基于LMI的框架结构分数阶控制方法研究

以框架结构为研究对象，采用分数阶状态方程进行控制器设计，提出了基于LMI的分数阶控制器设计方法。首先，把原系统振动方程改为阶次为1～2的分数阶状态方程，同时，构造同阶次分数阶控制器状态方程，进而组装为一个整体状态方程；其次，根据分数阶系统稳定性条件确定满足系统渐进稳定性的不等式。为了获得可行解，在不等式中附加了两个参数，同时，令控制器参数矩阵为对称；再次，从仿真结果来看，控制效果过好，但控制力偏大，为此，控制力计算时附加了调节因子，以期在满足控制效果的基础上，降低所需控制力；最后给出了一个算例说明本文方法的可行性。

Research on fractional-order control method of frame based on LMI

In this paper, a frame is taken as the research object.The fractional order state equation(FOSE) is used to design the controller, and a LMI-based controller design method is proposed.The concrete ideas are as follows:first, the original system vibration equation is changed to the FOSE of order between 1~2 meanwhile, the fractional order controller state equation of the same order is constructed, and then is assembled into a whole state equation.Secondly, the inequality is acquired according to the stability condition of the fractional order system.In order to obtain a feasible solution, two parameters are added to the LMI, and the parameter matrix of the controller remains symmetric.Thirdly, from the simulation results, the control effects are better but the control force is larger, so an adjustment factor is suggested to reduce the control force under the condition of control demand.Finally, an example is given to illustrate the feasibility of the proposed method.