School of Automation, Central South University, Changsha, Hunan 410083, China.
School of Automation, Central South University, Changsha, Hunan 410083, China.
ISA Trans. 2019 Oct;93:255-267. doi: 10.1016/j.isatra.2019.02.035. Epub 2019 Mar 8.
In general, the online computation burden of robust model predictive control (RMPC) is very heavy, and the mechanical model of a plant, which is used in RMPC, is hard to obtain precisely in real industry. These issues may largely restrict the applicability of RMPC in real applications. This paper proposes a RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model-based efficient robust predictive control (RBF-ARX-ERPC) approach to an inverted pendulum system, which is a complete and systematic method for designing robust MPC controller because it integrates the RBF-ARX modeling method and a fast RMPC approach. First, based on the offline identified RBF-ARX model without offset term, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, the optimization problem of implementing a quasi-min-max MPC algorithm including several linear matrix inequalities (LMIs) is formulated, and it is solved offline to synthesize a sequence of explicit control laws that correspond to a sequence of asymptotically stable invariant ellipsoids, of which all the optimization results are stored in a look-up table. During the online real-time control, the controller only needs to carry out a simple state-vector computation and bisection search. The proposed approach is applied to an actual linear one-stage inverted pendulum (LOSIP), which is a fast-responding and nonlinear plant. The real-time control experiments demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RMPC approach.
一般来说，鲁棒模型预测控制（RMPC）的在线计算负担非常重，并且在实际工业中，用于 RMPC 的植物机械模型很难精确获得。这些问题可能会在很大程度上限制 RMPC 在实际应用中的适用性。本文提出了一种基于 RBF-ARX（状态相关的自回归模型，具有外生输入和径向基函数网络类型系数）模型的高效鲁棒预测控制（RBF-ARX-ERPC）方法，用于倒立摆系统，这是一种设计鲁棒 MPC 控制器的完整而系统的方法，因为它集成了 RBF-ARX 建模方法和快速 RMPC 方法。首先，基于没有偏置项的离线识别的 RBF-ARX 模型，构建了两个凸多面体集合来包围系统的全局非线性行为。然后，制定了实施准最小最大 MPC 算法的优化问题，该算法包括几个线性矩阵不等式（LMIs），并离线求解以综合一系列显式控制律，这些控制律对应于一系列渐近稳定的不变椭球，所有的优化结果都存储在一个查找表中。在在线实时控制期间，控制器只需要进行简单的状态向量计算和二分搜索。所提出的方法应用于实际的一阶线性倒立摆（LOSIP），这是一个快速响应和非线性的植物。实时控制实验证明了所提出的基于 RBF-ARX 模型的高效 RMPC 方法的有效性。
