中文摘要：

针对传统LQR最优控制器权重矩阵确定困难以及由此导致的响应速度慢等问题,以具有多变量、强耦合、非线性特点的两轮自平衡小车为被控对象,提出了一种通过遗传算法实现LQR控制器参数寻优的方法。选择线性二次型性能指标为目标函数,利用遗传算法的全局优化搜索能力,获取权阵Q的最优解,从而设计状态反馈控制率K,搭建系统动力学模型进行仿真实验。实验结果表明：该方法设计的最优控制器相对于传统的极点配置和LQR方法具有更好的控制效果,系统响应速度更快,超调更小。

英文摘要：

Aiming at the problem of difficulty to determine the weighting matrix for a conventional linear quad- ratic regulator（LQR）optimal controller and the slow response caused by this difficulty, a two-wheel self-balan- cing vehicle with muhivariable, strongly coupling, non-linear characteristics is used as a controlled object, puts forward a parameter optimization method of LQR controller based on genetic algorithm. Choosing the line- ar quadratic performance index as a objective function, the optimal solution of weighting matrix Q is obtained by using global optimization search ability of genetic algorithm. Thus, the state feedback control rate K can be designed, and a dynamical model for the simulation experiment of a system will be built. The results indicate that the GA-LQR controller has a better control effect than a traditional pole placement and an LQR controller, and that the system has more quick response speed and smaller overshoot.