CN115509117A - Flexible joint movement speed tracking system for large-space inertia variable load - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及到空间机器人领域,特别是一种面向空间大惯量变负载的柔性关节运动速度跟踪系统。The invention relates to the field of space robots, in particular to a flexible joint motion speed tracking system for large space inertia variable loads.
背景技术Background technique
负载惯量是关节等空间机构的转动惯量施加到电机轴上产生的负载特性,表现为加减速过程中的惯性力,负载惯量对运动控制系统的控制精度、稳定性、动态响应有很大的影响。在电机设计时,需合理设计负载惯量比,以避免出现运动震荡等情况。Load inertia is the load characteristic generated by the moment of inertia of space mechanisms such as joints applied to the motor shaft, which is manifested as inertial force during acceleration and deceleration. Load inertia has a great influence on the control accuracy, stability and dynamic response of the motion control system . When designing the motor, it is necessary to design the load inertia ratio reasonably to avoid situations such as motion shock.
相比于地面重力环境,空间的微重力环境使负载惯量特性成为空间机构运动性能的主要影响因素。考虑空间应用成本和重量需求,在进行关节和电机设计时,负载惯量比通常会大幅超出地面机构的取值范围,这导致空间机构运动过程特别是加减速过程中,产生较大的震荡。同时,以空间机械臂为代表的空间多体系统在运动时其负载惯量时刻变化,且由于关节柔性和非线性因素的存在,极大的增加了空间大惯量变负载关节运动控制的难度。对于机器人柔性关节的控制方法主要包含传统的PD控制及奇异摄动、级联系统、智能控制等方法。其中,PD控制虽简单,但往往不能满足控制精度需求;其它方法由于需要解决机器人参数不确定引起的控制性能下降问题,还需要结合自适应控制或鲁棒控制来实现,导致许多控制方法实现过程相当复杂,并且目前大多尚处于理论研究或仿真阶段,在工程应用较少。Compared with the gravity environment on the ground, the microgravity environment of space makes the load inertia characteristics the main influencing factor of the motion performance of space mechanisms. Considering the cost and weight requirements of space applications, when designing joints and motors, the load inertia ratio usually exceeds the value range of the ground mechanism by a large margin, which leads to large vibrations during the movement of the space mechanism, especially during acceleration and deceleration. At the same time, the load inertia of the space multi-body system represented by the space manipulator changes all the time during motion, and due to the existence of joint flexibility and nonlinear factors, it greatly increases the difficulty of joint motion control with large space inertia and variable load. The control methods for robot flexible joints mainly include traditional PD control and singular perturbation, cascade system, intelligent control and other methods. Among them, although PD control is simple, it often cannot meet the control accuracy requirements; other methods need to solve the problem of control performance degradation caused by uncertain robot parameters, and need to be implemented in combination with adaptive control or robust control, resulting in many control methods. It is quite complicated, and most of them are still in the stage of theoretical research or simulation, and there are few engineering applications.
发明内容Contents of the invention
本发明解决的技术问题是:克服现有技术的不足,提供了一种适用于柔性关节大惯量、变负载的柔性关节运动速度跟踪系统,满足空间柔性关节的运动平稳性和到位精度的需求。The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to provide a flexible joint movement speed tracking system suitable for flexible joints with large inertia and variable loads, and to meet the needs of space flexible joints for motion stability and in-position accuracy.
本发明的技术解决方案是:Technical solution of the present invention is:
一种面向空间大惯量变负载的柔性关节运动速度跟踪系统,包括:关节位置检测单元、位置环控制器、速度环控制器、电流环控制器和电机驱动模块;A flexible joint motion speed tracking system for large space inertia variable loads, including: a joint position detection unit, a position loop controller, a speed loop controller, a current loop controller and a motor drive module;
位置环控制器:根据关节期望角度和关节位置检测单元采集到的实际关节角度,按位置环控制周期TP确定补偿速度Vconp(m)并传输给速度环控制器;Position loop controller: according to the joint expected angle and the actual joint angle collected by the joint position detection unit, the compensation speed V conp (m) is determined according to the position loop control period T P and transmitted to the speed loop controller;
速度环控制器:接收位置环控制器传输的补偿速度Vconp(m),接收输入的关节期望速度Vcmd(k),根据补偿速度Vconp(m)按速度环控制周期Tv对关节期望速度Vcmd(k)进行补偿,获得补偿后的期望速度VcmdIn(k);根据补偿后的期望速度VcmdIn(k)和电机驱动模块反馈的电机实际角速度Vm(k),确定输出期望电流iQcmd(k)并传输给电流环控制器;Speed loop controller: Receive the compensation speed V conp (m) transmitted by the position loop controller, receive the input joint expected speed V cmd (k), and control the joint expectation according to the speed loop control cycle T v according to the compensation speed V conp (m) The velocity V cmd (k) is compensated to obtain the compensated expected velocity V cmdIn (k); according to the compensated expected velocity V cmdIn (k) and the motor actual angular velocity V m (k) fed back by the motor drive module, the output expectation is determined The current i Qcmd (k) is transmitted to the current loop controller;
电流环控制器:接收速度环控制器传输的输出期望电流iQcmd(k),接收电机驱动模块反馈的电机输出电压对应的实际电流iQ(k),根据输出期望电流iQcmd(k)和实际电流iQ(k)调整输出给电机驱动模块的驱动电压,使实际电流iQ(k)持续对输出期望电流iQcmd(k)进行跟踪;Current loop controller: Receive the output expected current i Qcmd (k) transmitted by the speed loop controller, and receive the actual current i Q (k) corresponding to the motor output voltage fed back by the motor drive module, according to the output expected current i Qcmd (k) and The actual current i Q (k) adjusts the driving voltage output to the motor drive module, so that the actual current i Q (k) continues to track the output expected current i Qcmd (k);
电机驱动模块:接收电流环控制器输出的驱动电压,根据驱动电压驱动电机带动关节传动机构转动;反馈电机实际角速度Vm(k)给速度环控制器;反馈电机输出电压对应的实际电流iQ(k)给电流环控制器。Motor drive module: receives the drive voltage output by the current loop controller, drives the motor to drive the joint transmission mechanism to rotate according to the drive voltage; feeds back the actual angular velocity V m (k) of the motor to the speed loop controller; feeds back the actual current i Q corresponding to the output voltage of the motor (k) to the current loop controller.
优选地,位置环控制器确定补偿速度Vconp(m),具体为:Preferably, the position loop controller determines the compensation speed V conp (m), specifically:
根据当前第m个位置环控制周期的关节期望角度θcmd(m)和实际关节角度θj(m),确定当前第m个位置环控制周期的角度误差θerr(m);According to the expected joint angle θ cmd (m) and the actual joint angle θ j (m) of the current m-th position loop control cycle, determine the angle error θ err (m) of the current m-th position loop control cycle;
根据当前第m个位置环控制周期的实际关节角度θj(m)和第m-1个位置环控制周期的实际关节角度θj(m-1),确定当前第m个位置环控制周期的关节实际角度的微分值 According to the actual joint angle θ j (m) of the current m-th position loop control cycle and the actual joint angle θ j (m-1) of the m-1th position loop control cycle, determine the current m-th position loop control cycle Differential value of joint actual angle
根据所述角度误差θerr(m)和所述关节实际角度的微分值确定补偿速度Vconp(m)。According to the differential value of the angle error θ err (m) and the actual angle of the joint Determine the compensation speed V conp (m).
优选地,位置环控制器确定当前第m个位置环控制周期的角度误差θerr(m),具体为:Preferably, the position loop controller determines the angle error θ err (m) of the current mth position loop control cycle, specifically:
θerr(m)=θcmd(m)-θj(m)。θ err (m) = θ cmd (m) - θ j (m).
优选地,位置环控制器确定当前第m个位置环控制周期的关节实际角度的微分值具体为:Preferably, the position loop controller determines the differential value of the actual joint angle of the current mth position loop control cycle Specifically:
优选地,位置环控制器确定补偿速度Vconp(m),具体为:Preferably, the position loop controller determines the compensation speed V conp (m), specifically:
其中,KP-P为位置环控制器比例系数,KP-D为位置环控制器微分系数。Among them, K PP is the proportional coefficient of the position loop controller, and K PD is the differential coefficient of the position loop controller.
优选地,速度环控制器对关节期望速度Vcmd(k)进行补偿,获得补偿后的期望速度VcmdIn(k),具体为:Preferably, the velocity loop controller compensates the expected joint velocity V cmd (k) to obtain the compensated expected velocity V cmdIn (k), specifically:
VcmdIn(k)=Vcmd(k)+Vconp(m)V cmdIn (k) = V cmd (k) + V conp (m)
其中,在位置环控制周期TP与速度环控制周期Tv的比值Q为1时,m=k;Among them, when the ratio Q of the position loop control period T P to the speed loop control period T v is 1, m=k;
在Q为大于1的正整数时:When Q is a positive integer greater than 1:
其中,n为正整数。Wherein, n is a positive integer.
优选地,速度环控制器根据补偿后的期望速度VcmdIn(k)和电机实际角速度Vm(k),确定输出期望电流iQcmd(k),具体为:Preferably, the speed loop controller determines the output expected current i Qcmd (k) according to the compensated expected speed V cmdIn (k) and the actual angular velocity V m (k) of the motor, specifically:
速度环控制器根据获得的补偿后的期望速度VcmdIn(k)和电机实际角速度Vm(k),获得经抑制后的电机角速度误差Vm_errPF、速度误差积分值Vm_errI(k)、电机角速度微分值Vm_D(k),以及电机速度阻尼Vm_F(k);The speed loop controller obtains the suppressed motor angular velocity error V m_errPF , speed error integral value V m_errI ( k ), motor angular velocity Differential value V m_D (k), and motor speed damping V m_F (k);
速度环控制器根据获得的经抑制后的电机角速度误差Vm_errPF、速度误差积分值Vm_errI(k)、电机角速度微分值Vm_D(k)和电机速度阻尼Vm_F(k),确定输出期望电流iQcmd(k)。The speed loop controller determines the expected output current according to the obtained suppressed motor angular speed error V m_errPF , speed error integral value V m_errI (k), motor angular speed differential value V m_D (k) and motor speed damping V m_F (k) i Qcmd (k).
优选地,速度环控制器获得经抑制后的电机角速度误差Vm_errPF具体如下:Preferably, the velocity loop controller obtains the suppressed angular velocity error V m_errPF of the motor as follows:
Vm_err(k)=Vm_cmd(k)-Vm(k)V m_err (k) = V m_cmd (k) - V m (k)
Vm_cmd(k)=VcmdIn(k)×NV m_cmd (k) = V cmdIn (k) × N
其中,TPf为震荡抑制系数,TPf小于1,N为关节传动比;Among them, T Pf is the shock suppression coefficient, T Pf is less than 1, and N is the joint transmission ratio;
速度环控制器获得速度误差积分值Vm_errI(k)具体如下:The speed loop controller obtains the speed error integral value V m_errI (k) specifically as follows:
优选地,速度环控制器获得电机角速度微分值Vm_D(k)具体如下:Preferably, the speed loop controller obtains the motor angular velocity differential value V m_D (k) specifically as follows:
Vm_err(k)=Vm_cmd(k)-Vm(k)V m_err (k) = V m_cmd (k) - V m (k)
Vm_cmd(k)=VcmdIn(k)×N。V m_cmd (k)=V cmdIn (k)×N.
其中,N为关节传动比;Among them, N is the joint transmission ratio;
速度环控制器获得所述电机速度阻尼Vm_F(k)具体如下:The speed loop controller obtains the motor speed damping V m_F (k) specifically as follows:
Vm_F(k)=KV-F×Vm(k)V m_F (k) = K VF × V m (k)
其中,KV-F为速度环控制器阻尼系数。Among them, K VF is the damping coefficient of the speed loop controller.
优选地,速度环控制器确定输出期望电流iQcmd(k),具体为:Preferably, the speed loop controller determines the desired output current i Qcmd (k), specifically:
iQcmd(k)=KV-P×Vm_errPF(k)+KV-I×Vm_errI(k)+KV-D×Vm_D(k)-Vm_F(k)i Qcmd (k)=K VP ×V m_errPF (k)+K VI ×V m_errI (k)+K VD ×V m_D (k)-V m_F (k)
其中,KV-P为速度环控制器比例系数,KV-I为速度环控制器积分系数,KV-D为速度环控制器微分系数。Among them, K VP is the proportional coefficient of the speed loop controller, K VI is the integral coefficient of the speed loop controller, and K VD is the differential coefficient of the speed loop controller.
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:
本发明可以在空间大负载惯量、变负载的情况下,实现对关节等柔性机构速度稳定控制和运动精度控制,可以有效抑制关节启动和停止时的速度震荡,适应负载惯量大范围的变化。The present invention can realize speed stability control and motion precision control of flexible mechanisms such as joints under the condition of large space load inertia and variable load, can effectively suppress the speed oscillation when joints start and stop, and adapt to large-scale changes in load inertia.
附图说明Description of drawings
图1面向大惯量变负载柔性关节运动控制系统架构;Fig. 1 Architecture of flexible joint motion control system for large inertia variable load;
图2空间柔性关节速度控制框图。Fig. 2 Block diagram of space flexible joint velocity control.
具体实施方式detailed description
本发明一种面向空间大惯量变负载的柔性关节运动速度跟踪系统,利用PID控制器的基本原理,根据空间柔性关节运动控制的特点,提出如图1所示的运动控制架构,将位置环控制器的输出以补偿形式与期望速度求和,作为速度环的输入信息;在速度闭环比例项中引入高频震荡抑制传函;在速度闭环中增加负反馈阻尼控制。本发明提出如图2所示的速度控制方法,将柔性关节的期望速度转换为电机期望速度,与电机实际速度做差后,分别输入速度环比例控制、速度环积分控制、速度环微分控制,其中速度环比例控制设计了高频震荡抑制传函。设计速度环阻尼环节,通过引入电机实际速度实现速度负反馈。将所有控制环节求和(差)后输出期望电流进行电流控制。本发明可以应用到具备大惯量、变负载特性的空间柔性关节的运动控制中。The present invention is a flexible joint motion speed tracking system oriented to space large inertia variable load, using the basic principle of PID controller, according to the characteristics of space flexible joint motion control, a motion control architecture as shown in Figure 1 is proposed, the position loop control The output of the controller is summed with the expected speed in the form of compensation, which is used as the input information of the speed loop; the high-frequency oscillation suppression transfer function is introduced in the proportional item of the speed closed loop; the negative feedback damping control is added in the speed closed loop. The present invention proposes a speed control method as shown in Figure 2, which converts the expected speed of the flexible joint into the expected speed of the motor, and after making a difference with the actual speed of the motor, input the speed loop proportional control, speed loop integral control, and speed loop differential control respectively, Among them, the proportional control of the speed loop is designed with a high-frequency oscillation suppression transfer letter. The speed loop damping link is designed, and the speed negative feedback is realized by introducing the actual speed of the motor. After summing (difference) all the control links, the desired current is output for current control. The invention can be applied to the motion control of space flexible joints with large inertia and variable load characteristics.
负载惯量是关节等机构的转动惯量施加到电机轴上产生的负载特性。在地面,采用谐波、行星等减速器的关节,其负载惯量与电机的惯量比值通常小于10。在空间应用时,考虑空间微重力环境,关节的负载惯量与电机的惯量比值会达到10000甚至更高,且以机器人为代表的多体系统,关节的负载惯量随构型的变化持续变化。The load inertia is the load characteristic caused by the moment of inertia of the joint and other mechanisms applied to the motor shaft. On the ground, the ratio of load inertia to motor inertia is usually less than 10 for joints that use harmonic and planetary reducers. In space applications, considering the space microgravity environment, the ratio of the load inertia of the joint to the inertia of the motor will reach 10,000 or even higher, and in the multi-body system represented by the robot, the load inertia of the joint changes continuously with the change of the configuration.
本发明根据空间柔性关节大惯量、变负载运动控制的需求,按速度环控制周期Tv对关节期望速度Vcmd(k)进行补偿,获得补偿后的期望速度VcmdIn(k),描述为:According to the requirements of large inertia of space flexible joints and variable load motion control, the present invention compensates the joint expected speed V cmd (k) according to the speed loop control cycle T v , and obtains the compensated expected speed V cmdIn (k), which is described as:
VcmdIn(k)=Vcmd(k)+Vconp(m)V cmdIn (k) = V cmd (k) + V conp (m)
其中,Vcmd(k)为关节期望速度,Vconp(m)为由位置环控制器计算得出的补偿速度。位置环控制器的控制周期TP应不小于速度环控制器的控制周期Tv,且TP为Tv的Q倍,Q为正整数。在位置环控制周期TP与速度环控制周期Tv的比值Q为1时,m=k;Among them, V cmd (k) is the expected joint speed, and V conp (m) is the compensation speed calculated by the position loop controller. The control cycle T P of the position loop controller should not be less than the control cycle T v of the speed loop controller, and T P is Q times of T v , and Q is a positive integer. When the ratio Q of the position loop control period T P to the speed loop control period T v is 1, m=k;
在Q为大于1的正整数时:When Q is a positive integer greater than 1:
其中,n为正整数。Wherein, n is a positive integer.
第m个位置环控制周期的位置环控制器描述为:The position loop controller of the mth position loop control period is described as:
KP-P为位置环控制器比例系数,KP-D为位置环控制器微分系数,两个系数需要进行调试,初值可设置为1和0,然后进行调试,调试中获取位置环的响应曲线,并根据响应情况调整两个系数,直到满足响应时间、稳定时间、稳定裕度等指标要求。K PP is the proportional coefficient of the position loop controller, K PD is the differential coefficient of the position loop controller, the two coefficients need to be debugged, the initial value can be set to 1 and 0, and then debug, the response curve of the position loop is obtained during debugging, and Adjust the two coefficients according to the response until the requirements of the response time, stabilization time, stability margin and other indicators are met.
θerr(m)为角度误差,θerr(m)=θcmd(m)-θj(m),θcmd(m)为关节期望角度,θj(m)为关节位置检测单元采集到的实际关节角度。θ err (m) is the angle error, θ err (m) = θ cmd (m) - θ j (m), θ cmd (m) is the expected joint angle, θ j (m) is the joint position detection unit collected Actual joint angle.
为关节实际角度的微分,表示为: is the differential of the actual joint angle, expressed as:
按图2所示的速度控制方法,将补偿后的期望速度VcmdIn(k)转换为电机期望速度Vm_cmd(k),与电机实际速度做差后,获得电机角速度误差Vm_err(k)分别输入速度环比例控制、速度环积分控制、速度环微分控制。According to the speed control method shown in Figure 2, the compensated expected speed V cmdIn (k) is converted into the motor expected speed V m_cmd (k), and after making a difference with the actual speed of the motor, the motor angular speed error V m_err (k) is obtained respectively Input speed loop proportional control, speed loop integral control, speed loop differential control.
将输入的期望速度转换为电机期望速度:Convert the desired speed of the input to the desired speed of the motor:
Vm_cmd(k)=VcmdIn(k)×NV m_cmd (k) = V cmdIn (k) × N
N为关节传动比。N is the joint transmission ratio.
电机期望角速度Vm_cmd(k)与电机实际角速度Vm(k)求差,得到电机角速度误差Vm_err(k):Calculate the difference between the expected angular velocity V m_cmd (k) of the motor and the actual angular velocity V m (k) of the motor to obtain the angular velocity error V m_err (k) of the motor:
Vm_err(k)=Vm_cmd(k)-Vm(k)V m_err (k) = V m_cmd (k) - V m (k)
速度环比例控制包含高频震荡抑制传函和速度环比例环节。其中,高频震荡抑制传函可有效抑制启动时的震荡特性,经抑制后的电机角速度误差Vm_errPF为:Speed loop proportional control includes high-frequency oscillation suppression transfer letter and speed loop proportional link. Among them, the high-frequency oscillation suppression transfer letter can effectively suppress the oscillation characteristics at startup, and the motor angular velocity error V m_errPF after suppression is:
TPf为震荡抑制系数,TPf小于1。T Pf is the shock suppression coefficient, and T Pf is less than 1.
速度误差积分Vm_errI(k)表示为:The speed error integral V m_errI (k) is expressed as:
速度环微分项对电机角速度误差进行微分,电机角速度微分Vm_D(k)表示为:The speed loop differential item differentiates the motor angular velocity error, and the motor angular velocity differential V m_D (k) is expressed as:
Tv为速度环控制周期。T v is the control period of the speed loop.
阻尼环节可调整控制系统的阻尼特性,电机速度阻尼Vm_F(k)描述为:The damping link can adjust the damping characteristics of the control system, and the motor speed damping V m_F (k) is described as:
Vm_F(k)=KV-F×Vm(k)V m_F (k) = K VF × V m (k)
其中,Vm(k)为电机实际角速度,为电机驱动模块反馈的实测值,KV-F为速度环控制器阻尼系数,其取值需进行调试,可设初值为1,获取柔性关节运动速度跟踪系统在不同负载条件下的稳定裕度,并根据稳定裕度进行参数迭代调试,直到获得满足指标需求的稳定裕度。Among them, V m (k) is the actual angular velocity of the motor, which is the measured value fed back by the motor drive module, K VF is the damping coefficient of the speed loop controller, and its value needs to be adjusted. The initial value can be set to 1 to obtain the motion speed of the flexible joint Track the stability margin of the system under different load conditions, and perform parameter iterative debugging according to the stability margin until the stability margin that meets the index requirements is obtained.
将所有控制环节整合得到速度环控制器的输出期望电流iQcmd(k)为:Integrating all the control links, the output expected current i Qcmd (k) of the speed loop controller is:
iQcmd(k)=KV-P×Vm_errPF(k)+KV-I×Vm_errI(k)+KV-D×Vm_D(k)-Vm_F(k)i Qcmd (k)=K VP ×V m_errPF (k)+K VI ×V m_errI (k)+K VD ×V m_D (k)-V m_F (k)
其中,KV-P为速度环控制器比例系数,KV-I为速度环控制器积分系数,KV-D为速度环控制器微分系数,三个系数需要同步调试,可设置初值为1,0,0,获取柔性关节运动速度跟踪系统的响应时间、超调量、稳定裕度等参数,并据此进行三个系数的迭代调试,直到获得满足指标需求的参数。Among them, K VP is the proportional coefficient of the speed loop controller, K VI is the integral coefficient of the speed loop controller, K VD is the differential coefficient of the speed loop controller, the three coefficients need to be debugged synchronously, and the initial value can be set to 1, 0, 0, The response time, overshoot, stability margin and other parameters of the flexible joint motion speed tracking system are obtained, and the iterative debugging of the three coefficients is carried out accordingly, until the parameters that meet the index requirements are obtained.
电流环控制器:接收速度环控制器传输的输出期望电流iQcmd(k),接收电机驱动模块反馈的电机输出电压对应的实际电流iQ(k),根据输出期望电流iQcmd(k)和实际电流iQ(k)调整输出给电机驱动模块的驱动电压,使实际电流iQ(k)持续对输出期望电流iQcmd(k)进行跟踪。图1中UD为直轴电压、UQ为交轴电压。Current loop controller: Receive the output expected current i Qcmd (k) transmitted by the speed loop controller, and receive the actual current i Q (k) corresponding to the motor output voltage fed back by the motor drive module, according to the output expected current i Qcmd (k) and The actual current i Q (k) adjusts the driving voltage output to the motor drive module, so that the actual current i Q (k) continuously tracks the output expected current i Qcmd (k). U D in Fig. 1 is the direct axis voltage, U Q is the quadrature axis voltage.
本发明使用速度环控制器的输出期望电流,可采用不同的电机驱动方法实现对电机的驱动,从而实现对关节进行运动控制效果,以达到对关节期望位置或期望速度跟踪的效果。The present invention uses the output expected current of the speed loop controller, and different motor driving methods can be used to drive the motor, so as to achieve the effect of motion control on the joints, so as to achieve the effect of tracking the expected positions or speeds of the joints.
电机驱动模块:接收电流环控制器输出的驱动电压,根据驱动电压驱动电机带动关节传动机构转动;反馈电机实际角速度Vm(k)给速度环控制器;反馈电机输出电压对应的实际电流iQ(k)给电流环控制器。Motor drive module: receives the drive voltage output by the current loop controller, drives the motor to drive the joint transmission mechanism to rotate according to the drive voltage; feeds back the actual angular velocity V m (k) of the motor to the speed loop controller; feeds back the actual current i Q corresponding to the output voltage of the motor (k) to the current loop controller.
本发明虽然已以较佳实施例公开如上,但其并不是用来限定本发明,任何本领域技术人员在不脱离本发明的精神和范围内,都可以利用上述揭示的方法和技术内容对本发明技术方案做出可能的变动和修改,因此,凡是未脱离本发明技术方案的内容,依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化及修饰,均属于本发明技术方案的保护范围。在不冲突的情况下,本申请实施例以及实施例中的技术特征可以相互组合。Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention, and any person skilled in the art can use the methods disclosed above and technical content to analyze the present invention without departing from the spirit and scope of the present invention. Possible changes and modifications are made in the technical solution. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention, which do not depart from the content of the technical solution of the present invention, all belong to the technical solution of the present invention. protected range. In the case of no conflict, the embodiments of the present application and the technical features in the embodiments may be combined with each other.
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.
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