CN105045270A

CN105045270A - Rigid-flexible system attitude control method based on vibration compensation and state feedback

Info

Publication number: CN105045270A
Application number: CN201510336764.2A
Authority: CN
Inventors: 李智斌; 刘洁; 田科丰; 王晓磊; 郝永波; 涂俊峰; 杨林芳
Original assignee: Beijing Institute of Control Engineering
Current assignee: Beijing Institute of Control Engineering
Priority date: 2015-06-17
Filing date: 2015-06-17
Publication date: 2015-11-11
Anticipated expiration: 2035-06-17
Also published as: CN105045270B

Abstract

A rigid-flexible system attitude control method based on vibration compensation and state feedback, which directly uses the dynamic measurement information of the flexible vibration, and performs compensation and feedback control on the vibration effect in the attitude controller of the central rigid body, without the need for flexible Mount the actuator on the accessory. In order to overcome the situation that conventional PID control is difficult to adapt to the inaccurate or changing parameters of the controlled object, and there is an inherent conflict between ensuring steady-state performance and relying on continuous excitation in general adaptive control, the state feedback control parameters of the present invention change with estimated state changes It can still maintain a good steady-state performance index for changing systems and environments, and is especially suitable for the attitude control of satellites that have a large impact on flexibility but require high stability performance indexes.

Description

A Method of Attitude Control for Rigid-Flexible Systems Based on Vibration Compensation and State Feedback

技术领域technical field

本发明属于航天器姿态控制领域，涉及一种基于振动补偿与状态反馈的刚柔系统姿态控制方法。The invention belongs to the field of attitude control of spacecraft, and relates to an attitude control method of a rigid-flexible system based on vibration compensation and state feedback.

背景技术Background technique

对于“中心刚体+挠性附件”系统的控制主要研究方向主要有两类：一是在挠性结构上布置敏感器和执行器进行振动主动控制；二是不考虑振动结构敏感器和执行器，通过中心刚体的控制器对挠性振动进行被动抑制。There are two main research directions for the control of the "central rigid body + flexible attachment" system: one is to arrange sensors and actuators on the flexible structure for active vibration control; the other is not to consider the vibration structure sensors and actuators, Flexural vibrations are passively suppressed by a central rigid body controller.

本方法不需要在挠性附件上安装执行器，但利用挠性振动的动态测量信息，在中心刚体的姿态控制器中对振动影响进行振动补偿与反馈控制。The method does not need to install an actuator on the flexible attachment, but uses the dynamic measurement information of the flexible vibration to perform vibration compensation and feedback control on the vibration effect in the attitude controller of the central rigid body.

在挠性结构的振动测量方面，已经提出多种方式。如文献“挠性卫星大角度机动变结构控制的全物理仿真研究”(周军等，宇航学报,1999年第1期)采用在挠性附件自由端安装加速度计进行振动测量；针对加速度计测量存在的局限性，中国专利01279070.2，“挠性模态测量仪”提出采用电阻应变桥式电路进行振动模态测量；中国专利201010623825.0，“星上挠性振动的二元智能结构控制装置”提出采用压电陶瓷(PZT)进行振动模态测量，其中应变敏感器可以安装在铰链处，具有灵敏度高的特点。Various approaches have been proposed for vibration measurement of flexible structures. For example, the literature "Research on Full-Physical Simulation of Flexible Satellite Large Angle Maneuvering Variable Structure Control" (Zhou Jun et al., Acta Astronautics, No. 1, 1999) uses an accelerometer installed at the free end of the flexible attachment for vibration measurement; for accelerometer measurement Existing limitations, Chinese patent 01279070.2, "flexible modal measuring instrument" proposes to use resistance strain bridge circuit for vibration modal measurement; Piezoelectric ceramics (PZT) for vibration modal measurements, in which strain sensors can be mounted at the hinge, are characterized by high sensitivity.

在刚体姿态的基本控制器设计方面，常规PID控制难以适应被控对象参数不准或变化的情形，而一般自适应控制存在确保稳态性能与依赖持续激励之间的内在冲突，为此需要针对一些典型控制器的不足之处进行新的探索。In terms of basic controller design for rigid body attitude, conventional PID control is difficult to adapt to the situation where the parameters of the controlled object are inaccurate or changing, while general adaptive control has an inherent conflict between ensuring steady-state performance and relying on continuous excitation. The deficiencies of some typical controllers are explored.

发明内容Contents of the invention

本发明的技术解决问题是：克服现有技术的不足，提出一种基于振动补偿和状态反馈的刚柔系统姿态控制方法，解决了利用挠性振动的动态测量信息在中心刚体的姿态控制器中对振动影响进行补偿的姿态控制的问题。The technical problem of the present invention is: to overcome the deficiencies of the prior art, to propose a rigid-flexible system attitude control method based on vibration compensation and state feedback, and to solve the problem of using the dynamic measurement information of flexible vibration in the attitude controller of the central rigid body The problem of attitude control with compensation for vibration effects.

本发明的技术解决方案是：一种基于振动补偿与状态反馈的刚柔系统姿态控制方法，步骤如下：The technical solution of the present invention is: a rigid-flexible system attitude control method based on vibration compensation and state feedback, the steps are as follows:

(1)被控刚柔系统包括中心刚体和挠性附件，挠性附件包括一个或多个悬臂梁，该被控刚柔系统能够当作带一个或多个悬臂梁的中心刚体作平面转动，被控刚柔系统的动力学方程为：(1) The controlled rigid-flexible system includes a central rigid body and a flexible attachment, and the flexible attachment includes one or more cantilever beams. The controlled rigid-flexible system can be regarded as a central rigid body with one or more cantilever beams for plane rotation, The dynamic equation of the controlled rigid-flexible system is:

$[[{J J}_{r r} + + ρ ρ A A L L (({R R}^{22} + + R R L L + + \frac{11}{33} {L L}^{22}))]] \overset{\cdot\cdot \cdot\cdot}{θ θ} + + 22 ρ ρ A A {&Integral; &Integral;}_{00}^{L L} v v \overset{\cdot &Center Dot;}{v v} d d l l + + ρ ρ A A {&Integral; &Integral;}_{00}^{L L} ((R R + + l l)) \overset{\cdot\cdot \cdot\cdot}{v v} d d l l = = {T T}_{c c} + + {T T}_{d d} - - - - - - ((11))$

$ρ ρ A A \overset{\cdot\cdot \cdot\cdot}{v v} + + {EIv EIv}_{l l l l l l l l} + + ρ ρ A A ((R R + + l l)) \overset{\cdot\cdot \cdot\cdot}{θ θ} = = ρ ρ A A {\overset{\cdot \cdot}{θ θ}}^{22} v v - - - - - - ((22))$

v(0,t)＝v_l(0,t)＝v_ll(L,t)＝v_lll(L,t)＝0(3)v(0,t)=v _l (0,t)=v _ll (L,t)=v _lll (L,t)=0(3)

式(1)为姿态动力学方程，式(2)为悬臂梁弯曲振动方程，式(3)为边界条件，ρ,A,L,R分别为挠性悬臂梁的截面密度、截面积、长度、悬臂梁和中心刚体连接点相对刚体质心的距离，v为悬臂梁任意点处的弯曲位移，为弯曲位移的一阶导数，为弯曲位移的二阶导数，v_l,v_ll,v_lll分别为悬臂梁任意点处的弯曲位移v对悬臂梁上任意点未变形时相对悬臂梁和中心刚体连接点的距离l的一阶、二阶和三阶偏导数，θ，分别为中心刚体的姿态角、中心刚体的姿态角速度和中心刚体的姿态角加速度，t表示系统时间，T_c，T_d分别为作用在中心刚体上的控制力矩和干扰力矩，J_r，分别为中心刚体和悬臂梁相对系统姿态转轴的惯量，记总惯量为 Equation (1) is the attitude dynamics equation, Equation (2) is the bending vibration equation of the cantilever beam, Equation (3) is the boundary condition, ρ, A, L, R are the cross-sectional density, cross-sectional area, and length of the flexible cantilever beam, respectively , the distance between the connection point of the cantilever beam and the central rigid body relative to the center of mass of the rigid body, v is the bending displacement at any point of the cantilever beam, is the first derivative of the bending displacement, is the second order derivative of the bending displacement, v _l , v _ll , v _lll are respectively the first order of the bending displacement v at any point on the cantilever beam to the distance l between the cantilever beam and the central rigid body connection point when any point on the cantilever beam is not deformed , second and third order partial derivatives, θ, are the attitude angle of the central rigid body, the attitude angular velocity of the central rigid body and the attitude angular acceleration of the central rigid body, t represents the system time, T _c , T _d are the control torque and disturbance torque acting on the central rigid body, J _r , are the inertia of the central rigid body and the cantilever beam relative to the rotation axis of the system attitude, and the total inertia is

(2)对步骤(1)所述的被控刚柔系统，构建姿态控制系统，包括敏感器、执行机构和控制器，敏感器包括姿态敏感器、陀螺和位移传感器，姿态敏感器、陀螺安装在中心刚体上，位移传感器安装在悬臂梁上；控制器安装在中心刚体上，用于实时解算刚柔系统所需的控制力矩；执行机构安装在中心刚体上，用于将控制器解算出的控制力矩作用到中心刚体上。(2) For the controlled rigid-flexible system described in step (1), build an attitude control system, including sensors, actuators and controllers. The sensors include attitude sensors, gyro and displacement sensors, and the attitude sensors and gyro are installed On the central rigid body, the displacement sensor is installed on the cantilever beam; the controller is installed on the central rigid body to calculate the control moment required by the rigid-flexible system in real time; the actuator is installed on the central rigid body to solve the controller The control torque of is applied to the central rigid body.

(3)采用步骤(2)所述的敏感器对步骤(1)所述的被控刚柔系统进行测量，即通过姿态敏感器测得中心刚体姿态角θ的测量值θ_m，通过陀螺测得中心刚体姿态角速度的测量值通过位移传感器测得悬臂梁前n阶模态的动态坐标q_i(t)(i＝1,2,…n)的测量值q_mi(t)(i＝1,2,…n)，n取小于等于4的非零正整数；(3) Use the sensor described in step (2) to measure the controlled rigid-flexible system described in step (1), that is, measure the measured value θ _m of the attitude angle θ of the central rigid body through the attitude sensor, and use the gyroscope to measure Get the attitude angular velocity of the central rigid body measured value of The measurement value q _mi (t) (i=1,2,...n) of the dynamic coordinates q _i (t) (i=1,2,...n) of the first n order modes of the cantilever beam measured by the displacement sensor, n Take a non-zero positive integer less than or equal to 4;

(4)根据步骤(3)得到的悬臂梁前n阶模态的动态坐标的测量值q_mi(t)(i＝1,2,…n)，计算出悬臂梁任意点的弯曲振动位移(0≤l≤L)，并对v_m(l,t)进行差分得到弯曲振动速度再对进行差分得到弯曲振动加速度 (4) Calculate the bending vibration displacement at any point of the cantilever beam according to the measured value q _mi (t) (i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam obtained in step (3) (0≤l≤L), and take the difference of v _m (l,t) to obtain the bending vibration velocity again Differentiate to obtain the bending vibration acceleration

式中，In the formula,

Φ_i(l)＝sin(β_il)-sh(β_il)-σ_i[cos(β_il)-ch(β_il)],σ_i＝(sinβ_iL+sinhβ_iL)/(cosβ_iL+coshβ_iL)，且β₁L≈1.8751，β₂L≈4.6941，β₃L≈7.8548，β₄L≈10.9955。Φ _i (l)=sin(β _i l)-sh(β _i l)-σ _i [cos(β _i l)-ch(β _i l)],σ _i =(sinβ _i L+sinhβ _i L) /(cosβ _i L+coshβ _i L), and β ₁ L≈1.8751, β ₂ L≈4.6941, β ₃ L≈7.8548, β ₄ L≈10.9955.

根据所计算出的悬臂梁弯曲振动位移v_m(l,t)、弯曲振动速度和弯曲振动加速度进行挠性振动前馈控制u_v，公式如下：According to the calculated cantilever beam bending vibration displacement v _m (l,t), bending vibration velocity and bending vibration acceleration Perform flexible vibration feed-forward control u _v , the formula is as follows:

${u u}_{v v} = = 22 ρ ρ A A {&Integral; &Integral;}_{00}^{L L} {v v}_{m m} ((l l,, t t)) {\overset{\cdot \cdot}{v v}}_{m m} ((l l,, t t)) d d l l + + ρ ρ A A {&Integral; &Integral;}_{00}^{L L} ((R R + + l l)) {\overset{\cdot\cdot \cdot\cdot}{v v}}_{m m} ((l l,, t t)) d d l l - - - - - - ((44))$

(5)根据步骤(3)得到的悬臂梁前n阶模态的动态坐标的测量值q_mi(t)(i＝1,2,…n)，对位移测量值进行差分得到速度的测量值(i＝1,2,…n)，计算出模态坐标反馈控制量u_q，公式如下：(5) According to the measured value q _mi (t) (i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam obtained in step (3), the measured value of the velocity is obtained by making a difference to the measured value of the displacement (i=1,2,…n), calculate the modal coordinate feedback control quantity u _q , the formula is as follows:

${u u}_{q q} = = {Σ Σ}_{i i = = 11}^{n no} [[{K K}_{q q i i} {q q}_{m m i i} ((t t)) + + {K K}_{\overset{\cdot \cdot}{q q} i i} {\overset{\cdot &Center Dot;}{q q}}_{m m i i} ((t t))]] - - - - - - ((55))$

式中K_qi>0， where K _qi >0,

(6)根据步骤(4)所获取的中心刚体的姿态角θ和姿态角速度的测量值θ_m和得到姿态反馈控制的姿态角误差θ_e和姿态角速度误差分别为：(6) Attitude angle θ and attitude angular velocity of the central rigid body acquired according to step (4) The measured value of θ _m and Get the attitude angle error θ _e and attitude angle velocity error of attitude feedback control They are:

θ_e＝θ_d-θ_m(6)θ _e = θ _d - θ _m (6)

${\overset{\cdot \cdot}{θ θ}}_{e e} = = {\overset{\cdot \cdot}{θ θ}}_{d d} - - {\overset{\cdot &Center Dot;}{θ θ}}_{m m} - - - - - - ((77))$

式中θ_d和分别为姿态角和姿态角速度的指令输入；where θ _d and They are command input of attitude angle and attitude angular velocity respectively;

姿态反馈控制律为：The attitude feedback control law is:

${u u}_{θ θ} = = J J \cdot \cdot {K K}_{θD θD} \cdot \cdot [[{\overset{\cdot &Center Dot;}{θ θ}}_{e e} + + {K K}_{θP θP} \cdot &Center Dot; {θ θ}_{e e}]] + + {K K}_{θI θI} \cdot \cdot {&Integral; &Integral; θ θ}_{e e} {| |}_{| | \cdot \cdot | | < < γ γ} \cdot &Center Dot; dt dt,, ((0.1 0.1 > > γ γ > > 00)) - - - - - - ((88))$

式中，K_θP、K_θI、K_θD为控制参数；In the formula, K _θP , K _θI , K _θD are control parameters;

(7)将步骤(4)计算的挠性振动前馈控制力矩u_v、步骤(5)计算的模态坐标反馈控制力矩u_q和步骤(6)计算出的姿态反馈控制力矩u_θ相加，并进行限幅，得到综合的控制力矩T_c:(7) Add the flexible vibration feedforward control torque u _v calculated in step (4), the modal coordinate feedback control torque u _q calculated in step (5), and the attitude feedback control torque u _θ calculated in step (6) , and perform clipping to obtain the comprehensive control torque T _c :

T_c＝mlf(u_θ+u_v+u_q,T_max)(9)T _c ＝mlf(u _θ +u _v +u _q ,T _max )(9)

式中T_max为设定的实际系统控制力矩幅值的上限，T_max>0，mlf(第1个参数，第2个参数)为双参数限幅函数，即当第1个参数的绝对值大于等于第2个参数时，限幅函数在保持第1个参数的符号的前提下，综合的控制力矩T_c大小就取第2个参数T_max，当第1个参数的绝对值小于第2个参数时，综合控制力矩T_c大小直接取第1个参数；In the formula, T _max is the upper limit of the set actual system control torque amplitude, T _max >0, mlf (the first parameter, the second parameter) is a two-parameter limiting function, that is, when the absolute value of the first parameter When it is greater than or equal to the second parameter, under the premise of keeping the sign of the first parameter, the limit function takes the second parameter T _max for the comprehensive control torque T _c . When the absolute value of the first parameter is less than the second When there are two parameters, the size of the comprehensive control torque T _c directly takes the first parameter;

(8)将步骤(7)所计算出的最终控制力矩T_c输出给执行结构，并作用到步骤(1)所述的系统上，完成刚柔系统的姿态控制。(8) Output the final control torque T _c calculated in step (7) to the execution structure, and act on the system described in step (1), to complete the attitude control of the rigid-flexible system.

本发明与现有技术相比的优点在于：The advantage of the present invention compared with prior art is:

(1)本发明通过步骤(4)，通过理论计算挠性振动对姿态运动的干扰力矩，得到姿态控制时的前馈补偿力矩，实现了姿态控制对挠性振动的前馈补偿，降低了挠性振动对姿态运动的影响。(1) The present invention passes through step (4), by theoretically calculating the disturbance torque of the flexible vibration to the posture movement, obtains the feed-forward compensation torque during the posture control, realizes the feed-forward compensation of the posture control to the flexible vibration, reduces the torsion Effects of sexual vibrations on postural movements.

(2)本发明通过步骤(5)，利用位移敏感器的测量得到的模态振动坐标及差分得到的速度，通过增大模态振动阻尼的方法，实现了挠性振动抑制，使得挠性模态振动能够迅速衰减至零。(2) The present invention, through step (5), utilizes the modal vibration coordinates that the measurement of displacement sensor obtains and the speed that difference obtains, by increasing the method for modal vibration damping, has realized flexible vibration suppression, makes flexible mode The dynamic vibration can quickly decay to zero.

(3)本发明通过步骤(6)提出了一种带智能调节能力的姿态反馈控制律，控制器结构与常规PID控制器结构一致，但控制器参数均根据系统的特性进行在线调节。控制器参数随估计状态的变化而变化，使得本发明方法对变化的系统和环境仍然能保持较好的稳态性能指标。(3) The present invention proposes a posture feedback control law with intelligent adjustment capability through step (6). The controller structure is consistent with the conventional PID controller structure, but the controller parameters are all adjusted online according to the characteristics of the system. The parameters of the controller change with the change of the estimated state, so that the method of the present invention can still maintain a good steady-state performance index for the changing system and environment.

附图说明Description of drawings

图1为带悬臂梁的刚体作平面转动示意图；Fig. 1 is that the rigid body with cantilever beam is made plane rotation schematic diagram;

图2为本发明方法的系统框图；Fig. 2 is a system block diagram of the inventive method;

图3为采用常规PID控制方法时的振动抑制效果曲线；Fig. 3 is the vibration suppression effect curve when adopting conventional PID control method;

图4为采用本发明姿态控制方法时的振动抑制效果曲线。Fig. 4 is a vibration suppression effect curve when adopting the attitude control method of the present invention.

具体实施方式Detailed ways

下面结合附图和具体实施例对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

如图1所示为包括中心刚体和挠性附件的被控刚柔系统，挠性附件包括一个或多个悬臂梁，该被控刚柔系统能够当作带一个或多个悬臂梁的中心刚体作平面转动，被控刚柔系统的动力学方程为：As shown in Figure 1, the controlled rigid-flexible system includes a central rigid body and flexible accessories. The flexible accessory includes one or more cantilever beams. The controlled rigid-flexible system can be regarded as a central rigid body with one or more cantilever beams. For plane rotation, the dynamic equation of the controlled rigid-flexible system is:

式(1)为姿态动力学方程，式(2)为悬臂梁弯曲振动方程，式(3)为边界条件，ρ,A,L,R分别为挠性悬臂梁的截面密度、截面积、长度、悬臂梁和中心刚体连接点相对刚体质心的距离，v为悬臂梁任意点处的弯曲位移，为弯曲位移的一阶导数，为弯曲位移的二阶导数，v_l,v_ll,v_lll分别为悬臂梁任意点处的弯曲位移v对悬臂梁上任意点未变形时相对悬臂梁和中心刚体连接点的距离l的一阶、二阶和三阶偏导数，θ，分别为中心刚体的姿态角、中心刚体的姿态角速度和中心刚体的姿态角加速度，t表示系统时间，T_c，T_d分别为作用在中心刚体上的控制力矩和干扰力矩，J_r，分别为中心刚体和悬臂梁相对系统姿态转轴的惯量，记总惯量为 Equation (1) is the attitude dynamics equation, Equation (2) is the bending vibration equation of the cantilever beam, Equation (3) is the boundary condition, ρ, A, L, R are the cross-sectional density, cross-sectional area, and length of the flexible cantilever beam, respectively , the distance between the connection point of the cantilever beam and the central rigid body relative to the center of mass of the rigid body, v is the bending displacement at any point of the cantilever beam, is the first derivative of the bending displacement, is the second order derivative of the bending displacement, v _l , v _ll , v _lll are the first order of the bending displacement v at any point of the cantilever beam to the distance l between the cantilever beam and the central rigid body connection point when any point on the cantilever beam is not deformed , second and third order partial derivatives, θ, are the attitude angle of the central rigid body, the attitude angular velocity of the central rigid body and the attitude angular acceleration of the central rigid body, t represents the system time, T _c , T _d are the control torque and disturbance torque acting on the central rigid body, J _r , are the inertia of the central rigid body and the cantilever beam relative to the rotation axis of the system attitude, and the total inertia is

(2)针对图1所示被控刚柔系统，构建如图2所示的姿态控制系统，包括敏感器、执行机构和控制器，敏感器包括姿态敏感器、陀螺和位移传感器，姿态敏感器、陀螺安装在中心刚体上，位移传感器安装在悬臂梁上；控制器安装在中心刚体上，用于实时解算刚柔系统所需的控制力矩；执行机构安装在中心刚体上，用于将控制器解算出的控制力矩作用到中心刚体上。(2) For the controlled rigid-flexible system shown in Figure 1, build the attitude control system shown in Figure 2, including sensors, actuators and controllers. The sensors include attitude sensors, gyroscopes and displacement sensors, attitude sensors , The gyroscope is installed on the central rigid body, the displacement sensor is installed on the cantilever beam; the controller is installed on the central rigid body, which is used to solve the control torque required by the rigid-flexible system in real time; the actuator is installed on the central rigid body, which is used to control The control moment calculated by the controller solution acts on the central rigid body.

(3)通过姿态敏感器测得中心刚体姿态角θ的测量值θ_m，通过陀螺测得中心刚体姿态角速度的测量值通过位移传感器测得悬臂梁前n阶模态的动态坐标q_i(t)(i＝1,2,…n)的测量值q_mi(t)(i＝1,2,…n)，n取小于等于4的非零正整数，对常规的卫星姿态控制系统来说，主要是一阶挠性模态的振动影响，因此n取1即可。(3) The measured value θ _m of the attitude angle θ of the central rigid body is measured by the attitude sensor, and the attitude angular velocity of the central rigid body is measured by the gyroscope measured value of The measurement value q _mi (t) (i=1,2,...n) of the dynamic coordinates q _i (t) (i=1,2,...n) of the first n order modes of the cantilever beam measured by the displacement sensor, n Taking a non-zero positive integer less than or equal to 4, for the conventional satellite attitude control system, it is mainly the vibration effect of the first-order flexible mode, so n takes 1.

(4)根据悬臂梁前n阶模态的动态坐标的测量值q_mi(t)(i＝1,2,…n)，计算出悬臂梁任意点的弯曲振动位移(0≤l≤L)，并对v_m(l,t)进行差分得到弯曲振动速度再对进行差分得到弯曲振动加速度 (4) Calculate the bending vibration displacement at any point of the cantilever beam according to the measured value q _mi (t) (i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam (0≤l≤L), and take the difference of v _m (l,t) to obtain the bending vibration velocity again Differentiate to obtain the bending vibration acceleration

式中，Φ_i(l)＝sin(β_il)-sh(β_il)-σ_i[cos(β_il)-ch(β_il)],In the formula, Φ _i (l)=sin(β _i l)-sh(β _i l)-σ _i [cos(β _i l)-ch(β _i l)],

σ_i＝(sinβ_iL+sinhβ_iL)/(cosβ_iL+coshβ_iL)，且β₁L≈1.8751，β₂L≈4.6941，β₃L≈7.8548，β₄L≈10.9955。σ _i =(sinβ _i L+sinhβ _i L)/(cosβ _i L+coshβ _i L), and β ₁ L≈1.8751, β ₂ L≈4.6941, β ₃ L≈7.8548, and β ₄ L≈10.9955.

根据所计算出的悬臂梁弯曲振动位移v_m(l,t)、弯曲振动速度v&_m(l,t)和弯曲振动加速度进行挠性振动前馈控制u_v，公式如下：According to the calculated cantilever beam bending vibration displacement v _m (l,t), bending vibration velocity v& _m (l,t) and bending vibration acceleration Perform flexible vibration feed-forward control u _v , the formula is as follows:

其中公式(4)根据理论计算的挠性振动对姿态运动的干扰力矩，并将挠性振动位移、振动速度和振动加速度用测量计算值进行替换。通过在姿态控制中引入前馈补偿力矩，实现了姿态控制对挠性振动的前馈补偿，降低了挠性振动对姿态运动的影响，使得在挠性振动时中心刚体仍具有较高的姿态稳定度。The formula (4) is based on the theoretical calculation of the interference torque of the flexural vibration on the attitude motion, and the flexural vibration displacement, vibration velocity and vibration acceleration are replaced by measured and calculated values. By introducing the feedforward compensation torque in the attitude control, the feedforward compensation of the attitude control to the flexible vibration is realized, and the influence of the flexible vibration on the attitude movement is reduced, so that the central rigid body still has a high attitude stability during the flexible vibration Spend.

(5)根据悬臂梁前n阶模态的动态坐标的测量值q_mi(t)(i＝1,2,…n)，对位移测量值进行差分得到速度的测量值(i＝1,2,…n)，计算出模态坐标反馈控制量u_q，公式如下：(5) According to the measured value q _mi (t)(t)(i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam, the measured value of the velocity is obtained by making a differential of the measured value of the displacement (i=1,2,…n), calculate the modal coordinate feedback control quantity u _q , the formula is as follows:

${u u}_{q q} = = {Σ Σ}_{i i = = 11}^{n no} [[{K K}_{q q i i} {q q}_{m m i i} ((t t)) + + {K K}_{\overset{\cdot &Center Dot;}{q q} i i} {\overset{\cdot &Center Dot;}{q q}}_{m m i i} ((t t))]] - - - - - - ((55))$

式中K_qi>0，对实际系统来说，由于模态振动的阻尼较小，使得挠性模态起振后，需要较长的时间才能衰减至零，这对于中心刚体的姿态控制来说是不利的，需要尽快使得挠性模态振动衰减，因此在中心刚体的姿态控制中引入模态坐标反馈控制，利用位移敏感器的测量得到的模态振动坐标及差分得到的速度，通过增大模态振动阻尼的方法，实现了挠性振动抑制，使得挠性模态振动能够迅速衰减至零，使得中心刚体也能够尽快稳定。where K _qi >0, For the actual system, due to the small damping of the modal vibration, it takes a long time to decay to zero after the flexible mode starts to vibrate, which is unfavorable for the attitude control of the central rigid body, and it is necessary to make the The flexible modal vibration is attenuated, so the modal coordinate feedback control is introduced in the attitude control of the central rigid body, and the modal vibration coordinates obtained by the measurement of the displacement sensor and the speed obtained by the difference are used to increase the modal vibration damping method. The flexible vibration suppression is realized, so that the flexible mode vibration can be quickly attenuated to zero, so that the central rigid body can also be stabilized as soon as possible.

θ_e＝θ_d-θ_m(6)θ _e = θ _d - θ _m (6)

${\overset{\cdot \cdot}{θ θ}}_{e e} = = {\overset{\cdot &Center Dot;}{θ θ}}_{d d} - - {\overset{\cdot &Center Dot;}{θ θ}}_{m m} - - - - - - ((77))$

姿态反馈控制律为：The attitude feedback control law is:

${u u}_{θ θ} = = J J \cdot &Center Dot; {K K}_{θ θ D D.} \cdot &Center Dot; [[{\overset{\cdot \cdot}{θ θ}}_{e e} + + {K K}_{θ θ P P} \cdot &Center Dot; {θ θ}_{e e}]] + + {K K}_{θ θ I I} \cdot &Center Dot; &Integral; &Integral; {θ θ}_{e e} {| |}_{| | \cdot &Center Dot; | | < < γ γ} \cdot &Center Dot; d d t t,, ((11 > > > > γ γ > > 00)) - - - - - - ((88))$

式中，K_θP、K_θI、K_θD为控制参数；控制参数K_θP、K_θI、K_θD根据姿态角误差θ_e和姿态角速度误差进行确定，其中 $K_{θ P} = \frac{| n_{\overset{\cdot}{θ}} |_{m a x} + K_{θ D}^{- 1} \cdot J^{- 1} | T_{d} |_{m a x}}{| n_{θ} |_{\max}}, K_{θ I} = λ_{i} [1 + s g n (θ_{e} \cdot {\overset{\cdot}{θ}}_{e})] | θ_{e} | .$ 式中，和1>λ_i>0，1>λ_d>0；10≤t₀≤100,可取t₀＝50。In the formula, K _θP , K _θI , K _θD are the control parameters; the control parameters K _θP , K _θI , K _θD are based on the attitude angle error θ _e and the attitude angle velocity error to determine, where $K_{θ P} = \frac{| {no}_{\overset{\cdot}{θ}} |_{m a x} + K_{θ D.}^{- 1} &Center Dot; J^{- 1} | T_{d} |_{m a x}}{| {no}_{θ} |_{\max}}, K_{θ I} = λ_{i} [1 + the s g no (θ_{e} &Center Dot; {\overset{&Center Dot;}{θ}}_{e})] | θ_{e} | .$ In the formula, and 1>λ _i >0, 1>λ _d >0; 10≤t ₀ ≤100, preferably t ₀ =50.

可见，本方法提出的控制器的结构与常规PID控制器虽然结构一致，但本发明方法所提出的控制器参数均根据系统的特性进行在线调节，为具有智能调节能力的姿态控制器。控制器参数随估计状态的变化而变化，其中对系统状态的变化取一段时间的监测值，如将t₀取50秒，即K_θD的取值与当前时刻往后50秒内的所有状态有关，使得控制器的参数设置能够响应系统状态的变化，并能保持较好的稳态性能指标。。It can be seen that although the structure of the controller proposed by this method is consistent with that of the conventional PID controller, the parameters of the controller proposed by the method of the present invention are all adjusted online according to the characteristics of the system, and it is an attitude controller with intelligent adjustment capabilities. The parameters of the controller change with the change of the estimated state, and the change of the system state is monitored for a period of time. For example, _t0 is taken as 50 seconds, that is, the value of K _θD is related to all states within 50 seconds after the current moment , so that the parameter setting of the controller can respond to the change of the system state, and can maintain a good steady-state performance index. .

T_c＝mlf(u_θ+u_v+u_q,T_max)(9)T _c ＝mlf(u _θ +u _v +u _q ,T _max )(9)

式中T_max为设定的实际系统控制力矩幅值的上限，其中T_max>0，mlf(第1个参数，第2个参数)为双参数限幅函数，即当第1个参数的绝对值超过第2个参数时，限幅函数在保持第1个参数的符号的前提下，综合的控制力矩T_c大小就取第2个参数T_max，否则综合控制力矩T_c大小直接取第1个参数；In the formula, T _max is the upper limit of the set actual system control torque amplitude, where T _max >0, mlf (the first parameter, the second parameter) is a two-parameter limiting function, that is, when the absolute value of the first parameter When the value exceeds the second parameter, under the premise of keeping the sign of the first parameter, the limit function will take the second parameter T _max for the comprehensive control torque T _c , otherwise the comprehensive control torque T _c will directly take the first parameter parameters;

所述步骤(6)中基于本发明所设计的姿态反馈控制器对小卫星、一般应用卫星、大型应用平台以及类似哈勃的大型航天器等刚柔系统进行了仿真对比，结果如表1所示。可见，采用本发明方法时的姿态控制精度及姿态控制稳定度均小于常规PID控制方法，其中姿态控制稳定度中本发明方法结果较常规PID控制方法提高了3～5倍，姿态控制精度提高了30％～80％。对具体应用如卫星姿态控制来说，采用本发明方法较常规PID控制方法能够实现更高的控制精度，使得卫星具有更好的性能。In the described step (6), based on the attitude feedback controller designed by the present invention, the rigid-flexible systems such as small satellites, general application satellites, large-scale application platforms, and large spacecraft similar to Hubble have been simulated and compared, and the results are shown in Table 1. Show. Visible, when adopting the method of the present invention, attitude control precision and attitude control stability are all less than conventional PID control method, wherein in attitude control stability, the result of the method of the present invention has improved 3～5 times compared with conventional PID control method, and attitude control precision has improved 30% to 80%. For specific applications such as satellite attitude control, the method of the invention can achieve higher control precision than the conventional PID control method, so that the satellite has better performance.

表1本控制器与常规PID控制结果比较Table 1 Comparison between this controller and conventional PID control results

如图3、图4所示为采用常规PID控制方法和采用本发明姿态控制方法时的振动抑制对比曲线，其中图3采用常规PID控制方法，未引入振动反馈补偿，可见挠性振动虽然逐渐衰减，但收敛速度较慢。图4采用了本发明姿态控制方法，对振动进行反馈控制，使得振动衰减所用的时间大大减少。As shown in Fig. 3 and Fig. 4, the comparison curves of vibration suppression when adopting the conventional PID control method and the attitude control method of the present invention are used, wherein Fig. 3 adopts the conventional PID control method without introducing vibration feedback compensation, and it can be seen that although the flexible vibration is gradually attenuated , but the convergence rate is slow. Fig. 4 adopts the attitude control method of the present invention to perform feedback control on the vibration, so that the time used for vibration attenuation is greatly reduced.

本发明说明书中未作详细描述的内容属本领域技术人员的公知技术。The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A rigid-flexible system attitude control method based on vibration compensation and state feedback, characterized in that the steps are as follows:

(1) The controlled rigid-flexible system includes a central rigid body and a flexible attachment, and the flexible appendage includes one or more cantilever beams. The controlled rigid-flexible system can be regarded as a central rigid body with one or more cantilever beams for plane rotation, The dynamic equation of the controlled rigid-flexible system is:

[[{J J}_{r r} + + ρ ρ A A L L (({R R}^{22} + + R R L L + + \frac{11}{33} {L L}^{22}))]] \overset{\cdot\cdot \cdot\cdot}{θ θ} + + 22 ρ ρ A A {&Integral; &Integral;}_{00}^{L L} v v \overset{\cdot &Center Dot;}{v v} d d l l + + ρ ρ A A {&Integral; &Integral;}_{00}^{L L} ((R R + + l l)) \overset{\cdot\cdot \cdot\cdot}{v v} d d l l = = {T T}_{c c} + + {T T}_{d d} - - - - - - ((11))

ρ ρ A A \overset{\cdot\cdot \cdot\cdot}{v v} + + {EIv EIv}_{l l l l l l l l} + + ρ ρ A A ((R R + + l l)) \overset{\cdot\cdot \cdot\cdot}{θ θ} = = ρ ρ A A {\overset{\cdot &Center Dot;}{θ θ}}^{22} v v - - - - - - ((22))

v(0,t)=v _l (0,t)=v _ll (L,t)=v _lll (L,t)=0(3)

Equation (1) is the attitude dynamics equation, Equation (2) is the bending vibration equation of the cantilever beam, Equation (3) is the boundary condition, ρ, A, L, R are the cross-sectional density, cross-sectional area, and length of the flexible cantilever beam, respectively , the distance between the connection point of the cantilever beam and the central rigid body relative to the center of mass of the rigid body, v is the bending displacement at any point of the cantilever beam, is the first derivative of the bending displacement, is the second order derivative of the bending displacement, v _l , v _ll , v _lll are respectively the first order of the bending displacement v at any point on the cantilever beam to the distance l between the cantilever beam and the central rigid body connection point when any point on the cantilever beam is not deformed , second and third order partial derivatives, θ, are the attitude angle of the central rigid body, the attitude angular velocity of the central rigid body and the attitude angular acceleration of the central rigid body, t represents the system time, T _c , T _d are the control torque and disturbance torque acting on the central rigid body, J _r , are the inertia of the central rigid body and the cantilever beam relative to the rotation axis of the system attitude, and the total inertia is

(2) For the controlled rigid-flexible system described in step (1), build an attitude control system, including sensors, actuators and controllers. The sensors include attitude sensors, gyroscopes and displacement sensors. On the central rigid body, the displacement sensor is installed on the cantilever beam; the controller is installed on the central rigid body to calculate the control torque required by the rigid-flexible system in real time; the actuator is installed on the central rigid body to solve the controller The control torque of is applied to the central rigid body.

(3) Use the sensor described in step (2) to measure the controlled rigid-flexible system described in step (1), that is, measure the measured value θ _m of the attitude angle θ of the central rigid body through the attitude sensor, and use the gyroscope to measure Get the attitude angular velocity of the central rigid body measured value of The measurement value q _mi (t) (i=1,2,...n) of the dynamic coordinates q _i (t) (i=1,2,...n) of the first n order modes of the cantilever beam measured by the displacement sensor, n Take a non-zero positive integer less than or equal to 4;

(4) Calculate the bending vibration displacement at any point of the cantilever beam according to the measured value q _mi (t) (i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam obtained in step (3) (0≤l≤L), and take the difference of v _m (l,t) to obtain the bending vibration velocity again Differentiate to obtain the bending vibration acceleration

In the formula,

Φ _i (l)=sin(β _i l)-sh(β _i l)-σ _i [cos(β _i l)-ch(β _i l)],σ _i =(sinβ _i L+sinhβ _i L) /(cosβ _i L+coshβ _i L),

And β ₁ L ≈ 1.8751, β ₂ L ≈ 4.6941, β ₃ L ≈ 7.8548, and β ₄ L ≈ 10.9955.

According to the calculated cantilever beam bending vibration displacement v _m (l,t), bending vibration velocity and bending vibration acceleration Perform flexible vibration feed-forward control u _v , the formula is as follows:

{u u}_{v v} = = 22 ρ ρ A A {&Integral; &Integral;}_{00}^{L L} {v v}_{m m} ((l l,, t t)) {\overset{\cdot \cdot}{v v}}_{m m} ((l l,, t t)) d d l l + + ρ ρ A A {&Integral; &Integral;}_{00}^{L L} ((R R + + l l)) {\overset{\cdot\cdot \cdot\cdot}{v v}}_{m m} ((l l,, t t)) d d l l - - - - - - ((44))

(5) According to the measured value q _mi (t) (i=1,2,...n) of the dynamic coordinates of the first n-order modes of the cantilever beam obtained in step (3), the measured value of the velocity is obtained by making a difference to the measured value of the displacement Calculate the modal coordinate feedback control quantity u _q , the formula is as follows:

{u u}_{q q} = = {Σ Σ}_{i i = = 11}^{n no} [[{K K}_{q q i i} {q q}_{m m i i} ((t t)) + + {K K}_{\overset{\cdot \cdot}{q q} i i} {\overset{\cdot \cdot}{q q}}_{m m i i} ((t t))]] - - - - - - ((55))

In the formula

K_{q i} > 0, K_{\overset{\cdot}{q} i} > 5 K_{q i}

(6) Attitude angle θ and attitude angular velocity of the central rigid body acquired according to step (4) The measured value of θ _m and Get the attitude angle error θ _e and attitude angle velocity error of attitude feedback control They are:

θ _e = θ _d - θ _m (6)

{\overset{\cdot \cdot}{θ θ}}_{e e} = = {\overset{\cdot &Center Dot;}{θ θ}}_{d d} - - {\overset{\cdot &Center Dot;}{θ θ}}_{m m} - - - - - - ((77))

where θ _d and They are command input of attitude angle and attitude angular velocity respectively;

The attitude feedback control law is:

\begin{matrix} {u u}_{θ θ} = = J J \cdot \cdot {K K}_{θ θ D D.} \cdot &Center Dot; [[{\overset{\cdot &Center Dot;}{θ θ}}_{e e} + + {K K}_{θ θ P P} \cdot &Center Dot; {θ θ}_{e e}]] + + {K K}_{θ θ I I} \cdot &Center Dot; &Integral; &Integral; {θ θ}_{e e} {| |}_{| | \cdot &Center Dot; | | < < γ γ} \cdot &Center Dot; d d t t & ((0.1 0.1 > > γ γ > > 00)) \end{matrix} - - - - - - ((88))

In the formula, K _θP , K _θI , K _θD are control parameters;

(7) Add the flexible vibration feedforward control torque u _v calculated in step (4), the modal coordinate feedback control torque u _q calculated in step (5), and the attitude feedback control torque u _θ calculated in step (6) , and perform clipping to obtain the comprehensive control torque T _c :

T _c ＝mlf(u _θ +u _v +u _q ,T _max )(9)

In the formula, T _max is the upper limit of the set actual system control torque amplitude, T _max >0, mlf (the first parameter, the second parameter) is a two-parameter limiting function, that is, when the absolute value of the first parameter When it is greater than or equal to the second parameter, under the premise of keeping the sign of the first parameter, the limit function takes the second parameter T _max for the comprehensive control torque T _c . When the absolute value of the first parameter is less than the second When there are two parameters, the size of the comprehensive control torque T _c directly takes the first parameter;

(8) Output the final control torque T _c calculated in step (7) to the execution structure, and act on the system described in step (1), to complete the attitude control of the rigid-flexible system.

2. A kind of rigid-flexible system attitude control method based on vibration compensation and state feedback according to claim 1, characterized in that: in the step (6), the control parameters K _θP , K _θI , K _θD are based on the attitude angle error θ _e and attitude angular velocity error to determine that

K_{θ P} = \frac{| {no}_{\overset{&Center Dot;}{θ}} |_{m a x} + K_{θ D.}^{- 1} \cdot J^{- 1} | T_{d} |_{m a x}}{| θ |_{\max}}, K_{θ I} = λ_{i} [1 + sgn (θ_{e} \cdot {\overset{\cdot}{θ}}_{e})] | θ_{e} |,

In the formula, and |n _θ | _max are the maximum values of the angular velocity and angle measurement noise set according to the performance of the sensor, respectively, The value of 1×10 ^-5 ～1×10 ^-2° /s and the range of |n _θ | _max is 1×10 ^-4 ～0.1°, 1>λ _i >0, 1>λ _d > 0, 10 ≤ t ₀ ≤ 100.