基于遗传算法的环形二级倒立摆LQR控制

LQR Control of Circular-Rail Double Inverted Pendulum Based on Genetic Algorithm

在环形二级倒立摆系统中,基于线性二次型调节器(Linear Quadratic Regulator,LQR)理论,探讨了控制器中的加权矩阵Q和R的选择策略,针对试探法选取Q和R矩阵所带来的不足,提出采取智能控制算法进行寻优的问题.从控制效果出发,采用遗传算法对Q和R矩阵进行优化.算法首先选取二次型性能指标J作为个体适应值,改进了初始种群的选取,用不等长度的基因来编制算法.由理论分析和MAT-LAB仿真结果可知,该算法满足了控制指标要求,使上下两级摆杆阶跃响应的超调量减少了14%,运行实验同样实现了摆杆和水平连杆的良好控制效果,理论与实践均表明了该优化方法的有效性.

An optimal controller was designed based on linear quadratic regulator（LQR） for the circular rail double inverted pendulum, and the strategy of selecting the weighted matrix Q and R by experiments was investigated. For the shortcomings of the trial method strategy, intelligent control was proposed to searching the optimized value. Taking control effect as the starting point, an genetic algorithm to optimize the matrix was adopted. In the algorithm the quadratic performance indicator J was used as the individual adaptive value in the LQR, the selection of initial population was improved and the gene in the matrix was ranging in length. The theoretical analysis and simulation by MATLAB demonstrate that, the algorithm makes the control requirements satisfied, the step response overshoot of the two vertical poles reduces 14% on the average, and the running experiments achieve well controlled of the two vertical poles and the level rod.