Parameter identification of continuous-time systems using iterative learning control

This paper presents a system identification technique for continuous-time state-space system using the iterative learning control. The transfer function parameters are regarded as functions with respect to the state-space parameters which will be identified. The relationship between the state-space parameters and the response error is explicitly derived. An update law of the state-space parameters is proposed so as to improve the convergence speed. The effectiveness of the proposed identification technique is demonstrated by numerical examples.     

工业过程稳态优化进程中的噪声平滑型迭代学习控制

针对具有噪声的工业过程稳态优化进程，提出迭代学习控制以期改善控制系统的动态品质，建立了基本的加权噪声平滑型迭代学习控制算法结构。利用频域时域相结合的方法分析和论证了算法的收敛性，给出噪声平滑参数的确定策略，数字仿真表明，平滑型迭代学习控制算法能有效消除噪声对系统输出信号的影响，显著改善工业过程稳态优化进程中控制系统的动态品质。     

A novel iterative learning control scheme based on Broyden-class optimization method

This study proposes a novel iterative learning control scheme for discrete-time linear systems based on the Broyden-class optimization method. To overcome the difficulty of lacking system information, a cost function is introduced for the performance index by constructing a positive-definite matrix with little system information. An optimization-based learning control algorithm is proposed using a Hessian matrix approximation and the generated input sequence is demonstrated to exhibit a superlinear convergence rate. The proposed scheme is extended to address the point-to-point tracking problem. Numerical simulations are provided to verify the effectiveness of the proposed approach.     

All-pass filtering in iterative learning control

In iterative learning control (ILC), it is highly desirable to have a learning compensator with a unit-gain for all frequencies, in order to avoid noise amplification and learning speed degradation during the learning process. In this paper, we show that the realization of a unit-gain compensator is straightforward in ILC, using both forward and backward filtering. As an illustrative example, a unit-gain derivative is proposed to overcome the drawbacks of the conventional derivative. The proposed scheme is equivalent to an all-pass unit-gain phase shifter; the forward filtering uses a 0.5-order derivative and the backward filtering employs a 0.5-order integral. The all-pass phase shifter is deployed in a unit-gain D-type ILC. The advantages of the unit-gain feature are demonstrated by some experimental results on a robot manipulator.     

输入约束不确定系统的点对点迭代学习控制与优化

为解决工业过程中机械臂等特殊重复运行系统的输出在有限时间内无需实现全轨迹跟踪,仅需跟踪期望轨迹上某些特殊关键点的控制问题,针对线性时不变离散系统提出一种基于范数最优的点对点迭代学习控制算法.通过输入输出时间序列矩阵模型变换构建综合性多目标点性能指标函数,求解二次型最优解得到优化迭代学习控制律,同时给出模型标称和不确定情...     

Approximate adjoint-based iterative learning control

This paper characterises stochastic convergence properties of adjoint-based (gradient-based) iterative learning control (ILC) applied to systems with load disturbances, when provided only with approximate gradient information and noisy measurements. Specifically, conditions are discussed under which the approximations will result in a scheme which converges to an optimal control input. Both the cases of time-invariant step sizes and cases of decreasing step sizes (as in stochastic approximation) are discussed. These theoretical results are supplemented with an application on a sequencing batch reactor for wastewater treatment plants, where approximate gradient information is available. It is found that for such case adjoint-based ILC outperforms inverse-based ILC and model-free P-type ILC, both in terms of convergence rate and measurement noise tolerance.     

Estimation-based norm-optimal iterative learning control

The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.     

A pseudoinverse-based iterative learning control

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper, an iterative learning control (ILC) algorithm is proposed to accommodate a general class of nonlinear, nonminimum-phase plants with disturbances and initialization errors. The algorithm requires the computation of an approximate inverse of the linearized plant rather than the exact inverse. An advantage of this approach is that the output of the plant need not be differentiated. A bound on the asymptotic trajectory error is exhibited via a concise proof and is shown to grow continuously with a bound on the disturbances. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

On initial conditions in iterative learning control

Initial conditions, or initial resetting conditions, play a fundamental role in all kinds of iterative learning control methods. In this note, we study five different initial conditions, disclose the inherent relationship between each initial condition and corresponding learning convergence (or boundedness) property. The iterative learning control method under consideration is based on Lyapunov theory, which is suitable for plants with time-varying parametric uncertainties and local Lipschitz nonlinearities.     

网络控制系统中一种新形式的开闭环迭代学习控制

本文研究了网络控制系统中迭代学习控制方法, 借鉴网络控制系统的分层结构形式, 提出了一种远程开环本地闭环的迭代学习控制形式. 这种形式的学习律中, 只有开环学习律的离散数据通过网络传输, 对控制系统进行前馈补偿同时降低了网络丢包对系统的实时影响. 针对线性系统, 利用2–D系统的分析方法, 给出了网络控制中开闭环迭代学习控制的收敛性判别条件. 仿真和实验结果证实了所提方法的可行性和有效性.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.     

高阶参数优化迭代学习控制算法

针对线性时不变离散系统的跟踪问题提出一种高阶参数优化迭代学习控制算法.该算法通过建立考虑了多次迭代误差影响的参数优化目标函数,求解得出优化后的时变学习增益参数.从理论上证明了:对于线性离散时不变系统,该算法在被控对象不满足正定性的松弛条件下仍可保证跟踪误差单调收敛于零.同时,采用之前多次迭代信息的高阶算法具有更好的收敛性和鲁棒性.最后利用一个仿真实例验证了算法的有效性.     

Constrained data-driven optimal iterative learning control

A constrained optimal ILC for a class of nonlinear and non-affine systems, without requiring any explicit model information except for the input and output data, is proposed in this work. In order to address the nonlinearities, an iterative dynamic linearization method without omitting any information of the original plant is introduced in the iteration direction. The derived linearized data model is equivalent to the original nonlinear system and reflects the real-time dynamics of the controlled plant, rather than a static approximate model. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear matrix inequality, a novel constrained data-driven optimal ILC is developed by minimizing a predesigned objective function. The optimal learning gain is unfixed and updated iteratively according to the input and output measurements, which enhances the flexibility regarding modifications and expansions of the controlled plant. The results are further extended to the point-to-point control tasks where the exact tracking performance is required only at certain points and a constrained data-driven optimal point-to-point ILC is proposed by only utilizing the error measurements at the specified points only.     

Data-driven optimal terminal iterative learning control

This paper presents a data-driven optimal terminal iterative learning control (TILC) approach for linear and nonlinear discrete-time systems. The iterative learning control law is updated from only terminal output tracking error instead of entire output trajectory tracking error. The only required knowledge of a controlled system is that the Markov matrices of linear systems or the partial derivatives of nonlinear systems with respect to control inputs are bounded. Rigorous analysis and convergence proof are developed with sufficient conditions for the terminal ILC design and the results are developed for both linear and nonlinear discrete-time systems. Simulation results illustrate the applicability and effectiveness of the proposed approach.     

Disturbance aspects of iterative learning control

Disturbance aspects of iterative learning control (ILC) are considered. By using a linear framework it is possible to investigate the influence of the disturbances in the frequency domain. The effects of the design filters in the ILC algorithm on the disturbance properties can then be analyzed. The analysis is supported by simulations and experiments.     

迭代学习在网络控制中的应用*

针对网络拥塞控制中网络拥塞本身无法建立精确的数学模型的问题,基于迭代学习控制具有结构简单及对系统精确模型不依赖等优点,首次提出了用迭代学习控制算法来解决网络拥塞,其主要目的是提高网络资源的利用率并提供给信源公平的资源分配份额。在提出算法前,首先通过分析网络模型建立了网络拥塞被控系统;然后提出了针对该被控系统的开闭环PID型迭代学习控制算法并证明了其收敛性;最后运用此算法建立了网络拥塞控制模型。通过实验和仿真表明,该算法对解决网络拥塞问题有很好的效果。     

分数线性相位超前迭代学习控制

线性相位超前迭代学习控制的超前拍数需要取整,不利于控制系统的性能达到最优.对此提出分数线性相位超前迭代学习控制.对系统的收敛条件进行频域分析,得到超前拍数,学习增益和可学习带宽的范围.通过调节超前拍数来提高系统的可学习带宽,以达到更高的跟踪精度.给出了分数线性相位超前的具体实现方法,并在此基础上对整数与分数相位超前的补偿效果进行比较.以机械臂为被控对象的仿真结果表明了分数线性相位超前更能提高系统的可学习带宽及跟踪精度.     

Analysis of boundary effects in iterative learning control

Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.