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.     

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.     

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.     

Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system

To improve stability and convergence, feedback control is often incorporated with iterative learning control (ILC), resulting in feedback feed-forward ILC (FFILC). In this paper, a general form of FFILC is studied, comprising of two feedback controllers, a state feedback controller and a tracking error compensator, for the robustness and convergence along time direction, and an ILC for performance along the cycle direction. The integrated design of this FFILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. To describe the stability and convergence quantitatively along the time and the cycle direction, the concepts of robust stability and convergence along the two axes are introduced. A series of algorithms are established for the FFILC design. These algorithms allow the designer to balance and choose optimization objectives to meet the FFILC performance requirements. The applications to injection molding velocity control show the good effectiveness and feasibility of the proposed design methods.     

执行器不确定系统鲁棒预测动态控制分配策略

针对多操纵面级联飞行控制结构中执行器存在多面体不确定的问题, 提出了一种基于鲁棒预测控制理论的动态控制分配策略. 考虑位置约束和速率约束, 建立了多面体不确定冗余执行器的增广控制模型; 以执行器状态和虚拟指令跟踪误差为增广变量构造二次型李亚普诺夫函数, 将无穷时域Min-Max非线性规划转化为线性矩阵不等式凸优化问题, 设计了保守性小的鲁棒预测控制律. 各个控制指令汇集到一个混合优化控制分配器, 由它分派控制指令, 以最优地补偿执行器的不确定动态特性. 仿真结果表明, 该策略可综合补偿执行器的多面体不确定性, 在操纵面偏转范围内精确地跟踪虚拟指令, 保证了闭环系统的稳定性, 具有较好的鲁棒性.     

Two-time dimensional dynamic matrix control for batch processes with convergence analysis against the 2D interval uncertainty

A batch process can be treated as a 2-dimentional (2D) system with a time dimension within each batch and a batch dimension from batch to batch. This paper integrates the learning ability of iterative learning control (ILC) into the prediction model of model predictive control (MPC). Based on this integrated model, a 2D dynamic matrix control (2D-DMC) algorithm with a feedback control and an optimal feed-forward control is proposed. The sufficient conditions for exponentially asymptotic and monotonic convergence of the proposed 2D-DMC are established with proof under certain assumptions, in the presence of not only the completely repeatable uncertainties but also the non-repeatable interval uncertainties. The effectiveness of the proposed control scheme is tested through simulation and experimental implementation in the context of injection molding, a typical batch process. The results show that the batch process control performance is significantly improved.     

Composite predictive flight control for airbreathing hypersonic vehicles

The robust optimised tracking control problem for a generic airbreathing hypersonic vehicle (AHV) subject to nonvanishing mismatched disturbances/uncertainties is investigated in this paper. A baseline nonlinear model predictive control (MPC) method is firstly introduced for optimised tracking control of the nominal dynamics. A nonlinear-disturbance-observer-based control law is then developed for robustness enhancement in the presence of both external disturbances and uncertainties. Compared with the existing robust tracking control methods for AHVs, the proposed composite nonlinear MPC method obtains not only promising robustness and disturbance rejection performance but also optimised nominal tracking control performance. The merits of the proposed method are validated by implementing simulation studies on the AHV system.     

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min–max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min–max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min–max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.     

Iterative learning control with Smith time delay compensator for batch processes

How to improve the control of batch processes is not an easy task because of modeling errors and time delays. In this work, novel iterative learning control (ILC) strategies, which can fully use previous batch control information and are attached to the existing control systems to improve tracking performance through repetition, are proposed for SISO processes which have uncertainties in modeling and time delays. The dynamics of the process are represented by transfer function plus pure time delay. The stability properties of the proposed strategies for batch processes in the presence of uncertainties in modeling and/or time delays are analyzed in the frequency domain. Sufficient conditions guaranteeing convergence of tracking error are stated and proven. Simulation and experimental examples demonstrating these methods are presented.     

永磁同步电机高效非线性模型预测控制

永磁电机控制器要求电机有很强的转速跟踪能力,并且要保证系统参数变化及负荷扰动下系统的鲁棒性. 永磁电机包含很多不确定因素,是强耦合的非线性系统,传统的线性控制器很难对其进行控制. 针对永磁电机的转速控制构造非线性模型预测控制方法. 非线性永磁电机模型通过输入-输出反馈线性化策略解耦成为新的线性系统. 为保证可行解的收敛性,提出一种迭代二次规划方法来处理由输入-输出反馈线性化导致的非线性约束. 仿真结果表明,控制器能有效降低计算负担,具有很好的动态控制性能,能抑制转矩脉动,并保证在参数变化和负荷扰动下控制系统的鲁棒性.     

Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min–max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min–max problem. By finding an upper bound of the worst-case performance, the min–max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

基于互补滑模控制和迭代学习控制的永磁直线同步电动机速度控制

为满足永磁直线同步电动机(PMLSM)伺服系统高速度高精度的要求,抑制不确定性对系统性能的影响,提出一种互补滑模控制(CSMC)和迭代学习控制(ILC)相结合的控制方法.该方法结合了CSMC强鲁棒性的优点和ILC跟踪精度高的特点,以CSMC中积分滑模面为基础设计新型迭代学习律,既可利用ILC对系统未建模动态进行估计,抑制端部效应、齿槽效应和摩擦力等周期不确定性的影响,又可利用CSMC减小参数变化和外部扰动等非周期不确定性对系统的影响,从而提高控制器的收敛速度和收敛精度,保证系统具有较强的速度跟踪性能.实验结果表明,该方法有效地提高了系统的动态响应能力,改善了速度跟踪精度.     

Linearized min‐max robust model predictive control: Application to the control of a bioprocess

This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.     

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.     

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.