Abstract A robust switched predictive control method is designed to deal with the multi-phase batch processes with the inevitable uncertainties, time-varying delay and unknown disturbances. Firstly, the output tracking errors are augmented into the state variables and then the improved robust switched predictive control law is established using the new augmented state variables. To this end, the novel switched system is built to represent the different phases of multi-phase batch processes. Secondly, making full use of the robust predictive control theory, Lyapunov function theory, switched system theory, linear matrix inequality (LMI) theory and mode-dependent average dwell time method, the sufficient conditions in terms of LMI constraints are derived to ensure that the switching system is asymptotically controllable and stable. During the process of derivation, based on the traditional performance indicators, the H-infinite performance index is introduced, so that the system in different phases can still operate stably under the uncertainty and external interference. The average dwell time and the control law gain of each phase are thus calculated by solving these LMI constrains. Ultimately, the simulation results on the injection molding process show that the proposed method can make the controlled system run stably.

中文翻译：

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具有不确定性和未知干扰的多阶段批处理的鲁棒切换预测控制

摘要 针对具有不可避免的不确定性、时变延迟和未知扰动的多相批处理过程，设计了一种鲁棒切换预测控制方法。首先将输出跟踪误差增加到状态变量中，然后利用新增加的状态变量建立改进的鲁棒切换预测控制律。为此，构建了新颖的切换系统来表示多阶段批处理的不同阶段。其次，充分利用鲁棒预测控制理论、李雅普诺夫函数理论、切换系统理论、线性矩阵不等式（LMI）理论和模态相关平均驻留时间法，推导出LMI约束的充分条件，以确保切换系统是渐近可控且稳定的。在推导过程中，在传统性能指标的基础上，引入了H-无限性能指标，使不同阶段的系统在不确定性和外界干扰下仍能稳定运行。因此，通过求解这些 LMI 约束来计算每个相位的平均驻留时间和控制律增益。最终，注射成型过程的仿真结果表明，所提出的方法可以使受控系统稳定运行。