Data-based iterative learning control for multiphase batch processes

In order to cope with the problem of the robustness conditions dependence on system parameters information, this paper investigates a data-based iteration learning control (ILC) for multiphase batch processes with different dimensions and system uncertainty. Firstly, by minimizing the residual between the actual subsystem output and the approximated subsystem output, a gradient-type approximation law is designed to approximate the system lower triangular parameters matrix and initial state. Secondly, by minimizing the approximated tracking error between the desired trajectory and the approximated output, a data-based ILC is constructed in an interactive mode with the approximation law. Finally, the boundedness of the approximation error of the real system parameters from the approximated parameters is derived by means of vector norm theory, while the unconditional robustness of the proposed data-based ILC is proved. Simulation results illustrate the effectiveness and practicability of the proposed data-based ILC.     

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.     

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

Average dwell time-based optimal iterative learning control for multi-phase batch processes

Multi-phase batch process plays an important role in modern industry, especially for processes with different dimensional phases. As the different phases may interact with each others deeply, when and how to perform the transfer between adjacent phases highly affect the control performance and product quality. Meanwhile, the running time in different phases influence the production efficiency. Therefore it is of crucial importance to study the control of multi-phase batch processes with time constraints. Take the injection molding process as an example, a multi-phase batch process can be regarded as a switched system with different-dimensional subsystems in each batch. In this paper, the multi-phase batch process is converted to an equivalent two-dimensional (2D) switched system and the repetitive and 2D nature of batch processes is explored. Within the framework of 2D system theory, both the exponential stability and the shortest running time are considered. Meanwhile, a compound 2D controller with optimal performance is designed. The contributions of this paper are as follows: (1) the batch process studied is with different dimensions in each phase. (2) using the average dwell time method, a sufficient condition ensuring the exponential stability is obtained, meanwhile, the minimum running time of each subsystem, i.e., the running time of each phase can be calculated. Finally, the proposed method is illustrated with an injection molding process to show the effectiveness.     

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.     

执行器故障多率采样间歇过程的鲁棒 耗散迭代学习容错控制

针对一类具有干扰和执行器故障的多率采样间歇过程,提出一种具有鲁棒耗散性能的迭代学习容错控制算法.通过提升技术将多采样率过程用慢速率采样的状态空间模型来描述,并基于二维系统理论,把迭代学习控制过程转化为等价2D Roesser故障系统,再沿时间和迭代方向设计具有耗散性能的反馈容错控制器,并以线性矩阵不等式形式给出容错控制器存在的充分条件,同时确保多率采样间歇过程在正常和故障条件下的耗散性能.注塑过程的注射速度控制仿真验证了方法的有效性和可行性.     

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.     

间歇生产过程的R调节学习控制

针对间歇生产过程迭代学习控制难以进行跟踪性能分析的难题,本文提出一种变R调节迭代学习控制算法,借鉴经典控制理论定义有界跟踪和零跟踪概念.以此研究能够让系统输出误差达到零跟踪的迭代学习控制策略,并严格地证明了算法的性能,得出可以通过调节权值R使过程产品质量的误差收敛到与模型精度相关联的有界区域的结论,为相关理论结果实施于实际间歇过程提供了理论依据.     

Performance assessment of decentralized control systems: An iterative approach

In this work, an efficient approach for performance assessment of decentralized control systems based on a general quadratic performance index involving both system states and inputs is proposed. The performance assessment problem is formulated as an optimization problem subject to constraints in the form of linear/bilinear matrix inequalities which explicitly take the block-diagonal structural constraint on decentralized control systems into account. In order to solve the optimization problem efficiently, an iterative approach based on the original optimization problem and an equivalent transformation of the original one is proposed. Specifically, the proposed approach under the assumption that the full state feedback is available is first presented; and then the approach is extended to the case that only output feedback is available. The proposed approach solves for both the best achievable performance and the corresponding controller (and observer) gains. The application of the proposed approach to two examples including a reactor–separator chemical process example illustrates the applicability and effectiveness of the proposed approach.     

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.     

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.     

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.     

Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays

A robust feedback integrated with iterative learning control (FILC) scheme for batch processes with uncertain perturbations and interval time-varying delay is developed. The batch process is modeled as a two-dimensional (2D) Rosser system with a delay varying in a range. The design of FILC scheme is transformed into a robust control problem of uncertain 2D system. New delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities (LMIs), which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. Applications to injection velocity control show that the proposed FILC achieve the design objectives well.     

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