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针对具有七自由度化学机械抛光传输机器人(CMPTR),运用拉格朗日方程和牛顿力学相结合的方法,建立非线性系统CMPTR的动力学模型.对模型进行泰勒级数展开,并线性化得CMPTR状态空间方程,便于使用LQ最优控制对其进行控制.其中性能指标是由各状态量的累积运动误差与控制量的代数和构成,通过寻找一条最优控制律使其最小,从而使CMPTR的精度和控制能量消耗都取得满意效果.仿真实验验证了系统的稳定性,也验证了系统建模和LQ控制器设计的合理性和有效性.
A kinematic model of nonlinear system CMPTR is established for CMPTR with seven degree-of-freedom chemical mechanical polishing by using the combination of Lagrange’s equation and Newton’s mechanics. The model is Taylor series expansion and linearized CMPTR state space equation, which is easy to control using LQ optimal control.Among them, the performance index is composed of the algebraic sum of the cumulative motion error and control quantity of each state quantity, and minimizes by finding an optimal control law so that CMPTR The accuracy and control energy consumption are satisfied.The simulation results verify the stability of the system and also verify the rationality and effectiveness of the system modeling and LQ controller design.