Hexapod平台构型与振动控制一体化设计研究

基于Hexapod平台雅可比矩阵条件数最优条件，将平台构型——振动控制一体化设计问题转化为从满足条件数最优条件的构型中选择振动控制能耗指标最小的优化问题。优化模型以自适应扰动消减(Adaptive disturbance canceller, ADC)振动控制步长参数、Hexapod下平台半径、铰点半夹角为设计变量，以控制收敛、工作空间、铰点间距为约束条件，在条件数最小的构型种群中，选择使六杆振动控制能量平均值和方差加权和最小的设计。由于优化模型及其敏度为设计变量的隐函数，选择响应面方法对模型近似后，通过不断求解近似问题得到原问题的最优解。算例结果给出平台振动控制器设计和构型设计的规律和要点，说明方法的有效性，经过一体化设计的Hexapod平台在控制和构型指标上均优于平台的原始设计。

Integrated Design for Configuration/Vibration Control of Hexapod Platform

The Hexapod configuration and vibration control integrated design is treated as an optimal problem of choosing minimum control energy index among a family of Hexapod with optimal Jacobian condition number. Based on the theory of optimal Jacobian condition number, a programming problem is given, which takes control parameter of nonlinear feedback adaptive disturbance canceller(ADC) method, radius of Hexapod base plate and half separation angle between adjacent actuator attachment points on the up plate as design variables, control convergence condition, workspace, and space between attachment points as constrained conditions, and weighted sum of six actuators’ average energy consumption and its variance component as objective function. As the optimal model and its sensitivities contain implicit functions of design variables, the primal problem is approached by 2-rank elliptical response surface method with D-optimal test design. The original programming problem is settled by solving sequence of approximate problems. The example result gives out rules and key points of controller and configuration design of Hexapod, and demonstrates validity and feasibility of the proposed method. Compared with original developed Hexapod, the optimized Hexapod has the minimum condition number, and the advantages in control energy consumption and distribution.