变参考轨迹下的鲁棒迭代学习模型预测控制

迭代学习模型预测控制是针对间歇过程的先进控制方法.它能通过迭代高精度跟踪给定参考轨迹,并保证时域上的闭环稳定性.然而,现有的迭代学习模型预测控制算法大多基于线性/线性化系统,且没有考虑参考轨迹变化的情况.本文基于线性参变系统提出一种能有效跟踪变参考轨迹的鲁棒迭代学习模型预测控制算法.首先,采用线性参变模型准确涵盖原始非线性系统的动态特性.然后,将鲁棒H_∞控制与传统迭代学习模型预测控制相结合,抑制变参考轨迹带来的跟踪误差波动,通过优化线性矩阵不等式约束下的目标函数求得控制输入.深入分析了鲁棒迭代学习模型预测控制的鲁棒稳定性和迭代收敛性.最后,通过对数值例子和连续搅拌反应釜系统的仿真验证了所提出算法的有效性.     

离散非线性系统的迭代学习轨迹跟踪鲁棒算法优化及应用

针对一类存在随机输入状态扰动、输出扰动及系统初值与给定期望值不严格一致的离散非线性重复系统,提出了一种P型开闭环鲁棒迭代学习轨迹跟踪控制算法．基于λ范数理论证明了算法的严格鲁棒稳定性,并通过多目标函数性能指标优化P型开闭环迭代学习控制律的增益矩阵参数,保证了优化算法下系统输出期望轨迹跟踪误差的单调收敛性,达到提高学习算法收敛速度和跟踪精度的目的．最后应用于二维运动移动机器人的实例仿真,验证了本文算法的可行性和有效性．     

一种参数优化的非线性离散系统鲁棒迭代学习控制方法

针对带有扰动的一类离散非线性系统的鲁棒迭代学习控制问题, 设计一种基于参数优化的迭代学习控制算法. 该算法能够保证在有初始状态误差和状态、输出扰动的情况下使闭环系统具有鲁棒BIBO 稳定性, 系统输出能够单调收敛于给定输出轨迹的邻域内; 在没有初始状态误差和扰动的情况下能够以零稳态误差跟踪给定输出轨迹. 最后通过仿真分析验证了所提出算法的有效性.

     

参考轨迹更新的点到点迭代学习控制算法优化及应用

针对受非重复扰动作用的离散线性系统的输出跟踪控制问题,提出一种基于参考轨迹更新的点到点迭代学习控制算法.首先通过构建性能指标函数对控制器进行范数优化,并给出相应的收敛性条件,使得系统输出能够跟踪上更新后参考轨迹处的期望点.其次,当系统输出端受到某批次非重复扰动的影响时,进一步通过引入拉格朗日乘子算法构造多目标性能指标函数,以优化鲁棒迭代学习控制器,达到提高收敛速度和跟踪精度的目的.最后将该算法应用于电机驱动的单机械臂控制系统中,仿真结果验证了算法的合理性和有效性.     

一类非线性系统的误差轨迹跟踪鲁棒学习控制算法

针对一类含非参数不确定性的非线性系统,提出一种鲁棒迭代学习控制算法,该算法放宽了常规迭代学习控制方法的初始定位条件,迭代初值可任意取值.基于类Lyapunov方法设计误差轨迹跟踪控制器,通过鲁棒限幅学习机制对不确定性进行估计和补偿,能够在整个作业区间上实现误差对给定期望误差轨迹的精确跟踪,期望误差轨迹根据迭代起始时刻的误差值设置.利用期望误差轨迹的衰减性状,可使系统误差在预设的时间点后收敛于原点的邻域内,邻域半径的大小可根据需要任意设置.理论分析和仿真结果表明了控制方法的有效性.     

基于滑模迭代学习的永磁同步电动机鲁棒控制

永磁同步电机(PMSM)是一个典型的非线性、多变量、强耦合系统,对外界扰动及内部参数变化较为敏感.针对常规PI控制器参数整定困难,且对永磁同步电机非线性补偿有限,采用一种结合迭代学习控制与滑模变结构技术的控制器,用于永磁同步电机系统的鲁棒速度跟踪.迭代学习控制通过重复执行同一任务来减少误差,使系统输出尽可能逼近理想值,结合滑模变结构控制响应快、对参数变化及扰动不敏感等优点很好的解决了鲁棒性问题.试验结果证明了该方法的有效性和正确性.     

非最小相位系统的基函数型自适应迭代学习控制

针对重复运行的未知非最小相位系统的轨迹跟踪问题, 结合时域稳定逆特点, 提出了一种新的基函数型自适应迭代学习控制(Basis function based adaptive iterative learning control, BFAILC)算法. 该算法在迭代控制过程中应用自适应迭代学习辨识算法估计基函数模型, 采用伪逆型学习律逼近系统的稳定逆, 保证了迭代学习控制的收敛性和鲁棒性. 以傅里叶基函数为例, 通过在非最小相位系统上的控制仿真, 验证了算法的有效性.     

一种基于反步法的鲁棒自适应终端滑模控制

针对不确定严格反馈块控非线性系统, 提出了一种基于反步法的鲁棒自适应终端滑模变结构控制方法. 系统的未知不确定及外界干扰由模糊系统在线逼近, 利用反步法设计了变结构控制的终端滑模面, 并由此得到了鲁棒自适应终端滑模控制器, 使系统的跟踪误差在有限时间内趋于给定轨迹的任意小的邻域内. 通过Lyapunov定理证明了闭环系统所有信号最终有界. 对某战斗机6自由度机动仿真结果表明, 该方法具有强鲁棒性.     

一类非线性时变系统的迭代学习控制

针对一类具有任意初态的不确定非线性时变系统,应用校正期望轨迹方法把任意初态问题转换为零初始误差的变期望轨迹的迭代学习控制问题,提出了求解校正期望轨迹的过渡轨迹的计算方法.然后,针对变期望轨迹问题提出了一种新的迭代学习控制算法,在算法中引入了期望轨迹的高阶导数来克服期望轨迹的变化,并通过设计稳定的跟踪误差滑动面来处理系统中非线性时变不确定性.论文给出了相关定理,并应用类Lyapunov方法给出了详细证明.仿真结果表明所提出的算法是有效的,该算法不需要系统的模型结构信息,比自适应迭代学习控制算法具有更宽的适用范围.     

初态学习下的迭代学习控制

提出一种新的初态学习律，以放宽常规迭代学习控制方法的初始定位条件．它允许一定的定位误差，在迭代中不需要定位在某一具体位置上，使得学习控制系统具有鲁棒收敛性．针对二阶LTI系统，给出了输入学习律及初态学习律的收敛性充分条件．依据收敛性条件，学习增益的选取需系统矩阵的估计值，但在一定建模误差下，仍能保证算法的收敛性．所提出的初态学习律本身及其收敛性条件均与输入矩阵无关．     

A guaranteed monotonically convergent iterative learning control

This paper presents a new iterative learning control (ILC) scheme for linear discrete time systems. In this scheme, the input of the controlled system is modified by applying a semi‐sliding window algorithm, with a maximum length of n + 1, on the tracking errors obtained from the previous iteration (n is the order of the controlled system). The convergence of the presented ILC is analyzed. It is shown that, if its learning gains are chosen proportional to the denominator coefficients of the system transfer function, then its monotonic convergence condition is independent of the time duration of the iterations and depends only on the numerator coefficients of the system transfer function. The application of the presented ILC to control second‐order systems is described in detail. Numerical examples are added to illustrate the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust monotone gradient‐based discrete‐time iterative learning control

This paper considers the use of matrix models and the robustness of a gradient‐based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data‐dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean‐square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well‐known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non‐causal controller dynamics. The results are compared with recently published results for robust inverse‐model‐based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high‐frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.     

测量数据丢失的一类非线性系统迭代学习控制

迭代学习控制方法应用于网络控制系统时,由于通信网络的约束导致数据包丢失现象经常发生.针对存在输出测量数据丢失的一类非线性系统,研究P型迭代学习控制算法的收敛性问题.将数据丢失描述为一个概率已知的随机伯努利过程,在此基础上给出P型迭代学习控制算法的收敛条件,理论上证明了算法的收敛性,并通过仿真验证理论结果.研究表明,当非线性系统存在输出测量数据丢失时,迭代学习控制算法仍然可以保证跟踪误差的收敛性.     

数据丢失对迭代学习控制的影响分析

针对一类线性系统,分析数据丢失对迭代学习控制算法的影响.首先基于lifting方法给出跟踪误差渐近收敛和单调收敛的条件,并分析收敛速度与数据丢失率的关系,结果表明收敛速度随着数据丢失程度的增加而变慢.其次,为抑制迭代变化扰动的影响,给出一种存在数据丢失时的鲁棒迭代学习控制器设计方法,并将控制器设计问题转化为求取线性矩阵不等式的可行解.仿真示例验证了理论分析的结果以及鲁棒迭代学习控制算法的有效性.

     

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.     

Learning control for discrete-time nonlinear systems with sensor saturation and measurement noises

The iterative learning control (ILC) is investigated for a class of nonlinear systems with measurement noises where the output is subject to sensor saturation. An ILC algorithm is introduced based on the measured output information rather than the actual output signal. A decreasing sequence is also incorporated into the learning algorithm to ensure a stable convergence under stochastic noises. It is strictly proved with the help of the stochastic approximation technique that the input sequence converges to the desired input almost surely along the iteration axis. Illustrative simulations are exploited to verify the effectiveness of the proposed algorithm.     

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.     

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.     

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.