LMI Based Gain-Scheduled Sliding Mode Control for Nonlinear and Time Varying Systems

变结构系统或滑模控制使用不连续控制结构来控制非线性系统。它是一种功能强大的控制方法，在控制工程的许多领域中得到越来越多的应用。增益调度是一种特殊类型的非线性反馈，用于各种控制。鲁棒控制理论的最新进展提供了一个新的理论框架和系统增益的确定，线性参数变（LPV）对象可以被描述为线性时变对象或非线性对象的模型，这些对象可以用一个时变参数向量（如theta（t））线性化。利用LPV被控对象的定义，将增益调度H_* 控制设计问题广泛地表示为线性矩阵不等式（LMI）问题，其解属于有效的凸优化技术的范畴。在这里，我们的目标是将这种方法扩展到设计一个滑模超平面，并将其应用到一个实际的系统。对于LPV对象给出的所有定义和定理在我们的研究中也有效，这里不再重复。本研究项目涉及一类线性变参数（LPV）对象的滑动模式超平面设计，其状态空间矩阵是时变物理参数的仿射函数。所提出的超平面，涉及线性矩阵不等式（LMI）的方法，具有连续的动态，由于调度参数，并提供稳定性和鲁棒性对参数的不确定性，我们已经设计了一个时变超平面的转子磁轴承系统的陀螺效应，这可以被认为是一个LPV植物由于参数依赖于转速。所获得的超平面相对于旋转速度被连续调度。我们成功地进行了实验，使用商业上可获得的分子泵系统和结果是合理的和良好的。

A variable structure system or sliding mode control uses a discontinuous control structure to control nonlinear systems. It is a powerful control method with increasing application in many areas of control engineering. Gain scheduling is a special type of nonlinear feedback used in a variety of control. Recent advances in robust control theory have offered a new theoretical framework and systematic gain scheduling.A linerar parameter-varying (LPV) plant definition can be described as model of linear time-varying plants or nonlinear plants which are linearized using a vector of a time-varying parameter, such as theta(t). Using LPV plant definition, the gain scheduled H_* contol design is extensively presented in terms of linear matrix inequalitiees (LMI's), the solution of which are within the scope of efficient convex optimization techniques. Here, our aims are to extend this approach to designing a sliding mode hyperplane and applying it to a practical system. All definitions and theorems given for LPV plants are also valid in our study and will not be repeated here.This reserach project deals with slidiing mode hyperplane design for a class of linearr parameter-varying (LPV) plants, the state-space matrices' of which are an affine function of time varying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertainties, We have designcd a time-varying hyperplane for a rotor-magnetic bearing system with a gyroscopic effect, which can be considered an LPV plant due to parameter dependence on rotational speed. The obtained hyperplane is continuously scheduled with respect to rotational speed. We successfully carried out experiments using a commercially available turbomolecular pump system and results were reasonable and good.