数的概念结合吊舱推进电机的离散转速系统方程建立其紧格式动态线性化数据模型: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)吊舱推进电机是一个非线性系统,可表示为:1) The pod propulsion motor is a nonlinear system, which can be expressed as:
n(k+1)=f(n(k),n(k-1),…,n(k-ly),iq(k),iq(k-1),…,iq(k-lu))+fAL(k)(4)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)
其中,fAL(k)表示系统总扰动信号,包括负载扰动和未知扰动fld(k),f(·)是未知非线性函数,ly,lu∈R为系统未知阶数;令: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:
nm(k+1)=f(n(k),n(k-1),…,n(k-ly),iq(k),iq(k-1),…,iq(k-lu)) (5)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)
则吊舱推进电机系统可改写为:Then the pod propulsion motor system can be rewritten as:
n(k+1)=nm(k+1)+fAL(k) (6)n(k+1)=n m (k+1)+f AL (k) (6)
假设1:吊舱推进电机系统输入输出是可观测且可控的,对于给出的有界期望推进电机输出转速nw(k+1),总存在一有界的输入信号使推进电机在此控制输入信号的驱动下输出等于推进电机期望输出转速nw(k+1);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;
假设2:f(·)关于q轴电流iq(k)的偏导数是存在且连续的;Assumption 2: The partial derivative of f(·) with respect to the q-axis current i q (k) exists and is continuous;
假设3:系统是广义Lipschitz的,即满足对任意k时刻和|Δiq(k)|≠0有:Assumption 3: The system is generalized Lipschitz, that is, it satisfies for any k time and |Δi q (k)|≠0:
Δnm(k+1)=φ(k)Δiq(k) (7)Δn m (k+1)=φ(k)Δi q (k) (7)
则:but:
Δn(k+1)=φ(k)Δiq(k)+ΔfAL(k) (8)Δn(k+1)=φ(k)Δi q (k)+Δf AL (k) (8)
其中,Δn(k+1)=n(k+1)-n(k)为k时刻到k+1时刻推进电机的输出转速变化量,Δiq(k)=iq(k)-iq(k-1)为k时刻到k+1时刻q轴电流变化量;Among them, Δn(k+1)=n(k+1)-n(k) is the output speed change of the propulsion motor from time k to
假设4:系统中的负载扰动与未知扰动在两个相邻时刻的变化是有界的,满足广义Lipschitz条件: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:
|ΔfAL(k+1)|≤b|Δiq(k)| (9)|Δf AL (k+1)|≤b|Δi q (k)| (9)
其中,b是一个正常数;where b is a positive constant;
假设5:吊舱推进电机非线性系统具有一个全局渐近稳定的零动态。从实际应用的观点上看,上述假设是合理并可接受的。其中,假设1是对受控系统的一条基本假设,如果它不满足,这种系统是不可控的。假设2是许多控制律的典型条件,吊舱推进电机非线性系统满足这一条件。假设3是对系统输出变化量的一种限制,转速变化的大小不会是无限的,它要受限于转矩的大小,转矩改变受到输入电流的影响,单位时间内电流变化是有限的。假设4总扰动对系统应该是一个有限的影响。假设5是对系统内部动态的一种假设。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,
定理:对于吊舱推进电机系统,满足假设1~5,当|Δiq(t)|≠0时,一定存在一个被称为偏导数的量φ(k),使得:Theorem: For the pod propulsion motor system, the
Δn(k+1)=Δnm(k+1)+ΔfAL(k) (10)Δn(k+1)=Δn m (k+1)+Δf AL (k) (10)
其中,φ(k)为速度环控制律的伪偏导数;Among them, φ(k) is the pseudo-partial derivative of the velocity loop control law;
结合式(7),式(10)可改写为:Combined with formula (7), formula (10) can be rewritten as:
Δn(k+1)=φ(k)Δiq(k)+ΔfAL(k) (11)Δn(k+1)=φ(k)Δi q (k)+Δf AL (k) (11)
2)吊舱推进电机系统可采用如下参数估计算法来求取式(11)伪偏导数的估计值: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):
通过求解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:
当或|Δiq(k-1)|≤α, when or |Δi q (k-1)|≤α,
步骤S3:设计基于紧格式动态线性化的吊舱推进电机滑模控制律方案:Step S3: Design a sliding mode control law scheme for the pod propulsion motor based on compact dynamic linearization:
1)定义滑模平面函数为:1) Define the sliding mode plane function as:
s(k)=e(k)+ce(k-1) (14)s(k)=e(k)+ce(k-1) (14)
其中,c为大于0的常数,因此构成的误差多项式为稳定多项式,e(k)为转速跟踪误差,定义如下: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)e(k)= nw (k)-n(k) (15)
其中,nw(k)为k时刻推进电机的期望输出转速,采用趋近律如下: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)s(k+1)=(1-d)s(k)-εsgn(s(k)) (16)
其中,d、ε为大于0的常数;Among them, d and ε are constants greater than 0;
等效控制可以由式(16)所示的方程获得: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)s(k+1)=(1-d)s(k)-εsgn(s(k))=e(k+1)+ce(k) (17)
结合式(14)~(17)可得:Combining formulas (14) to (17), we can get:
e(k+1)=(1-d)s(k)-εsgn(s(k))-ce(k) (18)e(k+1)=(1-d)s(k)-εsgn(s(k))-ce(k) (18)
即:which is:
则基于紧格式动态线性化的吊舱推进电机滑模控制律如下:Then the sliding mode control law of the pod propulsion motor based on the compact dynamic linearization is as follows:
2)结合式(13)获得的速度环控制律的伪偏导数的估计值,可得到基于紧格式动态线性化的吊舱推进电机滑模控制方案如下: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:
式(20)中,可以做到使转速跟踪逐渐趋近于零。但是,在吊舱推进电机工作时时,由于未建模动态和未知扰动、负载扰动等不确定因素带来扰动的扰动影响,容易使系统出现抖振的现象,而且滑模控制一直存在强鲁棒性和系统抖振相矛盾的问题,如果可以对扰动进行估计,在控制输入端进行补偿会减小系统抖振的问题,步骤S4便是一种针对此问题提出的一种解决方案。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.
步骤S4:设计扩张状态观测器,其结构图如图2所示:Step S4: Design an expanded state observer, the structure of which is shown in Figure 2:
设计扩张状态观测器,对基于紧格式动态线性化的吊舱推进电机滑模控制方案中的总扰动信号fAL(k)进行估计: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:
令:make:
其中,x2(k)为扩张状态变量,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:
定义el(k)为观测速度误差,可构造二阶扩张状态观测器为:Defining e l (k) as the observed velocity error, the second-order extended state observer can be constructed as:
其中,β1、β2、β3为本系统中扩张状态观测器的参数且均大于0,el(k)为观测器中推进电机的输出转速误差,z1(k)为扩张状态观测器中推进电机的输出转速估计值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.
步骤S5:设计串联基于紧格式动态线性化的吊舱推进电机滑模控制方案:Step S5: Design the sliding mode control scheme of the pod propulsion motor based on the compact dynamic linearization in series:
1)吊舱推进电机系统输入输出是可观测且可控的,f(·)关于q轴期望电压uq(k)的偏导数是存在且连续的,故系统是广义Lipschitz的,即满足对任意k时刻和|Δuq(k)|≠0有: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:
iq(k+1)=φ1(k)Δuq(k) (26)i q (k+1)=φ 1 (k)Δu q (k) (26)
2)采用如下参数估计算法来求取内电流环控制律的伪偏导数的估计值: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:
通过求解可得:by solving Available:
当或|Δuq(k-1)|≤α1, when or |Δu q (k-1)|≤α 1 ,
3)内电流环作为推进电机转速系统的副回路,采用基于紧格式动态线性化模型的吊舱推进电机滑模控制器替代原有的电流PI控制器,进行二次调节,内电流环采取基于紧格式动态线性化的吊舱推进电机滑模控制方法,与速度环构成串级控制结构内电流环控制方法与速度外环不同的是,这里将交轴电流作为输出,uq(k)作为输入,并且去除扰动项,该控制器的设计可参考前面转速环控制器的设计,副控制回路同样采取基于数据驱动控制的方法,减少未建模动态对系统的影响,提高了推进电机转速系统的控制性能,控制方案如下: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:
其中,η1∈(0,1]是内电流环控制律的步长因子,μ1>0是内电流环控制律的权重因子,σ1>0为一个权重系数,用于限制q轴电压变化量,α1、d1、ε1均为大于0的常数,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)=iqw(k)-iq(k),uqw(k)为q轴期望电压,uq(k-1)为k-1时刻q轴电压,Δuq(k-1)=uq(k-1)-uq(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).
参见图3所示,使用MATLAB/Simulink建立本发明控制方案半潜船吊舱推进电机调速系统结构模型并进行仿真,半潜船吊舱推进电机调速系统主要由转速环、内电流环、SVPWM、扩张状态观测器和永磁同步电机组成,半潜船吊舱推进电机参数参考“泰安口”号半潜船推进电机,具体参数为:额定电压为660V;额定功率为4700kW;转子永磁体磁链为2.6458Wb;电阻为0.00164Ω;电机极对数为8;d轴电感为0.0085H;q轴电感为0.0085H。根据实际系统的调试情况,设计速度环控制器参数和内电流环控制器的参数,将内电流环控制器输出信号ud、uq进行Park变换,得到两相静止坐标系下的电压uα、uβ后,通过空间矢量脉宽调制算法SVPWM,得到逆变器的控制信号,由逆变器输出相应的三相电压信号,施加于永磁同步电机定子绕组上,对永磁同步电机进行速度调节。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.
参见图4所示,使用MATLAB/Simulink建立PI控制方案半潜船吊舱推进电机调速系统结构模型用于与本发明提出的控制方案进行仿真对比,半潜船吊舱推进电机参数同上。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.
参见图5所示,为了说明扩张状态观测器的有效性,系统使用本发明控制方案,对比有无状态观测器下的转速和转矩响应曲线。可以看出状态观测器可以很好的跟踪扰动的变化,有状态观测器对扰动进行补偿后,推进电机的转速超调减小,在到达设定值后更快的稳定下来。同时推进电机转矩脉冲减小,系统动态性能得到提高。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.
参见图6所示,为了说明半潜船吊舱推进电机在本发明控制方案下恒速作业的有效性,对比两种控制方案下推进电机转速和转矩响应曲线。仿真结果如图6所示,图6中本发明控制方案下推进电机转速在0.045s到达期望转速,最大转速波动14rpm,并在0.074s时到达稳定状态,持续波动较小,相较于PI控制第一次到达期望速度用时减少25%,系统达到稳定状态用时减少45%,最大转速波动减小了4.5rpm,转矩到达稳定状态提前了0.12s。相对而言本发明控制方案很好的抑制了负载变化带来的转速瞬态波动和转矩脉动,减少了对电动机的损害,在系统存在未知扰动影响时也可以保持系统稳定性,有效削弱系统抖振,表现出了更好的响应速度和抗干扰性能。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.
本实施例提出了一种基于紧格式动态线性化的吊舱推进电机滑模控制方法,用于半潜船吊舱推进电机控制。在MATLAB/Simulink仿真环境下比较了本发明方案与现有PI矢量控制方案下的推进电机动态性能及稳态性能,结果表明本实施例的基于紧格式动态线性化的吊舱推进电机滑模控制方法可以提高推进电机的转速和转矩控制精度,减小转矩脉动对电机的损害,对吊舱推进电机内部参数的不确定性以及未知扰动具有较强鲁棒性,为半潜船动力定位系统提供了一种有效的控制方法。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.
以上所述的具体描述,对发明的目的、技术方案和有益效果进行了进一步的详细说明,所应理解的是,实施例仅用于解释本发明,并不用于限定本发明的保护范围。任何本领域技术人员,在不脱离本发明的精神和范围内,均可作各种更动与修改,因此本发明的保护范围应当以权利要求所限定的范围为准。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.
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