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.     

内模强化学习型模型预测控制及其在人工胰脏上的应用

在学习型模型预测控制的框架里,迭代学习控制器被用来更新模型预测控制器的设定点.在已经发表的研究成果里,学习型模型预测控制用到的是比例型的学习率,这种学习率的学习能力有限,而且怎样设计学习增益仍然是一个开放性问题.在本文中,基于内模控制理论提出的PID型的迭代学习控制器被用来更新模型预测控制器的设定点.为了方便起见,本文提出的结合算法可称为内模强化学习型模型预测控制.本文提出的算法应用在(1)型糖尿病人的人工胰脏闭环控制上.仿真结果显示,本算法对比于比例学习型模型预测控制可以达到更好的收敛性能,而且对非重复干扰有很好的鲁棒性.     

Iterative learning control for position tracking of a pneumatic actuated X–Y table

The iterative learning control (ILC) obtains the unknown information from repeated control operations. Meanwhile, the tracking error from previous stages is used as the correction factor for the next control action. Therefore, the ILC controller can make the system tracking error converge to a small region within a limited number of iterations. This study builds a proportional-valve-controlled pneumatic X–Y table system for performing position tracking control experiments. The experiments involve implementing the ILC controllers and comparing the results. The P-type updating law with delay parameters is used for both the x- and y-axes in the repetitive trajectory tracking control. Experimental results demonstrate that the ILC controller can effectively control the system and track the desired circular trajectory at different speeds. The control parameters are varied to investigate their effects on the ILC convergence.     

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

In this paper, both output-feedback iterative learning control (ILC) and repetitive learning control (RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.      

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。     

Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking

A novel control technique is proposed by combining iterative learning control (ILC) and model predictive control (MPC) with updating-reference trajectory for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference trajectory, which passes through the desired points, is firstly designed as the tracking trajectory within a batch. The updating control law consists of P-type ILC part and MPC part, in which P-type ILC part can improve the performance by learning from previous executions and MPC part is used to suppress the model perturbations and external disturbances. Convergence properties of the integrated predictive iterative learning control (IPILC) are analyzed theoretically, and the sufficient convergence conditions of output tracking error are also derived for a class of linear systems. Comparing with other point-to-point tracking control algorithms, the proposed algorithm can perform better in robustness. Furthermore, updating-reference relaxes the constraints for system outputs, and it may lead to faster convergence and more extensive range of application than those of fixed-reference control algorithms. Simulation results on typical systems show the effectiveness of the proposed algorithm.     

一种间歇过程的综合预测迭代学习控制方法

为了提高迭代学习控制方法在间歇过程轨迹跟踪问题中的收敛速度,本文将批次间的比例型迭代学习控制与批次内的模型预测控制相结合,提出了一种综合应用方法.首先根据间歇过程的线性模型,预测出比例型迭代学习控制的系统输出,然后在批次内采用模型预测控制,通过极小化一个二次型目标函数来获得控制增量.该方法可使系统输出跟踪期望轨迹的速度比比例型迭代学习控制方法更快些.最后通过仿真实例验证了该方法的有效性.     

一类工业过程运行反馈优化控制方法

为了克服流程工业运行优化中控制回路闭环系统的动态误差对运行优化性能的影响,本文针 对一类工业过程提出了使运行指标实际值与目标值偏差和控制回路输出与设定值跟踪误差的二次性能 指标极小化的运行优化反馈控制方法. 该方法由运行层设定值反馈控制和回路控制层设定值跟踪控制组成,其中设定值反馈控制采用基于LMI的 模型预测控制,回路控制采用衰减率可调的带有积分项的状态反馈调节律. 本文给出了保证运行优化反馈控制闭环系统渐近稳定的充分条件,并开展了浮选过程运行优化反馈控制仿 真实验,实验结果表明所提方法的有效性.     

一类线性离散切换系统的迭代学习控制

考虑具有任意切换序列线性离散切换系统的迭代学习控制问题. 假设切换系统在有限时间区间内重复运行, P型ILC算法可实现该类系统在整个时间区间内的完全跟踪控制. 采用超向量方法给出了算法在迭代域内收敛的条件, 并在理论上分析了的收敛性. 仿真示例验证了理论的结果.     

HIGH-ORDER ILC WITH INITIAL STATE LEARNING FOR DISCRETE-TIME DELAYED SYSTEMS

This article addresses an iterative learning control (ILC) design for a class of linear discrete-time systems with multiple time delays. In order to improve the tracking performance, we introduce a P-type high-order iterative learning algorithm that makes use of information from several previous iterations. An initial state learning scheme is proposed to eliminate the effect of the initialization error on the final tracking error. Furthermore, we establish a sufficient condition to ensure asymptotic convergence. A simulation example is also provided to illustrate the effectiveness of the proposed result.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.     

Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties

This paper proposes the design of the integrated output feedback and iterative learning control (ILC) for batch processes with uncertain perturbations and interval time-varying delays, where the main idea is to transform the design into a robust delay-range-dependent H_∞ control of a 2D system described by a state-space model with varying delays. A sufficient criterion for delay-dependent H_∞ noise attenuation is derived through linear matrix inequality (LMI) by introducing a comprehensive 2D difference Lyapunov–Krasovskii functional candidate and adding a differential inequality to the difference in the Lyapunov function for the 2D system. Based on the criterion obtained, the delay-range-dependent output feedback controller combined with ILC is then developed. The developed system ensures that the closed-loop system for all admissible uncertainties is asymptotically stable and has a prescribed H_∞ performance level in terms of the LMI constraint. The controller is obtained by solving an LMI optimization problem with simple calculations and less constraint conditions. Moreover, the conditions can also be directly extended from delay-range-dependent to general delay-dependent stability. Applications in injection velocity control demonstrate the effectiveness and feasibility of the proposed method.     

机械臂带角度修正的开闭环迭代学习轨迹跟踪控制

在迭代学习控制研究中, 通常的一个假设是: 系统每次迭代初态与期望初态一致或迭代初态固定. 针对迭代学习控制律在迭代初态的限制下难以应用到机械臂轨迹跟踪控制中的问题, 本文对机械臂系统模型降阶变换, 将其转化为低阶系统. 对于变换设计后的机械臂系统模型, 提出一种带有角度修正的开闭环迭代学习控制算法, 该算法利用误差信号及相邻两次误差的偏差信号对系统控制律进行逐次修正, 与常规P型算法相比, 充分利用了系统已存的和当前的有效信息, 与常规PD型算法相比, 避免了由于微分作用而带来的不稳定影响. 同时, 用输出向量的角度关系作为评估控制输入好坏的标准对所设计的迭代学习律的变化趋势进行“奖-惩”, 从而实现了良好的跟踪效果并具有较快的收敛速度. 本文还针对机械臂系统存在关节转角限位的情况对控制算法进行改进, 以使机械臂在实际运作中真正实时地完成指定工作任务. 仿真结果表明了所提控制策略的有效性.     

On iterative learning control design for tracking iteration-varying trajectories with high-order internal model

In this paper, iterative learning control (ILC) design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models (HOIM). An HOIM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOIM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.     

IMC-based iterative learning control for batch processes with uncertain time delay

Based on the internal model control (IMC) structure, an iterative learning control (ILC) scheme is proposed for batch processes with model uncertainties including time delay mismatch. An important merit is that the IMC design for the initial run of the proposed control scheme is independent of the subsequent ILC for realization of perfect tracking. Sufficient conditions to guarantee the convergence of ILC are derived. To facilitate the controller design, a unified controller form is proposed for implementation of both IMC and ILC in the proposed control scheme. Robust tuning constraints of the unified controller are derived in terms of the process uncertainties described in a multiplicative form. To deal with process uncertainties, the unified controller can be monotonically tuned to meet the compromise between tracking performance and control system robust stability. Illustrative examples from the recent literature are performed to demonstrate the effectiveness and merits of the proposed control scheme.