基于改进型有限时间LQR的平衡车控制研究

Design of optimal controller for balanced vehicle based on improved LQR

针对平衡车启动及停止时发生抖动的问题开展了相应的研究.通过建立系统动力学模型,设计了系统的改进型有限时间LQR(LQR, Linear Quadratic Regulator)控制器;对系统矩阵及控制矩阵进行改进,增加小范围增量矩阵,系统能够实现自适应调节,并使最优控制率在小范围内可调,进而使性能指标达到最佳;通过仿真计算并选取最佳的加权矩阵Q和R,使性能指标达到最优.仿真实验表明该方法具有可行性和实用性,解决了小范围不稳定情况,有效克服了超调量过大而引起的不稳定.

In this paper, a systematic study is made on the jitter problem of balancing vehicle when starting and stopping. The improved LQR (LQR, Linear Quadratic Regulator) controller is designed by establishing the system dynamics model. The system matrix and control matrix are improved to increase the matrix of small range increment, the system realizes the adaptive adjustment, and the optimal control rate is adjustable in a small range so as to achieve the best performance index. The improved method solves the small-scale instability and effectively overcomes the instability of the overshoot. We can find the Q and R values that make the best performance by the simulation calculation of different Q and R. Through the simulation calculation and selecting the appropriate weight matrix Q and R, the performance index is optimized. Simulation experiments show that the method is feasible and practical.