Iterative learning control for integrated system of robot and machine tool

This study is concerned with the integrated system of a robot and a machine tool. The major task of robot is loading the workpiece to the machine tool for contour cutting. An iterative learning control (ILC) algorithm is proposed to improve the accuracy of the finished product. The proposed ILC is to modify the input command of the next machining cycle for both robot and machine tool to iteratively enhance the output accuracy of the robot and machine tool. The modified command is computed based on the current tracking/contour error. For the ILC of the robot, tracking error is considered as the control objective to reduce the tracking error of motion path, in particular, the error at the endpoint. Meanwhile, for the ILC of the machine tool, contour error is considered as the control objective to improve the contouring accuracy, which determines the quality of machining. In view of the complicated contour error model, the equivalent contour error instead of the actual contour error is taken as the control objective in this study. One challenge for the integrated system is that there exists an initial state error for the machine tool dynamics, violating the basic assumption of ILC. It will be shown in this study that the effects of initial state error can be significantly reduced by the ILC of the robot. The proposed ILC algorithm is verified experimentally on an integrated system of commercial robot and machine tool. The experimental results show that the proposed ILC can achieve more than 90% of reduction on both the RMS tracking error of the robot and the RMS contour error of the machine tool within six learning iterations. The results clearly validate the effectiveness of the proposed ILC for the integrated system.     

A generalized iterative learning controller against initial state error

In this paper, the previous results that the performance of iterative learning control (ILC) algorithm can be improved by adding a proportional term and/or an integral term of error in D-type ILC algorithm are generalized using an operator. Then, a sufficient condition for convergence and robustness of the generalized ILC algorithm are investigated against initial state error. As a special case of the operator, a non-linear ILC algorithm is also proposed and it is shown that the effect of initial state error can be reached to zero in a given finite time. It is shown that the bound of error reduction can be effectively controlled by tuning gains of the proposed non-linear ILC algorithm. In order to confirm validity of the proposed algorithms, two examples are presented.     

Initial state iterative learning for final state control in motion systems

In this work, an initial state iterative learning control (ILC) approach is proposed for final state control of motion systems. ILC is applied to learn the desired initial states in the presence of system uncertainties. Four cases are considered where the initial position or speed is a manipulated variable and the final displacement or speed is a controlled variable. Since the control task is specified spatially in states, a state transformation is introduced such that the final state control problems are formulated in the phase plane to facilitate spatial ILC design and analysis. An illustrative example is provided to verify the validity of the proposed ILC algorithms.     

Iterative Path Tracking of an Omni-Directional Mobile Robot

We propose a path-tracking algorithm that is developed using an iterative learning control (ILC) technique and use the algorithm to control an omni-directional mobile robot. The proposed algorithm can be categorized as an open–closed PD-type ILC; it generates robot velocity commands by a PD-type ILC update rule using both previous and current information. When applied to the omni-directional mobile robot, it can decrease position errors and track the desired trajectory. Under the general problem setting that includes a mobile robot, we show that the proposed algorithm guarantees that the system states, outputs and control inputs converge to within small error bounds around the desired ones even under state disturbances, measurement noises and initial state errors. By using simulation and experimental tests, we demonstrate that the proposed algorithm converges fast to the desired path, and results in small root-mean-square (r.m.s.) position error under various surface conditions. The proposed algorithm shows better path-tracking performance than the conventional PID algorithm and achieves faster convergence and lower r.m.s. error than the existing two ILC algorithms.     

An average operator-based PD-type iterative learning control for variable initial state error

This note studies the effect of variable initial state error in iterative learning control (ILC) systems and proposes a new ILC algorithm based on an average operator. Then, it is shown that, when the proposed algorithm is applied to linear time-invariant (LTI) systems, the effect of the initial state error can be exactly estimated under a specific condition, while the existing algorithms guarantee only the boundness of the error or the convergence from stochastic point of view. To show the validity of the proposed algorithm, a numerical example is given.     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree

In this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.     

具有通信约束的反馈辅助PD型量化迭代学习控制

本文针对网络线性系统, 研究了具有通信约束的反馈辅助PD型迭代学习控制问题. 信号从远程设备传输到 迭代学习控制器过程中, 存在数据量化与数据包丢失的情况. 将数据包丢失模型描述为具有已知概率的伯努利二 进制序列, 采用扇形界方法处理数据量化误差, 提出了一种反馈辅助PD型迭代学习控制算法. 采用压缩映射法分析 证明了在存在数据量化和丢失的情况下, 所提控制算法依然可以保证跟踪误差渐近收敛到零. 并进一步对存在初 始状态偏移时所提算法的鲁棒性进行了讨论. 最后, 通过仿真示例, 对比验证了理论结果的有效性和优越性.     

Iterative Learning Control for Linear Discrete‐Time Systems with Unknown High‐Order Internal Models: A Time‐Frequency Analysis Approach

This work focuses on the iterative learning control (ILC) for linear discrete‐time systems with unknown initial state and disturbances. First, multiple high‐order internal models (HOIMs) are introduced for the reference, initial state, and disturbances. Both the initial state and disturbance consist of two components, one strictly satisfies HOIM and the other is random bounded. Then, an ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For all known HOIMs, an ILC design criterion is introduced to achieve satisfactory tracking performance based on the 2‐D theory. Next, the case with unknown HOIMs is discussed, where a time‐frequency‐analysis (TFA)‐based ILC algorithm is proposed. In this situation, it is shown that the tracking error inherits the unknown augmented HOIM that is an aggregation of all unknown HOIMs. Then, a TFA‐based method, e.g., the short‐time Fourier transformation (STFT), is employed to identify the unknown augmented HOIM, where the STFT could ignore the effect of the random bounded initial state and disturbances. A new ILC law is designed for the identified unknown augmented HOIM, which has the ability to reject the unknown the initial state and disturbances that strictly satisfy HOIMs. Finally, a gantry robot system with iteration‐invariant or slowly‐varying frequencies is given to illustrate the efficiency of the proposed TFA‐based ILC algorithm.     

Selection of the learning gain matrix of an iterative learning control algorithm in presence of measurement noise

Arbitrary high precision output tracking is one of the most desirable control objectives found in industrial applications regardless of measurement errors. The main purpose of this paper is to supply to the iterative learning control (ILC) designer guidelines to select the corresponding learning gain in order to achieve this control objective. For example, if certain conditions are met, then it is necessary for the learning gain to converge to zero in the learning iterative domain. In particular, this paper presents necessary and sufficient conditions for boundedness of trajectories and uniform tracking in presence of measurement noise and a class of random reinitialization errors for a simple ILC algorithm. The system under consideration is a class of discrete-time affine nonlinear systems with arbitrary relative degree and arbitrary number of system inputs and outputs. The state function does not need to satisfy a Lipschitz condition. This work also provides a recursive algorithm that generates the appropriate learning gain functions that meet the arbitrary high precision output tracking objective. The resulting tracking output error is shown to converge to zero at a rate inversely proportional to square root of the number of learning iterations in presence of measurement noise and a class of reinitialization errors. Two illustrative numerical examples are presented.     

非参数不确定系统的有限时间迭代学习控制

针对任意初态情形,引入初始修正作用,研究一类非参数不确定时变系统能够达到实际完全跟踪性能的迭代学习控制方法. 采用Lyapunov-like综合,设计迭代学习控制器处理不确定性时变系统非参数化问题,其中含有有限时间控制作用,以实现在预先指定区间上的零误差跟踪. 并且,运用完全限幅学习机制,保证闭环系统中各变量的一致有界性以及跟踪误差的一致收敛性. 仿真结果表明了所提出控制方法的有效性.     

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control (ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis.      

Adaptive fuzzy ILC of nonlinear discrete-time systems with unknown dead zones and control directions

This paper presents an adaptive fuzzy iterative learning control (ILC) design for non-parametrized nonlinear discrete-time systems with unknown input dead zones and control directions. In the proposed adaptive fuzzy ILC algorithm, a fuzzy logic system (FLS) is used to approximate the desired control signal, and an additional adaptive mechanism is designed to compensate for the unknown input dead zone. In dealing with the unknown control direction of the nonlinear discrete-time system, a discrete Nussbaum gain technique is exploited along the iteration axis and applied to the adaptive fuzzy ILC algorithm. As a result, it is proved that the proposed adaptive fuzzy ILC scheme can drive the ILC tracking errors beyond the initial time instants into a tunable residual set as iteration number goes to infinity, and keep all the system signals bounded in the adaptive ILC process. Finally, a simulation example is used to demonstrate the feasibility and effectiveness of the adaptive fuzzy ILC scheme.     

A non-standard iterative learning control approach to tracking periodic signals in discrete-time non-linear systems

In this paper we use the formalism of iterative learning control (ILC) to solve the repetitive control problem of forcing a system to track a prescribed periodic reference signal. Although the systems we consider operate continuously in time, rather than with trials that have distinct starting and ending times, we use the ILC approach by defining a 'trial' in terms of completion of a single 'period' of the output trajectory, where a period is an interval from the start of the trial until the system returns to its initial state. The ILC scheme we develop does not use the standard assumption of uniform trial length. In the final result the periodic motion is achieved by 'repetition' of the learned ILC input signal for a single period. Analysis of the convergence of the algorithm uses an intermediate convergence result for the typical ILC problem. This intermediate result is based on a multi-loop control interpretation of the signal flow in ILC. The idea is demonstrated on an example and it is noted that it may be possible to generalize the ideas to broader classes of systems and ILC algorithms.     

城市交通信号的迭代学习控制及其对路网宏观基本图的影响

针对在城市交通信号控制中存在对交通流难以精确建模的问题,首先利用交通流的重复性特点,提出了一种基于迭代学习的城市交通信号控制方法,并证明了在不确定初态下迭代学习控制算法的收敛性.其次,结合路网宏观基本图的特性分析了基于迭代学习的交通信号控制策略对路网交通态势的影响.结果表明,当迭代的初始状态在期望初态值的小范围内波动时,系统的跟踪误差仍能收敛到一个界内;通过对交通信号的迭代学习控制,路段的实际占有率能够逐步逼近期望占有率,从而使路网内的车辆密度分布更加均匀,确保交通流在更优的宏观基本图下运行,防止因车辆密度分布不均引起的通行效率下降及交通拥堵的发生.最后,通过仿真实验对所提方法的有效性进行了验证.     

一类非线性时变系统的迭代学习控制

针对一类具有任意初态的不确定非线性时变系统,应用校正期望轨迹方法把任意初态问题转换为零初始误差的变期望轨迹的迭代学习控制问题,提出了求解校正期望轨迹的过渡轨迹的计算方法.然后,针对变期望轨迹问题提出了一种新的迭代学习控制算法,在算法中引入了期望轨迹的高阶导数来克服期望轨迹的变化,并通过设计稳定的跟踪误差滑动面来处理系统中非线性时变不确定性.论文给出了相关定理,并应用类Lyapunov方法给出了详细证明.仿真结果表明所提出的算法是有效的,该算法不需要系统的模型结构信息,比自适应迭代学习控制算法具有更宽的适用范围.     

Performance Enhancement for Rigid Tapping by Iterative Learning Control

In this study, an iterative learning control (ILC) algorithm is proposed to improve synchronous errors in rigid tapping. In rigid tapping, the displacements of the z‐axis and spindle must be kept synchronous to prevent damage. Using learning control provides better commands for both the z‐axis and spindle dynamics, improving the synchronicity of the output responses of the z‐axis and spindle. The proposed ILC makes use of synchronous errors in the previous cycle of tapping to modify the current position commands of both the z‐axis and spindle. A systematic algorithm is proposed for the computation of learning gains that guarantee the monotonic convergence of synchronous errors. A systematic procedure of applying ILC to rigid tapping is also proposed, where the ideas of effective learning gains and stop learning criteria are discussed. Experimental results on a tapping machine verify the effectiveness of the proposed ILC algorithm.     

Kinematic path‐tracking of mobile robot using iterative learning control

This paper develops a kinematic path‐tracking algorithm for a nonholonomic mobile robot using an iterative learning control (ILC) technique. The proposed algorithm produces a robot velocity command, which is to be executed by the proper dynamic controller of the robot. The difference between the velocity command and the actual velocity acts as state disturbances in the kinematic model of the mobile robot. Given the kinematic model with state disturbances, we present an ILC‐based path‐tracking algorithm. An iterative learning rule with both predictive and current learning terms is used to overcome uncertainties and the disturbances in the system. It shows that the system states, outputs, and control inputs are guaranteed to converge to the desired trajectories with or without state disturbances, output disturbances, or initial state errors. Simulations and experiments using an actual mobile robot verify the feasibility and validity of the proposed learning algorithm. © 2005 Wiley Periodicals, Inc.     

输入增益未知非参数不确定系统的准最优学习控制

为解决一类非参数不确定系统在任意初态且输入增益未知情形下的轨迹跟踪问题, 提出准最优误差跟踪学习控制方法.该方法综合准最优控制和迭代学习控制两种技术设计控制器, 在构造期望误差轨迹的基础上, 根据控制Lyapunov函数及Sontag公式给出标称系统的优化控制, 以鲁棒方法和学习方法相结合的策略处理非参数不确定性.闭环系统经过足够次迭代运行后, 经由实现系统误差对期望误差轨迹在整个作业区间上的精确跟踪, 获得系统状态对参考信号在预设的部分作业区间上的精确跟踪.仿真结果表明所设计学习系统在收敛速度方面快于非优化设计.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.