WO2024093507A1 - 用于实现机械手系统轨迹跟踪的广义动态预测控制方法 - Google Patents

用于实现机械手系统轨迹跟踪的广义动态预测控制方法 Download PDF

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WO2024093507A1
WO2024093507A1 PCT/CN2023/116963 CN2023116963W WO2024093507A1 WO 2024093507 A1 WO2024093507 A1 WO 2024093507A1 CN 2023116963 W CN2023116963 W CN 2023116963W WO 2024093507 A1 WO2024093507 A1 WO 2024093507A1
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manipulator system
predictive control
manipulator
control method
generalized
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PCT/CN2023/116963
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French (fr)
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郝皓
刘环宇
何杨华
王文杰
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上海第二工业大学
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

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  • the present invention relates to the technical field of predictive control of manipulator systems, and in particular to a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system.
  • Manipulators are commonly used in various scenarios with high-precision requirements, such as high-end manufacturing, aviation or various surgical operations. They are composed of motion chains connected by various joints.
  • manipulators are increasingly valued by engineers to cooperate in completing higher-precision engineering tasks, in which physical interaction between people and objects is essential.
  • high-precision control and flexible movements of manipulator trajectories are widely concerned.
  • the many existing control schemes for manipulator trajectory adjustment can be summarized as follows: proportional integral differential control (PID), robust control, model predictive control, adaptive neural network control and sliding mode control, etc.
  • PID proportional integral differential control
  • robust control robust control
  • model predictive control adaptive neural network control
  • sliding mode control etc.
  • the model predictive controller has a strong control performance optimization capability by solving the performance function optimization equation in real time, and can realize the constraint control of the position or speed of the manipulator system.
  • it has high requirements for the model accuracy of the manipulator system, and its anti-interference ability is relatively weak.
  • the manipulator system will inevitably encounter interference from different external forces. Modeling mismatch or even long service life will cause perturbation of the system's internal parameters. If the controller design process does not consider the mismatch of the model signal, it will inevitably cause the loss of model predictive control accuracy and even cause the system to crash.
  • a tracking error-oriented parameter self-adjustment mechanism is used to optimize the controller parameter setting of the closed-loop system, thereby further adaptively adjusting the control performance of the system according to the intensity of the disturbance to the system.
  • a natural idea is: Is there a prediction period self-tuning function related to the tracking error, which can calculate the optimal prediction period value for the current working condition according to the change in the external force intensity of the manipulator, so as to achieve a balance between the adaptability and robustness of the controlled manipulator system.
  • the present invention needs to design a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system to solve the above-mentioned problems.
  • the purpose of the present invention is to provide a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system in order to solve the above problems, and solve the problem of robustness redundancy that may occur in the system mentioned in the background technology.
  • a tracking error-oriented parameter self-adjustment mechanism is used to optimize the controller parameter setting of the closed-loop system, thereby further adaptively adjusting the control performance of the system according to the intensity of interference to the system.
  • the present invention provides a technical solution:
  • a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system comprises the following specific steps:
  • step S2 performing interference estimation calculation of the system model, and establishing a series of nonlinear interference estimators based on step S1 to reconstruct the uncertainty and external interference of the manipulator system;
  • the step S1 includes the following specific steps:
  • the system state is selected as The state space model M 2 of the controlled manipulator system is obtained:
  • step S2 the specific form of the reconstruction in step S2 can be described as:
  • ⁇ >0 is the parameter gain matrix of the designed estimator
  • p is the internal auxiliary matrix of an estimator
  • Auxiliary state vector symbol is the estimated vector of aggregate interference d.
  • the steady-state model of the system is established as:
  • the reference value in step S4 is:
  • T>0 is the prediction period
  • step S5 when maintaining the coordinate transformation:
  • L(t) ⁇ 1 is the auxiliary adaptive parameter introduced
  • c>0 is a parameter to be designed.
  • step S4 The design of the generalized predictive control law in step S4 can obtain the final input execution rate ⁇ of the controlled manipulator system as:
  • step S6 when performing parameter matrix tuning of the nonlinear disturbance estimator, constraints need to be met. It is first given as a sufficiently large positive number, with an order of magnitude of about 5-10. The larger its value, the faster the estimator converges, corresponding to the stronger robustness of the closed-loop system.
  • the estimation accuracy of the nonlinear disturbance estimator is positively correlated with the set control frequency of the controller design loop. The higher the control frequency, the higher the estimation accuracy. Conversely, the lower the control frequency, the lower the estimation accuracy.
  • the parameters to be tuned are c, T(0).
  • the control law gain is first optimized, which can be achieved through rolling optimization calculation. The larger the c value, the faster the T value converges, that is, the faster the system converges, and the smaller the steady-state static error. After the system enters the steady state, the trajectory will show obvious oscillation. The larger T(0) is, the slower the convergence speed of the manipulator closed-loop system, and the larger the steady-state error. As T(0) decreases, the adjustment time will become faster accordingly.
  • the present invention combines static error-free predictive control and adopts a feedforward control strategy based on disturbance estimation method, so that the trajectory tracking control of the controlled manipulator system can achieve higher tracking control accuracy;
  • the present invention uses the mechanism of predictive control time domain online update to ensure that the adaptive transient performance optimization capability of the manipulator closed-loop system can be well guaranteed when facing complex external interference or when the model parameter mismatch is high;
  • the present invention provides the selection specification of control parameters in theory through the design framework based on generalized predictive control.
  • the selection of control parameters has a concise and clear guidance mechanism, which is more conducive to engineering implementation.
  • the speed and position of each joint of the manipulator system are collected by measuring position and speed sensors with good performance, and then a nonlinear disturbance estimator is constructed by integrating the collected information, so that the internal uncertainty and external disturbance information of the model can be obtained as timely and accurately as possible during the operation of the manipulator system, and then the physical model of the manipulator is transformed into the state space model to be designed by mathematical model transformation; based on the transformed model, a new adaptive time domain update mechanism based on generalized predictive control is directly designed in one step, thereby greatly optimizing the traditional generalized predictive controller, so that the closed-loop manipulator system can adapt to various industrial scenarios, and has good trajectory adjustment performance, thereby improving the overall intelligent management level.
  • FIG1 is an overall flow chart of a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system according to the present invention
  • FIG2 is a system block diagram of a non-recursive composite controller of the present invention.
  • FIG3 is a diagram showing the change of d-axis current data of the PI controller under constant disturbance in the present invention
  • FIG4 is a diagram showing the change of d-axis current data of a conventional cascade PI controller under a constant disturbance
  • FIG5 is a q-axis current curve diagram of the PI controller under sinusoidal disturbance in the present invention.
  • FIG6 is a q-axis current curve diagram of a traditional cascade PI controller under sinusoidal disturbance.
  • Embodiment 1 is a diagrammatic representation of Embodiment 1:
  • a generalized dynamic predictive control method for realizing trajectory tracking of a manipulator system comprises the following specific steps:
  • step S2 performing interference estimation calculation of the system model, and establishing a series of nonlinear interference estimators based on step S1 to reconstruct the uncertainty and external interference of the manipulator system;
  • the step S1 includes the following specific steps:
  • M(q) is the inertia matrix, and it satisfies the matrix positive definite condition, is the centripetal force and Coriolis force matrix
  • G(q) is the gravity of the manipulator system
  • uncertain dynamics which includes the parameterized uncertainty of the system, unmodeled dynamics and external disturbances.
  • the state space model M 2 of the controlled manipulator system is obtained:
  • step S2 the specific form of the reconstruction in step S2 can be described as:
  • ⁇ >0 is the parameter gain matrix of the designed estimator
  • p is an internal auxiliary state vector of the estimator
  • symbol is the estimated vector of aggregate interference d.
  • the steady-state model of the system is established as:
  • the reference value in step S4 is:
  • T>0 is the prediction period
  • the performance function can be further calculated as:
  • step S5 when maintaining the coordinate transformation:
  • L(t) ⁇ 1 is the auxiliary adaptive parameter introduced
  • c>0 is a parameter to be designed.
  • step S4 The design of the generalized predictive control law in step S4 can obtain the final input execution rate ⁇ of the controlled manipulator system as:
  • step S6 when performing parameter matrix tuning of the nonlinear disturbance estimator, constraints need to be met. It is first given as a sufficiently large positive number with an order of magnitude of about 5-10. Its size directly affects the convergence speed of the estimator. Normally, the larger its value, the faster the convergence speed of the estimator, corresponding to the stronger robustness of the closed-loop system. In the early stage of convergence of the estimator, it will cause a large overshoot. Therefore, this is a parameter worthy of coordination. On this basis, using the idea of "trial and error method", according to the trajectory output by the closed-loop system, it is necessary to fine-tune the detailed value of.
  • the estimation accuracy of the nonlinear disturbance estimator is positively correlated with the set control frequency of the controller design loop. The higher the control frequency, the higher the estimation accuracy. Conversely, the lower the control frequency, the lower the estimation accuracy.
  • the parameter to be tuned is c, T(0).
  • the control law gain is first optimized, which can be accurately calculated by calculating the rolling optimization.
  • c as a parameter related to the convergence performance of the prediction period T, is usually manually adjusted by the "trial and error method". Specifically, the larger the c value, the faster the T value converges, that is, the faster the system converges and the smaller the steady-state static error.
  • the selection of c value cannot increase indefinitely. As the c value gradually increases, the convergence speed of T value is greatly accelerated, and the lower bound of T value convergence is gradually decreasing.
  • T(0) the lower bound of T value
  • Embodiment 3 is a diagrammatic representation of Embodiment 3
  • control parameters of the present invention are set as follows:
  • a dual closed-loop PI controller was selected as the control group, which more intuitively reflects the effectiveness of the proposed invention and has a certain degree of performance improvement.
  • the dual-loop PI controller can be designed as:
  • control parameters are selected as follows:
  • the developed controller has the following advantages.
  • the non-smooth non-recursive controller is highly adaptable and can cope with multiple types of disturbances.
  • its control accuracy is higher.
  • the proposed controller has a smaller control error, and at the moment of disturbance switching, the speed drop is smaller, and the system robustness is higher.
  • the traditional cascade PI controller is obviously inferior to the developed non-smooth non-recursive controller in these two aspects.
  • the proposed controller has no more obvious sudden change effect than the traditional PI controller at the moment of working condition change. This is caused by the developed control bandwidth self-adjustment mechanism, which effectively improves the dynamic performance and adaptability of the servo system.
  • the present invention combines the zero-static-error predictive control with a feedforward control strategy based on the disturbance estimation method, so that the trajectory tracking control of the controlled manipulator system can achieve higher tracking control accuracy; the present invention uses the predictive control time domain online update mechanism to ensure that the adaptive transient performance optimization capability of the manipulator closed-loop system can be well protected when facing complex external interference or when the model parameter mismatch is high; the present invention provides the selection specification of control parameters in theory through a design framework based on generalized predictive control, and at the same time, the selection of control parameters has a concise and clear guidance mechanism, which is more conducive to engineering implementation, and through the measurement of position and speed sensors with good performance
  • the device collects the speed and position of each joint of the manipulator system, and then integrates the collected information to build a nonlinear disturbance estimator, so that the manipulator system can obtain the internal uncertainty and external disturbance information of the model as timely and accurately as possible during the operation of the manipulator system, and then use mathematical model transformation to transform the physical model of the manipulator into the

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Abstract

提供一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，涉及机械手系统预测控制技术领域，包括生成机械手系统，通过机械手系统进行数学模型构建，通过设置结合了无静差预测控制，使得受控的机械手系统的轨迹跟踪控制可以实现更高的跟踪控制精度；通过预测控制时域在线更新的机制，其自适应的瞬态性能优化能力也可以得到很好的保障；通过基于广义预测控制的设计框架，同时控制参数的选取有简洁明确的指导机制，通过测量性能良好的位置、速度传感器对机械手系统的各关节速度及位置量进行采集，使闭环的机械手系统可以适应于各种工业场景,且具有较好的轨迹调节性能，提高了整体的智能化管理水平。

Description

[根据细则26改正 14.09.2023]用于实现机械手系统轨迹跟踪的广义动态预测控制方法 技术领域
本发明涉及机械手系统预测控制技术领域，具体为一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法。
 背景技术
机械手常见于各种具有高精度需求的场景,如高端制造业,航空或各种外科手术中,其是通过各关节连接成的运动链组成的，现如今,机械手越来越被工程师所看重以用于配合完成更高精度的工程任务,其中必不可少的即是人与物的物理交互，在此过程中,机械手轨迹的高精度控制和柔性动作广受关注。现有的诸多控制方案以用于机械手轨迹调节可归结为如下几个:比例积分微分控制(PID),鲁棒控制,模型预测控制,自适应神经网络控制和滑模控制等，但上述策略在性能要求越来越高、投入成本要求越来越低的应用趋势下,显得愈发力不从心。
现有控制方案存在以下优弱势：
1、首先是针对传统的PID控制而言,在参数较少的前提下,其还具有灵活,便捷的整定机制,工业场景下的适应性较强,所需要的性能可以通过整定参数灵活获取。但是对于所采用的参数往往适用于特定场景,而当场景存在较大范围内切换时,很难保障控制性能仍旧保持在设计预期,即PID参数被认为是局部最优值,这在工业机械手使用场景中是不希望看到的。再者PID策略控制下的闭环系统的稳定性能与鲁棒性能较难说明；
2、不可否认的是由系统建模的参数不确定性,未建模的高阶动力学状态,外部干扰等组成的集总不确定性普遍存在于各类工程对象中,其势必会造成控制性能的下降,甚至出现安全问题，传统鲁棒控制策略是有希望解决此类问题的,其通常通过完善的理论性证明,获取简单易实现的控制律,并在掌握了工况变化的前提下,对控制参数进行整定,从而使所整定的参数胜任机械手系统所处的各种工况，但如此设计思路在闭环系统的动态性能优化上并没有做过多考虑。受较大外力扰动时所采用的定参数的控制器面临扰动能量较小的工况时,不可避免地会造成系统内部的过鲁棒问题,此举无疑会导致机械手系统在遭受不同外力的情况下,实际的控制性能偏离设计预期,工业中可能带来工件损伤甚至工作人员受伤等问题；
3、模型预测控制器通过实时求解性能函数优化方程,从而具有较强的控制性能优化能力,且可以实现机械手系统的位置或速度的约束控制，但对于机械手系统的模型精度要求较高,其抗干扰能力也较为薄弱，在工业应用场景中,机械手系统难免会遇到不同外力的干扰,建模的失配甚至是使用年限过长也会造成系统内部参数摄动,控制器设计过程不考虑模型信号的失配势必会引起模型预测控制精度的丢失,甚至会造成系统的崩溃；
为一定程度上缓解系统可能出现的鲁棒性冗余问题,现有诸多值得参考的结果已被开发出来，从控制理论的角度出发利用了一个跟踪误差导向的参数自调节机制,优化了闭环系统的控制器参数整定,从而进一步地根据系统所受干扰强度,自适应地调节系统的控制性能。那么对于上述的传统预测控制所面临的可能存在的系统鲁棒性冗余的问题,一个自然而然的想法即是:是否存在一个与跟踪误差相关的预测周期自整定函数,可以根据机械手所受的外力强度的变化而计算出当前工况最优的预测周期值,从而实现受控机械手系统的自适应性和鲁棒性的平衡问题。
因此本发明需要设计一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法来解决上述出现的问题。
发明内容：
本发明的目的就在于为了解决上述问题而提供一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，解决了背景技术中提到缓解系统可能出现的鲁棒性冗余问题,现有诸多值得参考的结果已被开发出来，从控制理论的角度出发利用了一个跟踪误差导向的参数自调节机制,优化了闭环系统的控制器参数整定,从而进一步地根据系统所受干扰强度,自适应地调节系统的控制性能。那么对于上述的传统预测控制所面临的可能存在的系统鲁棒性冗余的问题,一个自然而然的想法即是:是否存在一个与跟踪误差相关的预测周期自整定函数,可以根据机械手所受的外力强度的变化而计算出当前工况最优的预测周期值,从而实现受控机械手系统的自适应性和鲁棒性的问题。
为了解决上述问题，本发明提供了一种技术方案：
一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，包括以下具体步骤：
S1、生成机械手系统，通过所述机械手系统进行数学模型构建；
S2、进行所述系统模型干扰估计计算，在步骤S1的基础上,建立系列非线性干扰估计器对所述机械手系统的不确定性及外部干扰进行重构；
S3、构建所述机械手系统的稳态模型及期望输出值，在步骤S1和S2的估计工作基础上建立稳态模型；
S4、通过所述机械手系统进行预测控制的同时进行稳态模型滚动优化，设定滚动优化性能指标以调节系统的输出以较优的姿态收敛至其参考值；
S5、进行所述机械手系统内部的预测周期的自调节机制设计，保持坐标变换；
S6、进行输出执行律设计，结合预测控制律的设计得出受控的所述机械手系统最终的输入执行率，同步进行非线性扰动估计器参数矩阵整定和广义动态预测控制器参数整定，得出最终广义动态预测控制方法。
作为优选，所述步骤S1包括具体以下步骤：
S101、在所述机械手系统内部安装六个关节角度传感器，通过六个关节角速度传感器得到各个关节电机的角位置q及角速度的采样信息,
S102、建立所述机械手操作系统的标准的数学动态模型M1。
作为优选，在完成数学动态模型M1生成后通过选取所述系统状态为得到所述受控机械手系统的状态空间模型M2:
其中：
作为优选，所述步骤S2中在进行重构时其具体形式可描述为:
其中κ＞0为所设计的估计器的参数增益矩阵,p为一个估计器的内部辅
助状态向量；符号为集总干扰d的估计向量。
作为优选，所述系统的稳态模型建立为：
其中yd为机械手的各关节的期望位置,为期望的角速度。
作为优选，所述步骤S4中的参考值为：
其中T＞0为预测周期；
通过忽略上述η系统中的估计误差项,可得其标称系统：
则在一个预测周期内,跟踪偏差沿着上述标称系统展开,具体为：
作为优选，所述步骤S5中在进行保持坐标变换时:
其中L(t)≥1为所引入的辅助自适应参数；
其中,c>0为一个待设计的参数。
作为优选，根据结合步骤S1中的定义u＝M-1(x1)τ；
及步骤S4中的广义预测控制律的设计可以得到受控的机械手系统最终的输入执行率τ为：
作为优选，所述步骤S6中在进行非线性扰动估计器参数矩阵整定时需要满足约束条件，先给定为一个足够大的正数,其量级为5-10左右，其值越大,估计器收敛速度越快,对应着闭环系统的鲁棒性越强，非线性扰动估计器的估计精度与控制器设计回路的设定控制频率呈正相关,控制频率越高,估计精度也就越高，反之控制频率越低,估计精度也就越低。
作为优选，所述步骤S6中在进行广义动态预测控制器参数整定时，需整定的参数为c,T(0)，对于控制器增益参数的选取原则,首先优化控制律增益,其可通过计算滚动优化,c值越大,T值收敛的速度越快,即系统的收敛速度越快,且稳态静差越小，在系统进入稳态后,轨迹会出现明显的振荡，T(0)越大,机械手闭环系统的收敛速度就越慢,且稳态误差就越大,随着T(0)的减小,调节时间会相应地变快。
本发明的有益效果是：
1、本发明通过设置结合了无静差预测控制,采用基于扰动估计法的前馈控制策略,使得受控的机械手系统的轨迹跟踪控制可以实现更高的跟踪控制精度；
2.本发明通过预测控制时域在线更新的机制,使得机械手闭环系统在面对复杂的外部干扰,或模型参数失配度较高时,其自适应的瞬态性能优化能力也可以得到很好的保障；
3、本发明通过基于广义预测控制的设计框架,从理论上给出控制参数的选择规范,同时控制参数的选取有简洁明确的指导机制,更利于工程实现，通过测量性能良好的位置、速度传感器对机械手系统的各关节速度及位置量进行采集,随后通过对所采得的信息进行整合,从而构建一个非线性扰动估计器,以求机械手系统在运行过程中,尽可能即时精确地获取模型内部不确定性及外部扰动信息，再利用数学模型变换,将机械手的物理模型变换为待设计的状态空间模型；基于变换后的模型,直接一步设计出一个新型的基于广义预测控制的自适应时域的更新机制,从而大幅优化传统的广义预测控制器,使闭环的机械手系统可以适应于各种工业场景,且具有较好的轨迹调节性能，提高了整体的智能化管理水平。
 附图说明：
为了易于说明，本发明由下述的具体实施及附图作以详细描述。
图1是本发明一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法整体流程图；
图2是本发明非递归复合控制器的系统框图；
图3是本发明中PI控制器在常值扰动下d轴电流数据变化图；
图4是传统串级PI控制器在常值扰动下d轴电流数据变化图；
图5是本发明中PI控制器在正弦扰动下q轴电流曲线图；
图6是传统串级PI控制器在正弦扰动下q轴电流曲线图。
 具体实施方式：
如图1、图2、图3、图4、图5和图6所示，本具体实施方式采用以下技术方案：
实施例1：
一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，包括以下具体步骤：
S1、生成机械手系统，通过所述机械手系统进行数学模型构建；
S2、进行所述系统模型干扰估计计算，在步骤S1的基础上,建立系列非线性干扰估计器对所述机械手系统的不确定性及外部干扰进行重构；
S3、构建所述机械手系统的稳态模型及期望输出值，在步骤S1和S2的估计工作基础上,含未知动态的机械手系统已可被修正为完全已知的，建立稳态模型；
S4、通过所述机械手系统进行预测控制的同时进行稳态模型滚动优化，设定滚动优化性能指标以调节系统的输出以较优的姿态收敛至其参考值；
S5、进行所述机械手系统内部的预测周期的自调节机制设计，保持坐标变换；
S6、进行输出执行律设计，结合预测控制律的设计得出受控的所述机械手系统最终的输入执行率，同步进行非线性扰动估计器参数矩阵整定和广义动态预测控制器参数整定，得出最终广义动态预测控制方法。
实施例2
如图1、图2、图3、图4、图5和图6所示，本具体实施方式采用以下技术方案：
作为优选，所述步骤S1包括具体以下步骤：
S101、在所述机械手系统内部安装六个关节角度传感器，通过六个关节角速度传感器得到各个关节电机的角位置q及角速度的采样信息,
S102、建立所述机械手操作系统的标准的数学动态模型M1，所述数学动态模型M1具体如下所示:
其中为所述机械手系统的关节角加速度,记为控制输入,M(q)为惯性矩阵,且其满足矩阵正定条件,为向心力和科里奥利力矩阵,G(q)为机械手系统的重力,表示为不确定动态，包含了系统的参数化不确定性,未建模动态和外部干扰。
作为优选，在完成数学动态模型M1生成后通过选取所述系统状态为x1＝q，得到所述受控机械手系统的状态空间模型M2:
其中：
作为优选，所述步骤S2中在进行重构时其具体形式可描述为:
其中κ＞0为所设计的估计器的参数增益矩阵,p为一个估计器的内部辅助状态向量；符号为集总干扰d的估计向量。
定义则观测器的估计误差动态系统为:
作为优选，所述系统的稳态模型建立为：
其中yd为机械手的各关节的期望位置,为期望的角速度。则至此物理意义上的机械手系统的轨迹调节控制已经可以转变为智能控制理论中的系统输出轨迹可追踪问题,需做如下的坐标变换：
则系统的紧密形式可简单写作为:
其中
。
作为优选，所述步骤S4中的参考值为：
其中T＞0为预测周期；
通过忽略上述η系统中的估计误差项,可得其标称系统：
则在一个预测周期内,跟踪偏差沿着上述标称系统展开,具体为：
其中r为系统的控制阶数,
至此,性能函数可被进一步计算为:
其中
接下来,作对V的偏导,并取在已知的基础上,得出最优控制律为
至此,可实施的优化中间控制律可描述为
其中E＝[In，0，…，0]，控制阶数r选作为0,则优化控制律可被直接写作为
其中可被直接计算得。
作为优选，所述步骤S5中在进行保持坐标变换时:
其中L(t)≥1为所引入的辅助自适应参数；
其中,c>0为一个待设计的参数。
作为优选，根据结合步骤S1中的定义u＝M-1(x1)τ；
及步骤S4中的广义预测控制律的设计可以得到受控的机械手系统最终的输入执行率τ为：
作为优选，所述步骤S6中在进行非线性扰动估计器参数矩阵整定时需要满足约束条件，先给定为一个足够大的正数,其量级为5-10左右,其大小直接影响着估计器的收敛速度,正常而言,其值越大,估计器收敛速度越快,对应着闭环系统的鲁棒性越强，在估计器收敛的前期,会带来较大的超调,因此这是一个值得协调的参数，在此基础上,利用“试错法”的思想,根据闭环系统所输出的轨迹,需要对的详细取值进行微调，非线性扰动估计器的估计精度与控制器设计回路的设定控制频率呈正相关,控制频率越高,估计精度也就越高，反之控制频率越低,估计精度也就越低。
作为优选，所述步骤S6中在进行广义动态预测控制器参数整定时，需整定的参数为,c,T(0)，对于控制器增益参数的选取原则,首先优化控制律增益,其可通过计算滚动优化,从而被精确计算得出,c作为一个与预测周期T收敛性能相关的参数,通常是通过“试错法”来人为调节的,具体地,c值越大,T值收敛的速度越快,即系统的收敛速度越快,且稳态静差越小。但c值的选取也并不能无限制的增大,随着c值的逐步增大,T值的收敛速度极具加快，T值收敛的下界也在逐步变小,而T值下界的变小又会造成系统鲁棒性的增强,当过一定的临界值时,会造成机械手闭环系统的过鲁棒性,这样反而会导致闭环系统的瞬态性能的下降,即出现一定的过渡超调,甚至在系统进入稳态后,轨迹会出现明显的振荡，T(0)越大,机械手闭环系统的收敛速度就越慢,且稳态误差就越大,随着T(0)的减小,调节时间会相应地变快,但过小又会引起鲁棒性冗余的问题,恢复过程会出现一定程度的超调。
实施例3：
如图1、图2、图3、图4、图5和图6所示，本具体实施方式采用以下技术方案：
为了验证本发明的优越性及有效性,该处设置了三种永磁同步电机的运行工况:
1)给定速度ωref＝1500rpm,1s后突加干扰力矩为TL＝0.5Nm；
2)给定时变速度给定信号ωref＝1500rpm,初始干扰力矩设置为TL＝0.5Nm,1s后干扰力矩切换为TL＝0.5+0.3sin(t)Nm。
根据上述给出的参数选取规则,结合本实例中选用的永磁无刷直流电机，本发明控制参数设置为：
与此同时,选取了一个双闭环PI控制器作为对照组,较为直观地体现所提发明的有效性及有一定程度的性能提升,此处双环路的PI控制器可设计为:
1)速度环PI控制器
2)电流环PI控制器
其中控制参数选取为:
从结果上来看,所开发的控制器主要有如下几个优点,首先,非光滑非递归控制器的适应性很强,可以应对多类型的干扰,同时其控制精度更高。具体来看,面对正弦负载,所提控制器的控制静差更小,且扰动切换的瞬间,速度跌落更小,系统的鲁棒性较高,而传统的串级PI控制器在这两方面都明显比不上所开发的非光滑非递归控制器。而从电流来看,所提控制器在工况变换的瞬间突变效应也没传统PI控制器明显，这是由开发的控制带宽自调节机制带来的,有效地提升了伺服系统的动态性能及适应性。
具体的：在实际的应用中，本发明通过设置结合了无静差预测控制,采用基于扰动估计法的前馈控制策略,使得受控的机械手系统的轨迹跟踪控制可以实现更高的跟踪控制精度；本发明通过预测控制时域在线更新的机制,使得机械手闭环系统在面对复杂的外部干扰,或模型参数失配度较高时,其自适应的瞬态性能优化能力也可以得到很好的保障；本发明通过基于广义预测控制的设计框架,从理论上给出控制参数的选择规范,同时控制参数的选取有简洁明确的指导机制,更利于工程实现，通过测量性能良好的位置、速度传感器对机械手系统的各关节速度及位置量进行采集,随后通过对所采得的信息进行整合,从而构建一个非线性扰动估计器,以求机械手系统在运行过程中,尽可能即时精确地获取模型内部不确定性及外部扰动信息，再利用数学模型变换,将机械手的物理模型变换为待设计的状态空间模型；基于变换后的模型,直接一步设计出一个新型的基于广义预测控制的自适应时域的更新机制,从而大幅优化传统的广义预测控制器,使闭环的机械手系统可以适应于各种工业场景,且具有较好的轨迹调节性能，提高了整体的智能化管理水平。
尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。

Claims (10)

  1. 一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于，包括以下具体步骤：
    S1、生成机械手系统，通过所述机械手系统进行数学模型构建；
    S2、进行所述系统模型干扰估计计算，在步骤S1的基础上,建立系列非线性干扰估计器对所述机械手系统的不确定性及外部干扰进行重构；
    S3、构建所述机械手系统的稳态模型及期望输出值，在步骤S1和S2的估计工作基础上建立稳态模型；
    S4、通过所述机械手系统进行预测控制的同时进行稳态模型滚动优化，设定滚动优化性能指标以调节系统的输出以较优的姿态收敛至其参考值；
    S5、进行所述机械手系统内部的预测周期的自调节机制设计，保持坐标变换；
    S6、进行输出执行律设计，结合预测控制律的设计得出受控的所述机械手系统最终的输入执行率，同步进行非线性扰动估计器参数矩阵整定和广义动态预测控制器参数整定，得出最终广义动态预测控制方法。
  2. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于，所述步骤S1包括具体以下步骤：
    S101、在所述机械手系统内部安装六个关节角度传感器，通过六个关节角速度传感器得到各个关节电机的角位置q及角速度的采样信息；
    S102、建立所述机械手操作系统的标准的数学动态模型M1。
  3. 根据权利要求2所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于：在完成数学动态模型M1生成后通过选取所述系统状态为得到所述受控机械手系统的状态空间模型M2:
    其中：
  4. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于：所述步骤S2中在进行重构时其具体形式可描述为:
    其中κ＞0为所设计的估计器的参数增益矩阵,p为一个估计器的内部辅助状态向量；符号为集总干扰d的估计向量。
  5. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于，所述系统的稳态模型建立为：
    其中yd为机械手的各关节的期望位置,为期望的角速度。
  6. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于，所述步骤S4中的参考值为：
    其中T＞0为预测周期；
    通过忽略上述η系统中的估计误差项,可得其标称系统：
    则在一个预测周期内,跟踪偏差沿着上述标称系统展开,具体为：
  7. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于，所述步骤S5中在进行保持坐标变换时:
    其中L(t)≥1为所引入的辅助自适应参数；
    其中,c>0为一个待设计的参数。
  8. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于：根据结合步骤S1中的定义
    u＝M-1(x1)τ；
    及步骤S4中的广义预测控制律的设计可以得到受控的机械手系统最终的输入执行率τ为：
  9. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于：所述步骤S6中在进行非线性扰动估计器参数矩阵整定时需要满足约束条件，先给定为一个足够大的正数,其量级为5-10左右，其值越大,估计器收敛速度越快,对应着闭环系统的鲁棒性越强，非线性扰动估计器的估计精度与控制器设计回路的设定控制频率呈正相关,控制频率越高,估计精度也就越高，反之控制频率越低,估计精度也就越低。
  10. 根据权利要求1所述的一种用于实现机械手系统轨迹跟踪的广义动态预测控制方法，其特征在于：所述步骤S6中在进行广义动态预测控制器参数整定时，需整定的参数为c,T(0)，对于控制器增益参数的选取原则,首先优化控制律增益,其可通过计算滚动优化,c值越大,T值收敛的速度越快, 即系统的收敛速度越快,且稳态静差越小，在系统进入稳态后,轨迹会出现明显的振荡，T(0)越大,机械手闭环系统的收敛速度就越慢,且稳态误差就越大,随着T(0)的减小,调节时间会相应地变快。
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