Learning rates in the digital iterative learning control of linear multivariable plants

The learning rates achievable in the digital iterative learning control of linear multi-variable plants are investigated. It is shown that the irregularity and stability characteristics of the plants under control impose severe constraints on the achievable learning rates. These results are not only significant in their own right but also strongly motivate the introduction of compensators to increase the learning rates achievable in irregular plants. These general results are illustrated by the presentation of numerical results for the iterative learning digital control of an uncompensated fourth-order completely irregular plant with two inputs and two outputs     

Digital iterative learning control of linear multivariable plants

It is shown that digital iterative learning controllers can be designed for linear multivariable plants using only the step-response matrices of such plants. This demonstration is effected by proving a fundamental theorem which establishes precise sufficient conditions under which iterative learning control is achieved by such digital controllers. These general results are illustrated by the presentation of numerical results for the digital iterative learning control of a third-order linear multivariable plant with two inputs and two outputs.     

非正则线性系统的闭环P型迭代学习控制

迭代学习控制是改善具有重复运行性质过程的跟踪性能的有效方法。开环迭代学习控制学习周期长，在迭代学习的初期容易出现不稳定和高增益的现象。对非正则系统的迭代学习控制，需要采用高阶微分学习律。该文针对一类非正则线性定常连续系统，讨论了闭环P型迭代学习控制律，给出并证明了闭环P型迭代学习控制律的收敛性条件的两个定理，解决了非正则系统的P型迭代学习控制问题。仿真实例说明闭环迭代学习律的有效性和快速性。     

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.     

误差约束严格反馈系统的迭代学习控制

针对一类严格反馈非线性系统,本文提出误差跟踪学习控制算法,旨在解决状态约束问题和系统的初值问题.文中构造了二次分式型对称障碍Lyapunov函数以及二次分式型非对称障碍Lyapunov函数,并结合反推技术来分别设计学习控制器.两种控制方案里分别采用积分学习律和微分–差分学习律估计未知系数.系统跟踪误差在控制器作用下囿于预设的界内,从而实现迭代过程中对状态的约束;引入期望误差轨迹,经迭代学习后,两种控制方案均能够实现状态误差在整个作业区间上对期望误差轨迹的完全跟踪,并且实现系统输出在预指定作业区间上精确跟踪参考信号.数值仿真结果表明了控制方案的有效性.     

Iterative learning control: A survey and new results

Learning control is an iterative approach to the problem of improving transient behavior for processes that are repetitive in nature. In this article, we present some results on iterative learning control. A complete review of the literature is given first. Then, a general formulation of the problem is given. Next, we present a complete analysis of the learning control problem for the case of linear, time-invariant plants and controllers. This analysis offers: (1) insight into the nature of the solution of the learning control problem by deriving sufficient convergence conditions; (2) an approach to learning control for linear systems based on parameter estimation; and (3) an analysis that shows that for finite-horizon problems it is possible to design a learning control algorithm that converges, with memory, in one step. Finally, a time-varying learning controller is given for controlling the trajectory of a nonlinear robot manipulator. A brief simulation example is presented to illustrate the effectiveness of this scheme.     

Robust control of linear time-invariant plants using periodic compensation

This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.     

基于强化迭代学习的四旋翼无人机轨迹控制

为进一步提升在未知环境下四旋翼无人机轨迹的跟踪精度,提出了一种在传统反馈控制架构上增加迭代学习前馈控制器的控制方法。针对迭代学习控制（ILC）中存在的学习参数整定困难的问题,提出了一种利用强化学习（RL）对迭代学习控制器的学习参数进行整定优化的方法。首先,利用RL对迭代学习控制器的学习参数进行优化,筛选出当前环境及任务下最优的学习参数以保证迭代学习控制器的控制效果最优;其次,利用迭代学习控制器的学习能力不断迭代优化前馈输入,直至实现完美跟踪;最后,在有随机噪声存在的仿真环境中把所提出的强化迭代学习控制（RL-ILC）算法与未经参数优化的ILC方法、滑模变结构控制（SMC）方法以及比例-积分-微分（PID）控制方法进行对比实验。实验结果表明,所提算法在经过2次迭代后,总误差缩减为初始误差的0.2%,实现了快速收敛;并且与SMC控制方法及PID控制方法相比,RL-ILC算法在算法收敛后不会受噪声影响产生轨迹波动。由此可见,所提算法能够有效提高无人机轨迹跟踪的准确性和鲁棒性。     

Adaptive learning with large variability of teaching signals for neural networks and its application to motion control of an industrial robot

Recently, various control methods represented by proportional-integral-derivative (PID) control are used for robotic control. To cope with the requirements for high response and precision, advanced feedforward controllers such as gravity compensator, Coriolis/centrifugal force compensator and friction compensators have been built in the controller. Generally, it causes heavy computational load when calculating the compensating value within a short sampling period. In this paper, integrated recurrent neural networks are applied as a feedforward controller for PUMA560 manipulator. The feedforward controller works instead of gravity and Coriolis/centrifugal force compensators. In the learning process of the neural network by using back propagation algorithm, the learning coefficient and gain of sigmoid function are tuned intuitively and empirically according to teaching signals. The tuning is complicated because it is being conducted by trial and error. Especially, when the scale of teaching signal is large, the problem becomes crucial. To cope with the problem which concerns the learning performance, a simple and adaptive learning technique for large scale teaching signals is proposed. The learning techniques and control effectiveness are evaluated through simulations using the dynamic model of PUMA560 manipulator.     

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic distrubances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control structure is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.     

Singular perturbation methods in the design of tracking systems incorprating inner-loop compensators and fast-sampling error-actuated controllers

Singular perturbation methods are used to exhibit the asymptotic structure of the transfer function matrices of discrete-time tracking systems incorporating linear multivariate plants which are amenable to fast-sampling error-actuated digital control only if extra plant output measurements are generated by the introduction of appropriate transducers and processed by inner-loop compensators. It is shown that these results greatly facilitate the determination of controller and transducer matrices which ensure that the closed-loop behaviour of such discrete-time tracking systems becomes increasingly non-interacting as the sampling frequency is increased. These general results are illustrated by designing a fast-sampling error-actuated digital controller for an aircraft.     

输出重定义下的非线性非最小相位系统迭代学习控制

讨论非线性非最小相位系统实现完全跟踪的迭代学习控制方法, 适于在有限作业区间上重复运行的受控系统. 在控制器设计时, 通过输出重定义以使非最小相位系统的零动态变成渐近稳定特性. 分别采用部分限幅和完全限幅两种学习算法设计控制器, 理论分析表明两种算法能够保证学习系统中所有变量的有界性和跟踪误差在整个作业区间上渐近收敛于零. 数值仿真验证了两种迭代学习控制系统的跟踪性能.     

Robust iterative learning controller design using the performance weighting function of feedback control systems

Iterative learning controllers combined with existing feedback controllers have prominent capability of improving tracking performance in repeated tasks. However, the iterative learning controller has been designed without utilizing effective information such as the performance weighting function to design a feedback controller. In this paper, we deal with a robust iterative learning controller design problem for an uncertain feedback control system using its explicit performance information. We first propose a robust convergence condition in the ?₂-norm sense for an iterative learning control (ILC) scheme. We present a method to design an iterative learning controller using the information on the performance of the existing feedback control system such as performance weighting functions and frequency ranges of desired trajectories. From the obtained results, several design criteria for iterative learning controller are provided. Through analysis on the remaining error, the loop properties before and after learning are compared. We also show that, in the ?₂-norm sense, the remaining error can be less than the initial error under certain conditions. Finally, to show the validity of the proposed method, simulation studies are performed.     

非正则分布参数系统的迭代学习控制

针对一类非正则分布参数系统的迭代学习控制问题进行讨论, 该类分布参数系统由抛物型偏微分方程构成. 基于非正则系统的特点, 使用D型学习律构建得到迭代学习控制律, 并基于压缩映射原理, 证明得到输出跟踪误差在??² 范数意义下沿迭代轴方向的收敛性结论. 仿真算例表明了所提出结论的有效性.

     

Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

Robustification of iterative learning control and repetitive control by averaging

This paper describes a recently developed averaging technique to robustify iterative learning and repetitive controllers. The robustified controllers are found by minimising cost functions that are averaged over either multiple analytical time-domain models or experimental frequency-domain data. The aim is to produce a technique that is simple and general, and can be applied to any iterative learning control (ILC) or repetitive control (RC) design that involves the minimisation of a cost function. Substantial improvement in convergence to zero tracking error in the presence of model uncertainties has been observed for both ILC and RC by this averaging technique.     

迭代学习控制理论的发展动态

迭代学习控制（ILC）适合于具有某种重复运动（运行）性质的被控对象，可 实现有限时间区间上的完全跟踪任务．本文综述了迭代学习控制的基本内容和最新发展动态 ，对迭代学习控制的基本理论进行了分类研究，并讨论其存在的问题和发展趋势．     

Recurrent neural robot controllers: feedback mechanisms for identifying environmental motion dynamics

In this paper a series of recurrent controllers for mobile robots have been developed. The system combines the iterative learning capability of neural controllers and the optimisation ability of particle swarms. In particular, three controllers have been developed: an Exo-sensing, an Ego-sensing and a Composite controller which is the hybrid of the latter two. The task for each controller is to learn to follow a moving target and identify its trajectory using only local information. We show how the learned behaviours of each architecture rely on different sensory representations, although good results are obtained in all cases.     

非线性重复运动系统的双迭代优化学习控制

本文针对一类具有非参数不确定性和输出约束的非线性系统,提出一种双迭代优化学习控制策略,将复杂的迭代学习过程简化为两个相对简单的迭代控制器.首先引入一类饱和非线性函数不仅可以满足系统的位置约束,同时能够保证系统跟踪误差收敛于给定的邻域,然后针对每次迭代初始误差设计参考轨迹自修正策略,在每个迭代周期上设置一个固定的调整时间域,根据上次迭代的输出调整下一次迭代的参考轨迹.双迭代的控制结构可以同时更新两个迭代控制器的参数,来处理系统的非参数不确定性.进一步利用Barrier复合能量函数证明双迭代控制策略的收敛性和稳定性,并给出收敛条件.最后,通过一个算例证明了该控制策略的有效性.     

Iterative learning controllers with time-varying gains for large-scale industrial processes to track trajectories with different magnitudes

In this article, a set of decentralised open-loop and closed-loop iterative learning controllers are embedded into the procedure of steady-state hierarchical optimisation utilising feedback information for large-scale industrial processes. The task of the learning controllers is to generate a sequence of upgraded control inputs iteratively to take responsibility for sequential step function-type control decisions, each of which is determined by the steady-state optimisation layer and then imposed on the real system for feedback information. In the learning control scheme, the learning gains are designated to be time-varying which are adjusted by virtue of expertise experiences-based IF-THEN rules, and the magnitudes of the learning control inputs are amplified by the sequential step function-type control decisions. The aim of learning schemes is to further effectively improve the transient performance. The convergence of the updating laws is deduced in the sense of Lebesgue 1-norm by taking advantage of the Hausdorff–Young inequality of convolution integral and the Hoelder inequality of Lebesgue norm. Numerical simulations manifest that both the open-loop and the closed-loop time-varying learning gain-based schemes can effectively decrease the overshoot, accelerate the rising speed and shorten the settling time, etc.