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CN114955011A - A fixed angle control method of frame system in DGVSCMG flywheel mode - Google Patents

A fixed angle control method of frame system in DGVSCMG flywheel mode Download PDF

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CN114955011A
CN114955011A CN202210379941.5A CN202210379941A CN114955011A CN 114955011 A CN114955011 A CN 114955011A CN 202210379941 A CN202210379941 A CN 202210379941A CN 114955011 A CN114955011 A CN 114955011A
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乔建忠
周常升
崔洋洋
郭雷
余翔
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Beihang University
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
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    • B64G1/00—Cosmonautic vehicles
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    • B64G1/286—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect using control momentum gyroscopes (CMGs)
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Abstract

本发明涉及一种DGVSCMG飞轮模式下框架系统定角控制方法，目标是通过设计抗干扰控制方法，实现DGVSCMG框架伺服系统的高精度锁定。首先，建立含多源干扰的DGVSCMG框架伺服系统的数学模型并将干扰分为低频干扰和高频干扰两类；其次，设计干扰观测器对低频干扰进行估计和前馈补偿；然后改进比例积分谐振控制器，抑制频率和幅值同时变化的动不平衡高频干扰；最后，复合干扰观测器和改进型比例积分谐振控制器，实现框架伺服系统的精确锁定。本发明具有结构简单、充分利用干扰信息和工程实践性强的优点。

Figure 202210379941

The invention relates to a frame system fixed angle control method in DGVSCMG flywheel mode, and aims to realize high-precision locking of the DGVSCMG frame servo system by designing an anti-interference control method. Firstly, the mathematical model of the DGVSCMG frame servo system with multi-source interference is established and the interference is divided into two types: low-frequency interference and high-frequency interference; secondly, the interference observer is designed to estimate and feedforward the low-frequency interference; then the proportional integral resonance is improved. The controller suppresses the dynamic unbalanced high-frequency interference whose frequency and amplitude change at the same time; finally, the composite interference observer and the improved proportional-integral resonance controller realize the precise locking of the frame servo system. The invention has the advantages of simple structure, full utilization of interference information and strong engineering practicability.

Figure 202210379941

Description

一种DGVSCMG飞轮模式下框架系统定角控制方法A fixed angle control method of frame system in DGVSCMG flywheel mode

技术领域technical field

本发明属于伺服系统控制领域，具体涉及一种DGVSCMG飞轮模式下框架系统定角控制方法，用于增强内、外框架伺服系统抗干扰的能力，实现内、外框架的精确锁定。The invention belongs to the field of servo system control, and in particular relates to a frame system fixed angle control method in DGVSCMG flywheel mode, which is used for enhancing the anti-interference ability of inner and outer frame servo systems and realizing precise locking of the inner and outer frames.

背景技术Background technique

作为一种新型的执行机构，双框架变速控制力矩陀螺具有两种主要的工作模式：控制力矩陀螺模式和飞轮模式。在飞轮模式下，通过使陀螺房转子加速或者减速，它可输出精细力矩。该力矩可用于奇异性避免、航天器的姿态稳定和能量存储。为了实现航天器的高精度姿态稳定，此时双框架变速控制力矩陀螺的框架角应不再变化。然而，框架系统中存在的多源干扰严重制约了框架转速的锁定精度。多源干扰主要包括两大类：(1)动不平衡干扰：因生产和装配误差而产生，令框架转速产生高频抖动。其频率和幅值随转子变速而同时变化，是一种高频、高幅值干扰，并是影响框架锁定精度的主要扰动；(2)转子变速干扰力矩、摩擦力矩和框架间耦合力矩：转子的变速会影响外框架转速的控制精度，进而因内、外框架耦合造成内框架转速波动，而摩擦力矩会给内、外框架转速带来跟踪静差和低速爬行的影响。由于框架转速很低，这三种扰动是一类低频、低幅值的干扰。因此，充分利用干扰信息，通过设计抗干扰控制方法实现框架伺服系统的高精度锁定具有重要的研究价值。As a new type of actuator, the dual-frame variable speed control torque gyro has two main working modes: control torque gyro mode and flywheel mode. In flywheel mode, it can output fine torque by accelerating or decelerating the rotor of the gyro room. This moment can be used for singularity avoidance, spacecraft attitude stabilization and energy storage. In order to achieve high-precision attitude stability of the spacecraft, the frame angle of the dual-frame variable-speed control torque gyro should not change at this time. However, the multi-source interference in the frame system severely restricts the locking accuracy of the frame speed. Multi-source interference mainly includes two categories: (1) Dynamic unbalanced interference: caused by production and assembly errors, causing high-frequency jitter in the frame speed. Its frequency and amplitude change simultaneously with the speed of the rotor, which is a high-frequency and high-amplitude interference, and is the main disturbance that affects the locking accuracy of the frame; (2) The rotor speed change interference torque, friction torque and coupling torque between frames: the rotor The speed change will affect the control accuracy of the speed of the outer frame, and then the speed of the inner frame will fluctuate due to the coupling of the inner and outer frames, and the friction torque will bring the influence of tracking static difference and low-speed creep to the speed of the inner and outer frames. Since the frame speed is very low, these three disturbances are a kind of low frequency, low amplitude disturbance. Therefore, it is of great research value to make full use of the interference information to realize the high-precision locking of the frame servo system by designing an anti-interference control method.

针对飞轮模式下多源干扰制约框架锁定精度提高这一问题，国内外专家学者提出一些控制方法。文献《Composite Decoupling Control of Gimbal Servo System inDouble-Gimbal Variable Speed CMG Via Disturbance Observer》(基于干扰观测器的双框架变速控制力矩陀螺框架伺服系统的复合解耦控制)提出了一种基于干扰观测器的状态反馈复合控制方法，实现了内、外框架伺服系统的解耦控制。文献《基于ESO的DGVSCMG双框架伺服系统不匹配扰动抑制》针对双框架变速控制力矩陀螺两种工作模式下内、外框架系统存在不匹配干扰的问题，通过扩张状态观测器进行干扰估计，并结合坐标变换、状态反馈控制有效减小了不匹配干扰对框架伺服系统的影响。然而，上述两种研究思路均未考虑动不平衡干扰的影响。In view of the problem of improving the locking accuracy of the multi-source interference control frame in the flywheel mode, domestic and foreign experts and scholars have proposed some control methods. The document "Composite Decoupling Control of Gimbal Servo System in Double-Gimbal Variable Speed CMG Via Disturbance Observer" (Composite Decoupling Control of Gimbal Servo System in Double-Gimbal Variable Speed CMG Via Disturbance Observer based on Disturbance Observer) proposes a disturbance observer-based state The feedback compound control method realizes the decoupling control of the inner and outer frame servo systems. The paper "Mismatch Disturbance Suppression of DGVSCMG Dual-Frame Servo System Based on ESO" aims at the problem of mismatched disturbance in the inner and outer frame systems under the two working modes of the dual-frame variable speed control torque gyroscope. Coordinate transformation and state feedback control effectively reduce the influence of mismatch interference on the frame servo system. However, the above two research ideas did not consider the influence of dynamic imbalance disturbance.

针对变频率、幅值未知的谐波干扰，文献《Rejection of time-varyingfrequency sinusoidal disturbance using refined observer for a class ofuncertain systems》(基于精细干扰观测器的一类不确定系统的时变频率正弦干扰抑制)提出了一种精细干扰观测器(Refined Disturbance Observer，RDO)，可对该类扰动进行实时估计并补偿，但该方法仅针对一类谐波干扰，对多源干扰的抑制能力有待加强。中国申请CN202110804350.3为了提高控制力矩陀螺模式下框架伺服系统的转速跟踪精度和稳定度，提出了一种复合控制方法，有效抑制了多源干扰的影响，但该方法并不适用于飞轮模式下的高精度框架锁定需求。For harmonic interference with variable frequency and unknown amplitude, the literature "Rejection of time-varyingfrequency sinusoidal disturbance using refined observer for a class of uncertain systems" A Refined Disturbance Observer (RDO) is proposed, which can estimate and compensate this type of disturbance in real time, but this method is only for one type of harmonic disturbance, and its ability to suppress multi-source disturbance needs to be strengthened. Chinese application CN202110804350.3 In order to improve the speed tracking accuracy and stability of the frame servo system in the control torque gyro mode, a composite control method is proposed, which effectively suppresses the influence of multi-source interference, but this method is not suitable for the flywheel mode. high precision frame locking requirements.

综上所述，在飞轮模式下，已有的控制方法不能有效减小双框架变速控制力矩陀螺框架伺服系统中多源干扰的影响，实现框架伺服系统的高精度锁定是亟需解决的难题。To sum up, in the flywheel mode, the existing control methods cannot effectively reduce the influence of multi-source interference in the dual-frame variable speed control torque gyro frame servo system, and it is an urgent problem to achieve high-precision locking of the frame servo system.

发明内容SUMMARY OF THE INVENTION

为克服现有技术的不足，本发明提供一种DGVSCMG飞轮模式下框架系统定角控制方法，DGVSCMG指双框架变速控制力矩陀螺。以双框架变速控制力矩陀螺框架伺服系统为研究对象，针对频率和幅值同时变化的多源干扰，提高系统的抗干扰能力，实现框架伺服系统的高精度锁定，并具有结构简单、充分利用干扰信息和工程实践性强的优点。In order to overcome the deficiencies of the prior art, the present invention provides a frame system fixed angle control method in DGVSCMG flywheel mode, where DGVSCMG refers to a dual-frame variable speed control torque gyro. Taking the double-frame variable speed control torque gyro frame servo system as the research object, aiming at the multi-source interference with simultaneous changes in frequency and amplitude, the anti-interference ability of the system is improved, the high-precision locking of the frame servo system is realized, and the structure is simple and the interference can be fully utilized. Information and engineering practical advantages.

本发明解决上述技术问题采用的技术方案为：依据欧拉动力学方程，建立含有多源干扰的双框架变速控制力矩陀螺框架伺服系统的数学模型，并将多源干扰分为低频干扰和高频干扰两类；其次，设计干扰观测器对低频干扰进行估计并前馈补偿；然后，根据可知的转子转速信息，改进传统的比例积分谐振控制器对频率和幅值同时变化的高频干扰进行抑制，从而实现飞轮模式下框架伺服系统的精确锁定。The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows: according to the Euler dynamics equation, a mathematical model of a dual-frame variable speed control torque gyro frame servo system containing multi-source interference is established, and the multi-source interference is divided into low-frequency interference and high-frequency interference Two types; secondly, a disturbance observer is designed to estimate low-frequency disturbances and feed-forward compensation; then, based on the known rotor speed information, the traditional proportional-integral resonance controller is improved to suppress high-frequency disturbances whose frequency and amplitude change at the same time. This enables precise locking of the frame servos in flywheel mode.

本发明的一种DGVSCMG飞轮模式下框架系统定角控制方法，包括以下步骤：A frame system fixed angle control method under a DGVSCMG flywheel mode of the present invention comprises the following steps:

第一步，考虑动不平衡干扰的影响，建立DGVSCMG框架伺服系统的数学模型，并根据干扰的频率特征将多源干扰分为低频干扰和高频干扰两类；The first step is to establish the mathematical model of the DGVSCMG frame servo system considering the influence of dynamic unbalanced interference, and divide the multi-source interference into two types: low-frequency interference and high-frequency interference according to the frequency characteristics of the interference;

第二步，根据第一步所述的数学模型，设计干扰观测器，对低频力矩dl1,dl2进行实时估计，得到低频干扰的估计值；In the second step, according to the mathematical model described in the first step, an interference observer is designed to estimate the low-frequency moments d l1 and d l2 in real time to obtain the estimated value of the low-frequency interference;

第三步，根据第一步所述的数学模型，利用可知的转子转速信息，设计改进型比例积分谐振控制器抑制频率和幅值同时变化的高频干扰dh1,dh2；In the third step, according to the mathematical model described in the first step, using the known rotor speed information, an improved proportional-integral resonance controller is designed to suppress the high-frequency disturbances d h1 , d h2 with simultaneous changes in frequency and amplitude;

第四步，将第二步的干扰观测器与第三步的改进型比例积分谐振控制器进行复合，提高框架伺服系统的抗干扰能力和锁定精度。The fourth step is to combine the disturbance observer in the second step with the improved proportional-integral resonance controller in the third step to improve the anti-interference ability and locking accuracy of the frame servo system.

所述第一步，确定被控对象的数学模型。在动力学分析过程中考虑动不平衡干扰的影响，并将多源干扰分为低频干扰和高频干扰两类。建立双框架变速控制力矩陀螺框架伺服系统的数学模型如下：In the first step, the mathematical model of the controlled object is determined. In the process of dynamic analysis, the influence of dynamic unbalanced interference is considered, and the multi-source interference is divided into two types: low-frequency interference and high-frequency interference. The mathematical model for establishing the dual-frame variable speed control torque gyro frame servo system is as follows:

Figure BDA0003592382240000031
Figure BDA0003592382240000031

其中，d1＝dh1+dl1，d2＝dh2+dl2，Wherein, d 1 =d h1 +d l1 , d 2 =d h2 +d l2 ,

Figure BDA0003592382240000032
Figure BDA0003592382240000032

Figure BDA0003592382240000033
Figure BDA0003592382240000033

θgx、

Figure BDA0003592382240000034
和
Figure BDA0003592382240000035
为内框架坐标系相对外框架坐标系转动的角位置、角速度和角加速度；θjy、
Figure BDA0003592382240000036
和
Figure BDA0003592382240000037
为外框架坐标系相对惯性坐标系转动的角位置、角速度和角加速度；uqgx,uqjy分别是内、外框架驱动电机定子电压的q轴分量；Jrx,Jry,Jrz为陀螺房高速转子绕转子坐标系三轴的转动惯量，且Jrx＝Jry＝Jrr；Jgx,Jgy,Jgz为内框架系统绕内框架坐标系三轴的转动惯量；Jx,Jy分别为内、外框架系统绕框架轴的等效转动惯量；Lqgx,Lqjy分别是内、外框架驱动电机的q轴电感分量；Rgx,Rjy分别是内、外框架驱动电机的定子电阻；Ktgx,Ktjy分别是内、外框架驱动电机的电磁力矩系数；iqgx,iqjy分别是内、外框架驱动电机定子电流的q轴分量；Kegx,Kejy分别是内、外框架驱动电机的反电势系数，且Ktgx＝1.5·Kegx，Ktjy＝1.5·Kejy；d1,d2为作用于内、外框架的多源干扰，其中dh1,dh2为高频干扰，dl1,dl2为低频干扰；
Figure BDA0003592382240000038
为外框架作用于内框架伺服系统的耦合力矩；
Figure BDA0003592382240000039
为内框架作用于外框架伺服系统的耦合力矩；Tfgx,Tfjy分别为内、外框架伺服系统中的摩擦力矩；
Figure BDA00035923822400000310
为陀螺房转子变速扰动；Tdx,Tdy为陀螺房转子动不平衡干扰在内环系x,y轴的分量；Ud为陀螺房转子的动不平衡量；Ω为陀螺房转子的转速；
Figure BDA00035923822400000311
为动不平衡质量在初始时刻的相位角。θ gx ,
Figure BDA0003592382240000034
and
Figure BDA0003592382240000035
are the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; θ jy ,
Figure BDA0003592382240000036
and
Figure BDA0003592382240000037
are the angular position, angular velocity and angular acceleration of the outer frame coordinate system rotating relative to the inertial coordinate system; u qgx , u qjy are the q-axis components of the stator voltage of the inner and outer frame drive motors, respectively; J rx , J ry , and J rz are the gyro room The moment of inertia of the high-speed rotor around the three axes of the rotor coordinate system, and J rx =J ry =J rr ; J gx , J gy , and J gz are the moments of inertia of the inner frame system around the three axes of the inner frame coordinate system; J x , J y are the equivalent moment of inertia of the inner and outer frame systems around the frame axis, respectively; L qgx , L qjy are the q-axis inductance components of the inner and outer frame drive motors, respectively; R gx , R jy are the stators of the inner and outer frame drive motors, respectively resistance; K tgx , K tjy are the electromagnetic torque coefficients of the inner and outer frame drive motors, respectively; i qgx , i qjy are the q-axis components of the stator currents of the inner and outer frame drive motors, respectively; K egx , K ejy are the inner and outer frame drive motors, respectively The back EMF coefficient of the frame drive motor, and K tgx = 1.5 · K egx , K tjy = 1.5 · Kejy ; d 1 , d 2 are the multi-source interference acting on the inner and outer frames, where d h1 , d h2 are high frequency interference, d l1 and d l2 are low frequency interference;
Figure BDA0003592382240000038
is the coupling moment of the outer frame acting on the inner frame servo system;
Figure BDA0003592382240000039
is the coupling torque of the inner frame acting on the outer frame servo system; T fgx , T fjy are the friction torques in the inner and outer frame servo systems, respectively;
Figure BDA00035923822400000310
is the variable speed disturbance of the gyro room rotor; T dx , T dy are the components of the gyro room rotor dynamic unbalance disturbance on the x and y axes of the inner ring system; U d is the dynamic unbalance of the gyro room rotor; Ω is the rotational speed of the gyro room rotor;
Figure BDA00035923822400000311
is the phase angle of the dynamic unbalanced mass at the initial moment.

所述第二步中，低频干扰的估计值实现如下：In the second step, the estimated value of the low frequency interference is realized as follows:

为了补偿低频扰动dl1,dl2，设计频域干扰观测器对其进行实时估计，得到低频干扰的估计值：In order to compensate the low-frequency disturbance d l1 , d l2 , a frequency-domain disturbance observer is designed to estimate it in real time, and the estimated value of the low-frequency disturbance is obtained:

Figure BDA0003592382240000041
Figure BDA0003592382240000041

其中，s为拉氏变换复变量算子；

Figure BDA0003592382240000042
为低频干扰估计值；
Figure BDA0003592382240000043
为框架伺服系统的角速度；
Figure BDA0003592382240000044
为框架伺服系统速度环的复合控制量；Q(s)为频域干扰观测器中的滤波器；G0(s)为框架伺服系统的标称模型。Among them, s is the Laplace transform complex variable operator;
Figure BDA0003592382240000042
is the estimated value of low frequency interference;
Figure BDA0003592382240000043
is the angular velocity of the frame servo system;
Figure BDA0003592382240000044
is the composite control quantity of the speed loop of the frame servo system; Q(s) is the filter in the frequency domain disturbance observer; G 0 (s) is the nominal model of the frame servo system.

为了避免低频干扰的补偿效果受限于电流环的带宽，在标称模型G0(s)中考虑电流环的动态。同时为了有效估计低频干扰并减少检测噪声的引入，Q(s)应取为低通滤波器。G0(s)和Q(s)表示为：To avoid that the compensation effect of low frequency disturbances is limited by the bandwidth of the current loop, the dynamics of the current loop are considered in the nominal model G 0 (s). At the same time, in order to effectively estimate low-frequency interference and reduce the introduction of detection noise, Q(s) should be taken as a low-pass filter. G 0 (s) and Q(s) are expressed as:

Figure BDA0003592382240000045
Figure BDA0003592382240000045

其中，ωn和ξ分别为Q(s)的截止频率和阻尼比；Kt和Ke分别为力矩系数和反电势系数；Ci(s)为电流环的控制器；Gi(s)＝1/(Lq+R)，Lq和R分别为驱动电机的q轴电感分量和定子电阻；G(s)＝1/(Js)，J为驱动电机轴向的转动惯量。Among them, ω n and ξ are the cut-off frequency and damping ratio of Q(s), respectively; K t and Ke are the torque coefficient and the back-EMF coefficient, respectively; C i (s) is the controller of the current loop; G i ( s) =1/(L q +R), L q and R are the q-axis inductance component and stator resistance of the drive motor respectively; G(s)=1/(Js), J is the rotational inertia of the drive motor in the axial direction.

所述第三步，改进传统的比例积分谐振控制器抑制频率和幅值同时变化的高频干扰dh1,dh2。传统的比例积分谐振控制器为：In the third step, the traditional proportional-integral resonance controller is improved to suppress high-frequency interference d h1 , d h2 whose frequency and amplitude change simultaneously. The traditional proportional-integral resonant controller is:

Figure BDA0003592382240000046
Figure BDA0003592382240000046

其中，s为拉氏变换复变量算子；uPIR(s)为比例积分谐振控制器；ksp,ksi分别为比例和积分控制系数；

Figure BDA00035923822400000413
为谐振增益；
Figure BDA0003592382240000047
为相位调整角；eω(s)为角速度跟踪误差；
Figure BDA0003592382240000048
是谐振频率。Among them, s is the Laplace transform complex variable operator; u PIR (s) is the proportional-integral resonance controller; k sp , k si are the proportional and integral control coefficients, respectively;
Figure BDA00035923822400000413
is the resonance gain;
Figure BDA0003592382240000047
is the phase adjustment angle; e ω (s) is the angular velocity tracking error;
Figure BDA0003592382240000048
is the resonant frequency.

1)首先，为了弥补传统比例积分谐振控制器不能应对变频率谐波干扰的缺点，令谐振频率

Figure BDA0003592382240000049
同时对相角
Figure BDA00035923822400000410
进行实时调节。当速度环采用PI控制并保证系统稳定时，对速度环的闭环传递函数Gcl(s)进行辨识。1) First, in order to make up for the disadvantage that the traditional proportional-integral resonant controller cannot cope with the harmonic interference of variable frequency, the resonant frequency is
Figure BDA0003592382240000049
Simultaneous opposite phase angle
Figure BDA00035923822400000410
Make real-time adjustments. When the speed loop adopts PI control and the system is stable, the closed-loop transfer function G cl (s) of the speed loop is identified.

Figure BDA00035923822400000411
Figure BDA00035923822400000411

其中，CsPI(s)为速度环的PI控制器。接下来，加入谐振控制器后，根据开环传递函数Gopen(s)复极点处根轨迹的出射角应处于(90°,270°)范围内，得到相角

Figure BDA00035923822400000412
在不同转子转速下使系统稳定的范围，Among them, C sPI (s) is the PI controller of the speed loop. Next, after adding the resonant controller, according to the open-loop transfer function G open (s), the exit angle of the root locus at the complex pole should be in the range of (90°, 270°) to obtain the phase angle
Figure BDA00035923822400000412
The range to stabilize the system at different rotor speeds,

Figure BDA0003592382240000051
Figure BDA0003592382240000051

其中，Gcl0(s)＝Gcl(s)/CsPI(s)，Gcl0(s)是PI控制下因期望转速产生的速度环控制量到框架转速的传递函数；开环传递函数

Figure BDA0003592382240000052
εΩ为谐振增益；
Figure BDA0003592382240000053
∠Gcl0(jΩ)为Gcl0(s)在频率Ω处的相角，j为虚轴的单位长度。Among them, G cl0 (s)=G cl (s)/C sPI (s), G cl0 (s) is the transfer function from the speed loop control quantity generated by the desired speed under PI control to the frame speed; the open-loop transfer function
Figure BDA0003592382240000052
ε Ω is the resonance gain;
Figure BDA0003592382240000053
∠G cl0 (jΩ) is the phase angle of G cl0 (s) at frequency Ω, and j is the unit length of the imaginary axis.

由于

Figure BDA0003592382240000054
和
Figure BDA0003592382240000055
受电机参数的影响，考虑到电机参数的辨识误差，取相角
Figure BDA0003592382240000056
随时间t的变化律为：because
Figure BDA0003592382240000054
and
Figure BDA0003592382240000055
Influenced by the motor parameters, considering the identification error of the motor parameters, take the phase angle
Figure BDA0003592382240000056
The law of change with time t is:

Figure BDA0003592382240000057
Figure BDA0003592382240000057

2)其次，为了加入谐振控制器后进一步使系统保持稳定，利用Gopen(s)的根轨迹，在已知转子转速变化范围内选取一定数量的转速点(如10～20个)，得到不同转子转速下使系统临界稳定的谐振增益εSΩ值。对得到的εSΩ值与选取的转速点进行拟合，可得谐振增益εΩ随时间t的变化律：2) Secondly, in order to further stabilize the system after adding the resonant controller, use the root locus of G open (s) to select a certain number of speed points (such as 10 to 20) within the known rotor speed variation range, and obtain different The value of resonance gain ε SΩ that makes the system critically stable at rotor speed. By fitting the obtained ε SΩ value with the selected rotational speed point, the variation law of resonance gain ε Ω with time t can be obtained:

εΩ(t)＝εSΩ(Ω)/Nε Ω (t)=ε SΩ (Ω)/N

其中，N为大于1的常数。where N is a constant greater than 1.

所述第四步，复合控制器为：In the fourth step, the composite controller is:

Figure BDA0003592382240000058
Figure BDA0003592382240000058

Figure BDA0003592382240000059
Figure BDA0003592382240000059

其中，s为拉氏变换复变量算子；uIPIR(s)为改进型比例积分谐振控制器的输出；eω(s)为角速度跟踪误差；

Figure BDA00035923822400000510
为低频干扰的估计值；
Figure BDA00035923822400000511
为速度环的复合控制量。Among them, s is the Laplace transform complex variable operator; u IPIR (s) is the output of the improved proportional-integral resonance controller; e ω (s) is the angular velocity tracking error;
Figure BDA00035923822400000510
is the estimated value of low frequency interference;
Figure BDA00035923822400000511
It is the compound control quantity of the speed loop.

本发明与现有技术相比的优点在于：针对飞轮模式下双框架变速控制力矩陀螺框架伺服系统扰动抑制问题，现有技术减小了框架间耦合力矩的影响，实现了内、外框架伺服系统的解耦，但未考虑动不平衡干扰。本发明较现有技术具有结构简单、充分利用干扰信息和工程实践性强的优点。首先，本发明在动力学分析过程中考虑了动不平衡干扰的影响，使双框架变速控制力矩陀螺框架伺服系统的数学模型更符合工程实际。其次，设计了干扰观测器对转子变速扰动、摩擦力矩和框架间耦合力矩三种低频干扰实时估计补偿，并改进传统的比例积分谐振控制器对飞轮模式下动不平衡干扰进行抑制。最后，通过将干扰观测器与改进型比例积分谐振控制器复合，增强了框架伺服系统的抗干扰能力，实现了飞轮模式下框架伺服系统的高精度锁定。Compared with the prior art, the present invention has the advantages that: in view of the disturbance suppression problem of the double-frame speed change control torque gyro frame servo system in the flywheel mode, the prior art reduces the influence of the coupling torque between the frames, and realizes the inner and outer frame servo systems. decoupling, but dynamic unbalance interference is not considered. Compared with the prior art, the present invention has the advantages of simple structure, full utilization of interference information and strong engineering practicability. First of all, the present invention considers the influence of dynamic unbalance interference in the dynamic analysis process, so that the mathematical model of the double-frame variable speed control torque gyro frame servo system is more in line with engineering practice. Secondly, a disturbance observer is designed to estimate and compensate three low-frequency disturbances of rotor speed change disturbance, friction torque and inter-frame coupling torque in real time, and improve the traditional proportional-integral resonance controller to suppress the dynamic unbalance disturbance in flywheel mode. Finally, by combining the disturbance observer with the improved proportional-integral resonance controller, the anti-interference ability of the frame servo system is enhanced, and the high-precision locking of the frame servo system in the flywheel mode is realized.

附图说明Description of drawings

图1为本发明的DGVSCMG飞轮模式下框架伺服系统定角控制方法流程图；Fig. 1 is the flow chart of the fixed angle control method of the frame servo system under the DGVSCMG flywheel mode of the present invention;

图2为本发明采用的框架伺服系统速度环频域干扰观测器原理框图；Fig. 2 is the frame servo system speed loop frequency domain interference observer principle block diagram adopted in the present invention;

图3为本发明中开环传递函数Gopen(s)的根轨迹；Fig. 3 is the root locus of open-loop transfer function G open (s) in the present invention;

图4为本发明中开环传递函数Gopen(s)根轨迹的局部放大图；4 is a partial enlarged view of the root locus of the open-loop transfer function G open (s) in the present invention;

图5为本发明提出的内、外框架伺服系统抗干扰控制结构框图；5 is a block diagram of the anti-jamming control structure of the inner and outer frame servo systems proposed by the present invention;

图6为基于本发明的飞轮模式下外框架伺服系统低频干扰估计及其估计误差图；其中，第一张子图为低频干扰真实值，第二张子图为干扰观测器的估计量，第三张子图为低频干扰的补偿误差；Fig. 6 is a low-frequency interference estimation and estimation error diagram of the outer frame servo system based on the flywheel mode of the present invention; wherein, the first sub-picture is the real value of the low-frequency interference, the second sub-picture is the estimated amount of the interference observer, and the third sub-picture is the low-frequency interference Compensation error of interference;

图7为基于本发明的改进型比例积分谐振控制器相位和谐振增益参数的变化曲线；其中，左图为相位的变化曲线，右图为谐振增益的变化曲线；Fig. 7 is the change curve of phase and resonance gain parameter of the improved proportional-integral resonance controller based on the present invention; wherein, the left figure is the change curve of the phase, and the right figure is the change curve of the resonance gain;

图8为基于本发明和对比方法的飞轮模式下内框架伺服系统转速锁定效果图；8 is an effect diagram of rotational speed locking of the inner frame servo system under the flywheel mode based on the present invention and the comparative method;

图9为基于本发明和对比方法的飞轮模式下外框架伺服系统转速锁定效果图。FIG. 9 is a diagram showing the rotational speed locking effect of the outer frame servo system in the flywheel mode based on the present invention and the comparative method.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明作进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

如图1所示，本发明一种DGVSCMG飞轮模式下框架系统定角控制方法步骤为：As shown in Figure 1, the steps of the frame system fixed angle control method under a DGVSCMG flywheel mode of the present invention are:

首先，建立被控对象的数学模型。利用欧拉动力学方程，改进已有的双框架变速控制力矩陀螺框架伺服系统的数学模型，并通过实验和最小二乘算法辨识驱动电机的相关参数；其次，设计干扰观测器实时估计转子变速扰动、框架间耦合力矩和摩擦力矩；然后，采用改进型比例积分谐振控制器抑制频率和幅值同时变化的动不平衡干扰；最后，将干扰观测器和改进型比例积分谐振控制器进行复合，实现对飞轮模式下多源干扰的估计、前馈补偿和抑制，提高双框架伺服系统的锁定精度。First, establish the mathematical model of the controlled object. Using Euler's dynamic equation, the existing mathematical model of the dual-frame variable speed control torque gyro frame servo system is improved, and the relevant parameters of the drive motor are identified through experiments and least squares algorithm. Secondly, a disturbance observer is designed to estimate the rotor variable speed disturbance in real time, The coupling torque and friction torque between frames; then, an improved proportional-integral resonance controller is used to suppress the dynamic unbalanced disturbance whose frequency and amplitude change at the same time; finally, the disturbance observer and the improved proportional-integral resonance controller are combined to realize the Estimation, feedforward compensation and suppression of multi-source disturbances in flywheel mode to improve the locking accuracy of dual-frame servo systems.

具体实施步骤如下：The specific implementation steps are as follows:

第一步，建立被控对象的数学模型。在动力学分析过程中考虑动不平衡干扰的影响，并根据干扰的频率分布特征将多源干扰分为低频干扰和高频干扰两类，建立永磁同步电机直接驱动的双框架变速控制力矩陀螺框架伺服系统数学模型如下：The first step is to establish the mathematical model of the controlled object. In the dynamic analysis process, the influence of dynamic unbalanced interference is considered, and the multi-source interference is divided into two types: low-frequency interference and high-frequency interference according to the frequency distribution characteristics of the interference, and a dual-frame variable-speed control torque gyro directly driven by permanent magnet synchronous motor is established The mathematical model of the frame servo system is as follows:

Figure BDA0003592382240000071
Figure BDA0003592382240000071

其中，d1＝dh1+dl1，d2＝dh2+dl2，Wherein, d 1 =d h1 +d l1 , d 2 =d h2 +d l2 ,

Figure BDA0003592382240000072
Figure BDA0003592382240000072

Figure BDA0003592382240000073
Figure BDA0003592382240000073

θgx、

Figure BDA0003592382240000074
和
Figure BDA0003592382240000075
为内框架坐标系相对外框架坐标系转动的角位置、角速度和角加速度；θjy、
Figure BDA0003592382240000076
和
Figure BDA0003592382240000077
为外框架坐标系相对惯性坐标系转动的角位置、角速度和角加速度；uqgx,uqjy分别是内、外框架驱动电机定子电压的q轴分量；Jrx,Jry,Jrz为陀螺房高速转子绕转子坐标系三轴的转动惯量，且Jrx＝Jry＝Jrr；Jgx,Jgy,Jgz为内框架系统绕内框架坐标系三轴的转动惯量；Jx,Jy分别为内、外框架系统绕框架轴的等效转动惯量；Lqgx,Lqjy分别是内、外框架驱动电机的q轴电感分量；Rgx,Rjy分别是内、外框架驱动电机的定子电阻；Ktgx,Ktjy分别是内、外框架驱动电机的电磁力矩系数；iqgx,iqjy分别是内、外框架驱动电机定子电流的q轴分量；Kegx,Kejy分别是内、外框架驱动电机的反电势系数，且Ktgx＝1.5·Kegx，Ktjy＝1.5·Kejy；d1,d2为作用于内、外框架的多源干扰，其中dh1,dh2为高频干扰，dl1,dl2为低频干扰；.
Figure BDA0003592382240000078
为外框架作用于内框架伺服系统的耦合力矩；
Figure BDA0003592382240000079
为内框架作用于外框架伺服系统的耦合力矩；Tfgx,Tfjy分别为内、外框架伺服系统中的摩擦力矩；
Figure BDA00035923822400000710
为陀螺房转子变速扰动；Tdx,Tdy为陀螺房转子动不平衡干扰在内环系x,y轴的分量；Ud为陀螺房转子的动不平衡量；Ω为陀螺房转子的转速；
Figure BDA00035923822400000711
为动不平衡质量在初始时刻的相位角。θ gx ,
Figure BDA0003592382240000074
and
Figure BDA0003592382240000075
are the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; θ jy ,
Figure BDA0003592382240000076
and
Figure BDA0003592382240000077
are the angular position, angular velocity and angular acceleration of the outer frame coordinate system rotating relative to the inertial coordinate system; u qgx , u qjy are the q-axis components of the stator voltage of the inner and outer frame drive motors, respectively; J rx , J ry , and J rz are the gyro room The moment of inertia of the high-speed rotor around the three axes of the rotor coordinate system, and J rx =J ry =J rr ; J gx , J gy , and J gz are the moments of inertia of the inner frame system around the three axes of the inner frame coordinate system; J x , J y are the equivalent moment of inertia of the inner and outer frame systems around the frame axis, respectively; L qgx , L qjy are the q-axis inductance components of the inner and outer frame drive motors, respectively; R gx , R jy are the stators of the inner and outer frame drive motors, respectively resistance; K tgx , K tjy are the electromagnetic torque coefficients of the inner and outer frame drive motors, respectively; i qgx , i qjy are the q-axis components of the stator currents of the inner and outer frame drive motors, respectively; K egx , K ejy are the inner and outer frame drive motors, respectively The back EMF coefficient of the frame drive motor, and K tgx = 1.5 · K egx , K tjy = 1.5 · Kejy ; d 1 , d 2 are the multi-source interference acting on the inner and outer frames, where d h1 , d h2 are high frequency interference, d l1 , d l2 are low frequency interference;
Figure BDA0003592382240000078
is the coupling moment of the outer frame acting on the inner frame servo system;
Figure BDA0003592382240000079
is the coupling torque of the inner frame acting on the outer frame servo system; T fgx , T fjy are the friction torques in the inner and outer frame servo systems, respectively;
Figure BDA00035923822400000710
is the variable speed disturbance of the gyro room rotor; T dx , T dy are the components of the gyro room rotor dynamic unbalance disturbance on the x and y axes of the inner ring system; U d is the dynamic unbalance of the gyro room rotor; Ω is the rotational speed of the gyro room rotor;
Figure BDA00035923822400000711
is the phase angle of the dynamic unbalanced mass at the initial moment.

内、外框架伺服系统的参数及动不平衡干扰参数如表1所示。The parameters of the inner and outer frame servo systems and the dynamic unbalance interference parameters are shown in Table 1.

表1内、外框架伺服系统和动不平衡干扰参数Table 1 Inner and outer frame servo system and dynamic unbalance interference parameters

Figure BDA0003592382240000081
Figure BDA0003592382240000081

为了充分体现摩擦力矩的特性，采用LuGre摩擦模型表征内、外框架伺服系统中的摩擦力矩Tfgx,Tfjy：In order to fully reflect the characteristics of the friction torque, the LuGre friction model is used to characterize the friction torque T fgx , T fjy in the inner and outer frame servo systems:

Figure BDA0003592382240000082
Figure BDA0003592382240000082

其中，σ0是摩擦刚性系数，σ0＝1.00Nm/rad；σ1是摩擦阻尼系数，σ1＝0.50Nm/(rad/s)；σ2为粘性摩擦系数，σ2＝0.60Nm/(rad/s)；Tcf是库伦摩擦力矩，Tcf＝0.0080Nm；Tsf是静摩擦力矩，Tsf＝0.10Nm；ωs是Stribeck特征角速度，ωs＝0.10rad/s；z是表征摩擦接触表面不可测量的动态特性的状态变量；g(ω)是大于0的有界函数；ω为框架转速。Among them, σ 0 is the friction stiffness coefficient, σ 0 =1.00Nm/rad; σ 1 is the friction damping coefficient, σ 1 =0.50Nm/(rad/s); σ 2 is the viscous friction coefficient, σ 2 =0.60Nm/( rad/s); T cf is the Coulomb friction torque, T cf =0.0080Nm; T sf is the static friction torque, T sf =0.10Nm; ω s is the Stribeck characteristic angular velocity, ω s =0.10rad/s; z is the characteristic friction contact The state variable of the seemingly unmeasurable dynamic characteristics; g(ω) is a bounded function greater than 0; ω is the frame speed.

第二步，为了补偿低频扰动dl1,dl2，设计频域干扰观测器对其进行实时估计，得到低频干扰的估计值：In the second step, in order to compensate the low-frequency disturbance d l1 , d l2 , a frequency-domain disturbance observer is designed to estimate it in real time, and the estimated value of the low-frequency disturbance is obtained:

Figure BDA0003592382240000083
Figure BDA0003592382240000083

其中，s为拉氏变换复变量算子；

Figure BDA0003592382240000084
为低频干扰估计值；
Figure BDA0003592382240000085
为框架伺服系统的角速度；
Figure BDA0003592382240000086
为框架伺服系统速度环的复合控制量；Q(s)为频域干扰观测器中的滤波器；G0(s)为框架伺服系统的标称模型。Among them, s is the Laplace transform complex variable operator;
Figure BDA0003592382240000084
is the estimated value of low frequency interference;
Figure BDA0003592382240000085
is the angular velocity of the frame servo system;
Figure BDA0003592382240000086
is the composite control quantity of the speed loop of the frame servo system; Q(s) is the filter in the frequency domain disturbance observer; G 0 (s) is the nominal model of the frame servo system.

频域干扰观测器的结构框图如图2所示。为了避免低频干扰的补偿效果受限于电流环的带宽，在标称模型G0(s)中考虑电流环的动态。同时为了有效估计低频干扰并减少检测噪声的引入，Q(s)应取为低通滤波器。G0(s)和Q(s)表示为：The structural block diagram of the frequency-domain interference observer is shown in Figure 2. To avoid that the compensation effect of low frequency disturbances is limited by the bandwidth of the current loop, the dynamics of the current loop are considered in the nominal model G 0 (s). At the same time, in order to effectively estimate low-frequency interference and reduce the introduction of detection noise, Q(s) should be taken as a low-pass filter. G 0 (s) and Q(s) are expressed as:

Figure BDA0003592382240000091
Figure BDA0003592382240000091

其中，ωn和ξ分别为Q(s)的截止频率和阻尼比；Kt和Ke分别为力矩系数和反电势系数；Ci(s)为电流环的控制器；Gi(s)＝1/(Lq+R)，Lq和R分别为驱动电机的q轴电感分量和定子电阻；G(s)＝1/(Js)，J为驱动电机轴向的转动惯量。Among them, ω n and ξ are the cut-off frequency and damping ratio of Q(s), respectively; K t and Ke are the torque coefficient and the back-EMF coefficient, respectively; C i (s) is the controller of the current loop; G i ( s) =1/(L q +R), L q and R are the q-axis inductance component and stator resistance of the drive motor respectively; G(s)=1/(Js), J is the rotational inertia of the drive motor in the axial direction.

由于内框架伺服系统中的低频干扰幅值低，且转子变速扰动主要作用于外框架，因此只在外框架伺服系统中加入干扰观测器。经多次仿真调试，干扰观测器的参数为：ξ＝0.71，ωn＝250.00rad/s。Since the low-frequency disturbance amplitude in the inner frame servo system is low, and the rotor speed change disturbance mainly acts on the outer frame, only the disturbance observer is added to the outer frame servo system. After many simulations and debugging, the parameters of the interference observer are: ξ=0.71, ωn =250.00rad/s.

第三步，根据第一步建立的数学模型，设计改进型比例积分谐振控制器抑制频率和幅值同时变化的动不平衡干扰dh1,dh2。传统的比例积分谐振控制器为：In the third step, according to the mathematical model established in the first step, an improved proportional-integral resonance controller is designed to suppress the dynamic unbalanced disturbances d h1 , d h2 whose frequency and amplitude change simultaneously. The traditional proportional-integral resonant controller is:

Figure BDA0003592382240000092
Figure BDA0003592382240000092

其中，s为拉氏变换复变量算子；uPIR(s)为比例积分谐振控制器；ksp,ksi分别为比例和积分控制系数；

Figure BDA00035923822400000910
为谐振增益；
Figure BDA0003592382240000093
为相位调整角；eω(s)为角速度跟踪误差；
Figure BDA0003592382240000094
是谐振频率。未加入谐振控制之前，选取令系统稳定的PI控制参数如表2所示。Among them, s is the Laplace transform complex variable operator; u PIR (s) is the proportional-integral resonance controller; k sp , k si are the proportional and integral control coefficients, respectively;
Figure BDA00035923822400000910
is the resonance gain;
Figure BDA0003592382240000093
is the phase adjustment angle; e ω (s) is the angular velocity tracking error;
Figure BDA0003592382240000094
is the resonant frequency. Before adding resonance control, select the PI control parameters to stabilize the system as shown in Table 2.

1)首先，为了弥补传统比例积分谐振控制器不能应对变频率谐波干扰的缺点，令谐振频率

Figure BDA0003592382240000095
同时对相角
Figure BDA0003592382240000096
进行实时调节。当速度环采用PI控制并保证系统稳定时，对速度环的闭环传递函数Gcl(s)进行辨识。其中，1) First, in order to make up for the disadvantage that the traditional proportional-integral resonant controller cannot cope with the harmonic interference of variable frequency, the resonant frequency is
Figure BDA0003592382240000095
Simultaneous opposite phase angle
Figure BDA0003592382240000096
Make real-time adjustments. When the speed loop adopts PI control and the system is stable, the closed-loop transfer function G cl (s) of the speed loop is identified. in,

Figure BDA0003592382240000097
Figure BDA0003592382240000097

其中，CsPI(s)为速度环的PI控制器。接下来，加入谐振控制器后，根据开环传递函数Gopen(s)复极点处根轨迹的出射角应处于(90°,270°)范围内(如图3所示)，得到相角

Figure BDA0003592382240000098
在不同转子转速下使系统稳定的范围，即：Among them, C sPI (s) is the PI controller of the speed loop. Next, after adding the resonance controller, according to the open-loop transfer function G open (s), the exit angle of the root locus at the complex pole should be in the range of (90°, 270°) (as shown in Figure 3), and the phase angle is obtained.
Figure BDA0003592382240000098
The range to stabilize the system at different rotor speeds, namely:

Figure BDA0003592382240000099
Figure BDA0003592382240000099

其中，Gcl0(s)＝Gcl(s)/CsPI(s)，Gcl0(s)是PI控制下因期望转速产生的速度环控制量到框架转速的传递函数；开环传递函数

Figure BDA0003592382240000101
εΩ为谐振增益；
Figure BDA0003592382240000102
∠Gcl0(jΩ)为Gcl0(s)在频率Ω处的相角，j为虚轴的单位长度。Among them, G cl0 (s)=G cl (s)/C sPI (s), G cl0 (s) is the transfer function from the speed loop control quantity generated by the desired speed under PI control to the frame speed; the open-loop transfer function
Figure BDA0003592382240000101
ε Ω is the resonance gain;
Figure BDA0003592382240000102
∠G cl0 (jΩ) is the phase angle of G cl0 (s) at frequency Ω, and j is the unit length of the imaginary axis.

由于

Figure BDA0003592382240000103
和
Figure BDA0003592382240000104
受电机参数的影响，考虑到电机参数的辨识误差，取相角
Figure BDA0003592382240000105
随时间t的变化律为：because
Figure BDA0003592382240000103
and
Figure BDA0003592382240000104
Influenced by the motor parameters, considering the identification error of the motor parameters, take the phase angle
Figure BDA0003592382240000105
The law of change with time t is:

Figure BDA0003592382240000106
Figure BDA0003592382240000106

2)其次，如图4所示，以转子转速1000rpm为起点、10000rpm为终点，中间每隔500rpm选取1个转速点，利用Gopen(s)的根轨迹，得到19个转子转速下使系统临界稳定的谐振增益εSΩ值。对εSΩ值与选取的转速点进行拟合，分别可得内、外框架系统临界稳定εSΩ值随Ω的变化律为：内框架，εSΩ(Ω)＝0.42Ω-18.61；外框架，εSΩ(Ω)＝0.99Ω+418.82。为了加入谐振控制器后进一步使系统保持稳定，最终选取谐振增益的变化律为：内框架，εΩ(Ω)＝(0.42Ω-18.61)/5；外框架，εΩ(Ω)＝(0.99Ω+418.82)/10。2) Secondly, as shown in Fig. 4, taking the rotor speed of 1000rpm as the starting point and 10000rpm as the end point, select a speed point every 500rpm in the middle, and use the root locus of G open (s) to obtain 19 rotor speeds that make the system critical. Stable resonance gain ε SΩ value. Fitting the ε SΩ value and the selected rotational speed point, respectively, the variation law of the critical stable ε SΩ value of the inner and outer frame systems with Ω can be obtained as follows: the inner frame, ε SΩ (Ω)=0.42Ω-18.61; the outer frame, ε SΩ (Ω)=0.99Ω+418.82. In order to further stabilize the system after adding the resonance controller, the change law of the resonance gain is finally selected as: inner frame, ε Ω (Ω)=(0.42Ω-18.61)/5; outer frame, ε Ω (Ω)=(0.99 Ω+418.82)/10.

表2比例积分控制项参数Table 2 Proportional-integral control term parameters

Figure BDA0003592382240000107
Figure BDA0003592382240000107

第四步，本发明提出的双框架变速控制力矩陀螺飞轮模式下框架伺服系统定角控制框图如图5所示。将第二步的干扰观测器与第三步的改进型比例积分谐振控制器进行复合，增强框架伺服系统应对多源干扰的能力，保证飞轮模式下双框架伺服系统的锁定精度。得到的复合控制器为：In the fourth step, the frame servo system fixed-angle control block diagram under the dual-frame variable speed control torque gyro flywheel mode proposed by the present invention is shown in FIG. 5 . The interference observer in the second step is combined with the improved proportional-integral resonance controller in the third step to enhance the ability of the frame servo system to deal with multi-source interference and ensure the locking accuracy of the double frame servo system in the flywheel mode. The resulting composite controller is:

Figure BDA0003592382240000108
Figure BDA0003592382240000108

Figure BDA0003592382240000109
Figure BDA0003592382240000109

其中，uIPIR(s)为改进型比例积分谐振控制器的输出；eω(s)为角速度跟踪误差；

Figure BDA00035923822400001010
为低频干扰的估计值；
Figure BDA00035923822400001011
为速度环的复合控制量。Among them, u IPIR (s) is the output of the improved proportional-integral resonance controller; e ω (s) is the angular velocity tracking error;
Figure BDA00035923822400001010
is the estimated value of low frequency interference;
Figure BDA00035923822400001011
It is the compound control quantity of the speed loop.

在飞轮工作模式下，取内、外框架伺服系统的初始角度为(θgx)0＝10.00°、(θjy)0＝0.00°，期望转速为

Figure BDA0003592382240000111
陀螺房转子的转速变化规律为：Ω＝0.00rpm，t≤2s；Ω＝1000*(t-2)rpm，2＜t＜12s。基于传统比例积分谐振控制、论文《Rejection oftime-varying frequency sinusoidal disturbance using refined observer for aclass of uncertain systems》(基于精细干扰观测器的一类不确定系统的时变频率正弦干扰抑制)和本发明的内、外框架锁定效果如图6-图9所示。其中，图6为干扰观测器对外框架低频干扰的估计和估计误差(第一张子图为低频干扰真实值，第二张子图为干扰观测器的估计量，第三张子图为低频干扰的补偿误差)，图7为改进型比例积分谐振控制器的相位和谐振增益参数的变化曲线(左图为相位的变化曲线，右图为谐振增益的变化曲线)，图8为内框架伺服系统的转速锁定效果，图9为外框架伺服系统的转速锁定效果。从图6可以看出，所设计的干扰观测器可以对低频干扰dl2进行有效估计并补偿。虽然干扰估计误差中存在高频分量，但改进型比例积分谐振控制器可以对其进行抑制。由图7知，改进型比例积分谐振控制器的相位和谐振增益参数随转子转速的变化而变化。根据图8和图9，可以看出传统比例积分谐振控制不能较好地应对变频率、变幅值的高频干扰dh1,dh2；对比改进型比例积分谐振控制和“改进型比例积分谐振控制+干扰观测器”两种方法，可知干扰观测器可以较好地补偿转子变速扰动，减小框架转速偏移量；在能量消耗相同的情况下，“状态反馈+精细干扰观测器”方法的内框架转速控制精度相对较高、外框架转速控制精度较低，而本发明提出的“改进型比例积分谐振控制+干扰观测器”方法下内外框架转速的控制精度不受转子变速的影响，实现了多源干扰下双框架伺服系统的高精度锁定。In the flywheel working mode, take the initial angles of the inner and outer frame servo systems as (θ gx ) 0 = 10.00°, (θ jy ) 0 = 0.00°, and the expected rotational speed is
Figure BDA0003592382240000111
The rotational speed variation rule of the rotor of the gyro room is: Ω=0.00rpm, t≤2s; Ω=1000*(t-2)rpm, 2<t<12s. Based on traditional proportional-integral resonance control, the paper "Rejection of time-varying frequency sinusoidal disturbance using refined observer for a class of uncertain systems" and the present invention , The outer frame locking effect is shown in Figure 6-Figure 9. Among them, Figure 6 shows the estimation and estimation error of the low-frequency interference of the external frame by the interference observer (the first sub-picture is the real value of the low-frequency interference, the second sub-picture is the estimated amount of the interference observer, and the third sub-picture is the compensation error of the low-frequency interference). 7 is the change curve of the phase and resonance gain parameters of the improved proportional-integral resonance controller (the left picture is the change curve of the phase, and the right picture is the change curve of the resonance gain). Figure 8 is the speed locking effect of the inner frame servo system. 9 is the speed locking effect of the outer frame servo system. It can be seen from Fig. 6 that the designed interference observer can effectively estimate and compensate the low frequency interference d l2 . Although there are high-frequency components in the disturbance estimation error, the improved proportional-integral resonant controller can suppress them. It can be seen from Fig. 7 that the phase and resonance gain parameters of the improved proportional-integral resonance controller change with the change of the rotor speed. According to Figure 8 and Figure 9, it can be seen that the traditional proportional-integral resonance control cannot cope with the high-frequency disturbances d h1 and d h2 of variable frequency and variable amplitude. Control + disturbance observer" two methods, it can be seen that the disturbance observer can better compensate the rotor speed change disturbance and reduce the frame speed offset; under the same energy consumption, the "state feedback + fine disturbance observer" method The inner frame speed control accuracy is relatively high, while the outer frame speed control accuracy is low, and the control accuracy of the inner and outer frame speed under the method of "improved proportional-integral resonance control + disturbance observer" proposed by the present invention is not affected by the speed change of the rotor. High-precision locking of double-frame servo system under multi-source interference.

为了更加具体地对比“状态反馈+精细干扰观测器”和“改进型比例积分谐振控制+干扰观测器”两种控制方法的控制效果，在能量消耗相同的情况下，采用转速锁定误差的标准差σ(°/s)和锁定误差绝对值的均值e(°/s)两种指标进行评价，两种控制方法的性能指标如表3所示。In order to more concretely compare the control effects of the two control methods "state feedback + fine disturbance observer" and "improved proportional integral resonance control + disturbance observer", under the condition of the same energy consumption, the standard deviation of the speed locking error is used. σ(°/s) and the mean value of the absolute value of the locking error e(°/s) are evaluated. The performance indicators of the two control methods are shown in Table 3.

表3两种控制方法的性能指标Table 3 Performance indicators of the two control methods

Figure BDA0003592382240000112
Figure BDA0003592382240000112

由表3得，当消耗相同能量时，本发明的内、外框架转速锁定误差的标准差较对比方法减小了72.19％和91.97％，内、外框架转速锁定误差较对比方法减小了62.87％和90.29％。这说明，消耗能量相近时，本发明具有更强的抗干扰能力；框架锁定精度相近时，本发明更节能。From Table 3, when the same energy is consumed, the standard deviation of the rotational speed locking error of the inner and outer frames of the present invention is reduced by 72.19% and 91.97% compared with the comparative method, and the rotational speed locking error of the inner and outer frames is reduced by 62.87% compared with the comparative method. % and 90.29%. This shows that when the energy consumption is similar, the present invention has stronger anti-interference ability; when the frame locking accuracy is similar, the present invention is more energy-saving.

本发明说明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。Contents that are not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art. Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (5)

1. A fixed angle control method for a frame system under a DGVSCMG flywheel mode is characterized by comprising the following steps:
the method comprises the steps of firstly, considering the influence of dynamic unbalance interference, establishing a mathematical model of a DGVSCMG frame servo system, and classifying according to the frequency distribution characteristics of multi-source interference;
secondly, designing a disturbance observer according to the mathematical model in the first step, and estimating three low-frequency moments of rotor variable-speed disturbance, coupling moment between frames and friction moment in real time in a flywheel mode to obtain an estimated value of the low-frequency disturbance;
thirdly, designing an improved proportional-integral resonance controller to inhibit dynamic unbalance high-frequency interference in a flywheel mode by using known rotor rotation speed information according to the mathematical model in the first step;
and fourthly, combining the interference observer in the second step with the improved proportional-integral resonance controller in the third step, and improving the anti-interference capability and locking precision of the DGVSCMG frame servo system.
2. The angle-fixing control method for the frame system under DGVSCMG flywheel mode as claimed in claim 1, wherein: the first step comprises: in the dynamic analysis process, the influence of dynamic unbalance interference is considered, a mathematical model of a controlled object is determined, and multi-source interference is classified according to the frequency distribution characteristics of the interference; the mathematical model of the DGVSCMG frame servo system is established as follows:
Figure FDA0003592382230000011
wherein d is 1 ＝d h1 +d l1 ，d 2 ＝d h2 +d l2 ，
Figure FDA0003592382230000012
Figure FDA0003592382230000013
Wherein, theta gx 、
Figure FDA0003592382230000014
And
Figure FDA0003592382230000015
the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; theta jy 、
Figure FDA0003592382230000021
And
Figure FDA0003592382230000022
the angular position, the angular velocity and the angular acceleration of the rotation of the outer frame coordinate system relative to the inertial coordinate system; u. of qgx ,u qjy Q-axis components of the stator voltages of the driving motor of the inner frame and the outer frame respectively; j. the design is a square rx ,J ry ,J rz For the moment of inertia of the high-speed rotor of the spinning top room about three axes of the rotor coordinate system, and J rx ＝J ry ＝J rr ；J gx ,J gy ,J gz The moment of inertia of the inner frame system around the three axes of the inner frame coordinate system; j is a unit of x ,J y Equivalent rotational inertia of the inner frame system and the outer frame system around the frame shaft respectively; l is a radical of an alcohol qgx ,L qjy Q-axis inductance components of the inner frame driving motor and the outer frame driving motor respectively; r gx ,R jy Stator resistors of the driving motor of the inner frame and the outer frame respectively; k is tgx ,K tjy The electromagnetic torque coefficients of the driving motors of the inner frame and the outer frame are respectively; i.e. i qgx ,i qjy Q-axis components of stator currents of the driving motor of the inner frame and the outer frame are respectively; k egx ,K ejy Back electromotive force coefficients of the inner and outer frame driving motors, respectively, and K tgx ＝1.5·K egx ，K tjy ＝1.5·K ejy ；d 1 ,d 2 For multi-source interference acting on the inner and outer frames, wherein d h1 ,d h2 For high frequency interference, d l1 ,d l2 Low frequency interference;
Figure FDA0003592382230000023
the coupling moment of the inner frame servo system is acted on by the outer frame;
Figure FDA0003592382230000024
is insideThe frame acts on the coupling moment of the outer frame servo system; t is fgx ,T fjy Friction torque in the inner frame servo system and the outer frame servo system respectively;
Figure FDA0003592382230000025
the variable speed disturbance is carried out on the gyro room rotor; t is dx ,T dy The dynamic unbalance interference of the rotor of the gyro room is a component of an x axis and a y axis of an inner ring system; u shape d The dynamic unbalance amount of the gyro room rotor is obtained; omega is the rotating speed of the gyro room rotor;
Figure FDA0003592382230000026
is the phase angle of the dynamically unbalanced mass at the initial instant.
3. The method of claim 1, wherein the step of controlling the angle of the DGVSCMG flywheel mode lower frame system comprises the steps of: in the second step, the estimation of the low frequency interference is implemented as follows:
to compensate for low frequency disturbances d l1 ,d l2 Designing a frequency domain interference observer to carry out real-time estimation on the low-frequency interference observer to obtain an estimated value of the low-frequency interference:
Figure FDA0003592382230000027
wherein s is a Laplace transform complex variable operator;
Figure FDA0003592382230000028
is a low frequency interference estimation value;
Figure FDA0003592382230000029
angular velocity of the frame servo system;
Figure FDA00035923822300000210
a composite control quantity of a speed loop of a frame servo system; q(s) is a filter in a frequency domain disturbance observer; g 0 (s) is the nominal value of the frame servo systemA model;
in order to avoid that the compensation effect of the low-frequency interference is limited by the bandwidth of the current loop, in the nominal model G 0 The dynamics of the current loop are taken into account in(s). Meanwhile, in order to effectively estimate low-frequency interference and reduce the introduction of detection noise, Q(s) should be taken as a low-pass filter;
G 0 (s) and Q(s) are represented by:
Figure FDA00035923822300000211
wherein, ω is n And ξ are the cut-off frequency and the damping ratio of Q(s), respectively; k t And K e Respectively a moment coefficient and a counter electromotive force coefficient; c i (s) a controller for the current loop; g i (s)＝1/(L q +R)，L q And R is the q-axis inductance component and the stator resistance of the driving motor respectively; g(s) ═ 1/(Js), and J is the moment of inertia in the axial direction of the drive motor.
4. The angle-fixing control method for the frame system under DGVSCMG flywheel mode as claimed in claim 1, wherein: the third step includes: high-frequency interference d for suppressing simultaneous change of frequency and amplitude by improving traditional proportional-integral resonance controller h1 ,d h2 (ii) a The conventional proportional-integral resonant controller is:
Figure FDA0003592382230000031
wherein s is a Laplace transform complex variable operator; u. of PIR (s) is a proportional-integral resonant controller; k is a radical of formula sp ,k si Proportional and integral control coefficients, respectively;
Figure FDA00035923822300000315
is the resonant gain;
Figure FDA0003592382230000032
for adjusting the phaseAngle trimming; e.g. of the type ω (s) is angular velocity tracking error;
Figure FDA0003592382230000033
is the resonance frequency.
1) Firstly, in order to make up for the defect that the traditional proportional-integral resonance controller can not deal with the harmonic interference of the variable frequency, the resonant frequency is enabled
Figure FDA0003592382230000034
Simultaneous phase angle pair
Figure FDA0003592382230000035
Real-time regulation is carried out, when the speed loop adopts PI control and ensures the stability of the system, the closed loop transfer function G of the speed loop is controlled cl (s) performing identification;
Figure FDA0003592382230000036
wherein, C sPI (s) is a PI controller for the speed loop. Next, after the resonant controller is added, according to the open-loop transfer function G open The emergence angle of the root track at the(s) multiple pole point is in the range of (90 DEG, 270 DEG), and the phase angle is obtained
Figure FDA0003592382230000037
Range for system stability at different rotor speeds:
Figure FDA0003592382230000038
wherein G is cl0 (s)＝G cl (s)/C sPI (s)，G cl0 (s) is a transfer function of the speed loop control quantity to the frame rotational speed due to the desired rotational speed under PI control; open loop transfer function
Figure FDA0003592382230000039
ε Ω Is the resonant gain;
Figure FDA00035923822300000310
∠G cl0 (j Ω) is G cl0 (s) the phase angle at the frequency Ω, j being the unit length of the imaginary axis.
Due to the fact that
Figure FDA00035923822300000311
And
Figure FDA00035923822300000312
affected by motor parameters, considering the identification error of the motor parameters, and taking phase angle
Figure FDA00035923822300000313
The law of variation with time t is:
Figure FDA00035923822300000314
2) secondly, to further stabilize the system after the addition of the resonance controller, G is used open (s) selecting a certain number of rotation speed points in the known rotor rotation speed variation range to obtain the resonance gain epsilon for making the system critical stable under different rotor rotation speeds SΩ A value; for the obtained epsilon SΩ Fitting the value with the selected rotation speed point to obtain the resonance gain epsilon Ω Law of variation with time t:
ε Ω (t)＝ε SΩ (Ω)/N
wherein N is a constant greater than 1.
5. The method of claim 1, wherein the step of controlling the angle of the DGVSCMG flywheel mode lower frame system comprises the steps of: in the fourth step, the composite controller is:
Figure FDA0003592382230000041
Figure FDA0003592382230000042
wherein s is a Laplace transform complex variable operator; u. of IPIR (s) is the output of the improved proportional-integral resonant controller; e.g. of the type ω (s) is the angular velocity tracking error;
Figure FDA0003592382230000043
is an estimate of low frequency interference;
Figure FDA0003592382230000044
is a composite control quantity of the speed loop.
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