量化反馈系统的鲁棒预测控制

研究具有丢包的量化反馈系统的鲁棒预测控制器设计问题.所考虑的系统采用对数量化器,并给出了量化密度选择方法;网络中的丢包现象采用Bernoulli过程描述.主要目的是对控制信号进行量化,同时考虑量化后数据在网络传输过程中的丢包问题.设计了基于线性矩阵不等式(LMI)方法的鲁棒预测控制算法求解控制器,使得闭环系统渐近稳定,并满足一定的预测性能指标.最后通过仿真研究验证了所提出方法的有效性.     

饱和约束系统的鲁棒模型预测控制

针对饱和约束系统提出了一种鲁棒模型预测控制算法,分别考虑了多面体不确定性和结构反馈不确定性.考虑无穷时域的最坏二次性能指标,通过采用带有饱和特性的反馈控制结构,将控制律的求解转化为一个在线的线性矩阵不等式优化问题.初始时刻优化问题的可行性保证了闭环控制系统的鲁棒稳定性.最后的仿真结果说明了算法的优越性.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

离散不确定系统的鲁棒预测控制

对预测控制中模型不确定性的处理一直是预测控制算法亟待解决的问题.考虑一类包含模型不确定性的控制对象模型,提出一种极大极小预测控制器设计方法.在滚动优化的每一步,考虑了状态变量不完全可测的情况,引入动态输出反馈的思想得到一个最坏条件下的性能指标的最优解,以最坏条件下的性能指标为求解优化问题的上界,通过线性矩阵不等式的方法求解凸优化问题.并从理论上证明了所设计的鲁棒预测控制器对不确定模型是稳定的.通过仿真算例的分析,证明了极大极小鲁棒预测控制器设计的有效性.     

基于LMI的航空发动机鲁棒弹性保性能控制

针对范数有界不确定性系统设计鲁棒弹性保性能控制器,将鲁棒弹性保性能控制器的设计问题转化为线性矩阵不等式（LMI）的可行解问题。以LMI的形式给出了鲁棒弹性保性能控制器存在的充分必要条件及控制器的设计步骤,并将该方法用于某型双转子涡喷发动机稳态双变量控制仿真,利用LMI/Matlab工具箱进行数值求解。既保持了鲁棒性也解决了传统鲁棒控制器的脆性问题,在系统和控制器增益存在摄动的情况下仍然保持稳定性和良好的性能指标。     

一种改进的鲁棒约束预测控制器的综合设计方法

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.高线设计多包系统worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的rain-max优化问题.设计方法采用了时变的终端约束集,扩大了初始可行域,并能获得较优的控制性能.仿真结果验证了该方法的有效性.     

执行器随机失效系统鲁棒预测容错切换控制

针对一类具有执行器随机失效问题的离散线性系统,提出一种基于故障概率情况下的鲁棒预测容错切换控制方法。首先,将工业过程建立成新型多自由度状态空间模型,设计含有故障概率的容错控制器;其次,引入系统故障和其恢复时的随机概率,利用李雅普诺夫判据给出基于线性矩阵不等式形式的稳定性条件,再通过指数稳定的相关证明求解出不同执行器切换时的稳定条件,以保证系统故障时容错控制与无故障时常规控制间的切换;然后,控制器设计时还充分考虑了设定值变化时所产生的跟踪误差带来的影响。最后,通过仿真结果验证了所提方法的可行性。     

基于状态观测器的直接约束鲁棒预测控制

针对多包描述线性离散不确定系统,提出一种在系统状态不可测时的直接约束鲁棒预测控制算法.将控制器与观测器综合设计,利用观测状态直接构造性能指标,通过求解无穷时域性能指标的最小最大优化问题,得到系统的最优状态反馈控制律.采用参数依赖Lyapunov函数,在满足输入和状态约束的情况下保证闭环系统稳定.仿真结果验证了算法的有效性.     

基于LMI的多模型鲁棒预测控制

用线性矩阵不等式 (LMI)方法研究多模型鲁棒预测控制, 提出了状态反馈的综合方法, 并分析了闭环系统的可行性, 同时证明闭环系统渐近稳定. 在此基础上, 研究了带终端零状态的有限优化时域预测控制和无穷优化时域预测控制的性能, 证明了两者在性能上的一致性.     

时变轨迹下工业过程鲁棒模糊预测控制

针对具有不确定性、外界未知干扰和跟踪轨迹变化的非线性工业过程,提出一种时变轨迹鲁棒模糊预测控制方法。该方法将非线性工业过程根据模糊规则表示为Takagi-Sugeno(T-S)模糊模型,并扩展输出跟踪误差到模糊模型中得到新型多自由度状态空间模型。针对扩展模型设计控制器,并给出基于线性矩阵不等式形式的稳定性充分条件,通过求解稳定性条件中参数计算对应子模型的控制律,并根据当前时刻的系统状态确定每个子模型和控制律的权值。同时,由于在实际生产过程中被控变量需要根据外界变化来实时调节,在设计控制器时充分考虑跟踪轨迹变化的影响。在啤酒发酵罐温度系统仿真研究结果表明设计的控制器能够满足控制需求,保证系统的稳定性和最优性能。     

离线鲁棒预测控制器综合方法的改进方案

对离线鲁棒预测控制器综合方法进行改进.离线鲁棒预测控制算法离线确定一个控制律序列,对应一组吸引域;在线根据当前状态位于哪个吸引域内部(或哪两个吸引域之间)选择相应的一个控制律(或相邻的两个控制律的线性插值).引入参数Lyapunov函数得到多包椭圆型吸引域和多包二次稳定的离线控制律,改进了控制器的可行性和最优性.改进的控制器保持了稳定性以及控制律关于系统状态的连续性.     

Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches

This paper proposes a fault-tolerant control scheme for linear systems with mismatched uncertainties which are assumed to be norm-bounded, affine and polytopic, respectively. The linear fractional transformation (LFT) and linear matrix inequality (LMI) techniques are introduced to handle the mismatched uncertainties, and the adaptive techniques are used to compensate actuator faults. By using the cone complementary linearisation algorithm, the resulting stability criteria are converted into solvable ones. Then, on the basis of Lyapunov stability theory, it is shown that the solutions to the closed-loop system and error system are uniformly bounded, especially, the states converge asymptotically to zero. Finally, simulations are given to illustrate the effectiveness and advantages of the proposed theoretical results.     

汽轮机系统的鲁棒预测控制仿真研究

为了进一步提高汽轮机的动态控制性能，本文在阐述了汽轮机的数学模型的基础上。提出将鲁棒广义预测自校正控制算法应用于汽轮机的转速控制中，包括控制结构和控制器设计。仿真结果显示当核动力装置模型失配时，鲁棒广义预测控制能够提高汽轮机系统的鲁棒稳定性。表明所采用的鲁棒广义预测控制算法能够较好的控制汽轮机主要参数的输出，对蒸汽轮机模型的不确定性具有良好的适应性和鲁棒性。     

A new robust model predictive control method I: theory and computation

The success of the single-model MPC (SMPC) controller depends on the accuracy of the process model. Modeling errors cause sub-optimal control performance and may cause the control system to become closed-loop unstable. The goal of this paper is to examine the control performance of the robust MPC (RMPC) method proposed by Wang and Rawlings [34] on several illustrative examples. In this paper, we show the RMPC method successfully controls systems with time-varying uncertainties in the process gain, time constant and time delay and achieves offset-free non-zero set point tracking and non-zero disturbance rejection subject to input and output constraints.     

Tube‐based robust nonlinear model predictive control

This paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Tube-based robust economic model predictive control

In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. Instead of simply transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework, we rather propose to consider the influence of the disturbance explicitly within the design of the MPC controller, which can lead to an improved closed-loop average performance. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that the algorithm enjoys similar properties as a nominal economic MPC algorithm (i.e., without disturbances), in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system, as well as stability and optimal steady-state operation.     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

Design of robust model predictive control with input constraints

This article addresses the problem of designing a robust output feedback model predictive control (MPC) with input constraints, which ensures a parameter-dependent quadratic stability and guaranteed cost for the case of linear polytopic systems. A new heuristic method is introduced to guarantee input constraints for the MPC. To reject disturbances and maintain the process at the optimal operating conditions or setpoints, the integrator is added to the controller design procedure. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.