Abstract: The secondary pump differential pressure control in the Variable Air Volume（VAV） air conditioning system can effectively reduce energy consumption. In order to overcome secondary pump model uncertainty, and improve the response speed and precision of secondary pump frequency control, it uses robust Model Predictive Control（MPC） strategy based on the Linear Matrix Inequality（LMI）. The algorithm can be divided into offline and online parts. The upper bound of the objective function is set as a known quantity which is obtained by offline algorithm, and re-optimizes to get a sequence of asymptotically larger stable invariant ellipsoid sets. According to the measured current state variables online at each sampling period, the position of the state variables can be accurately located to obtain the system control variable by three adjacent ellipsoid sets. In this paper, the online optimization theory is proven rigorously. Simulation results indicate that the algorithm is more effective than traditional algorithm. The experiment results of secondary pump differential pressure control show that the new algorithm can get bigger feasible domain, faster system response and better control effect.

Key words: variable air volume air conditioning system, model predictive control, differential pressure control, linear matrix inequality, robustness, optimization

摘要： 在变风量空调系统中二次泵压差控制可以有效地减少空调能耗，为克服二次泵模型的不确定性，提高二次泵变频调速控制的响应速度和精度，采用基于线性矩阵不等式的鲁棒预测控制策略。算法分为离线和在线两个部分，离线时首先用传统算法得出目标函数上界，以此为已知量重新优化得到一系列较大的渐近稳定的不变椭圆集。在线时，每个采样周期用三个相邻的椭圆集优化来对状态变量进行精确定位，并给出控制量。给出在线优化的理论证明。通过和传统算法的仿真比较，表明该算法的有效性。二次泵压差控制的实验表明该算法可得到较大的可行域，系统响应快，控制效果好。

关键词: 变风量空调系统, 模型预测控制, 压差控制, 线性矩阵不等式, 鲁棒性, 优化