机械手臂之LQG/LTR最佳控制综合设计

The LQG/LTR Design Procedure for Nonlinear Robot Manipulators

摘要: 本研究综合计算扭矩法与LQG/LTR对非线性机械手臂系统进行多变量强健控制设计，解决存在于系统内部的不确定性与受到随机干扰情况下的非线性机械手臂系统之控制设计问题，使得非线性机械手臂控制系统具有良好的强健性与满足性能要求。文中首先使用计算扭矩法对非机械手臂系统中各项的估计值进行控制律的设计与回授线性化，并使用变异渐进法对回授系统进行适当的加权扩增；接着使用LQG/LTR设计，使得输出回授控制器(output feedback controller)能够趋近于预先设计的目标回授回路(target feedback loop)。至于非线性机械手臂闭回路系统在形成Lu’re-type问题后，可讨论非线性项之稳定性容许在一定的上界与下界，根据多变量圆稳定准则理论(multivariable circle criterion)探索此控制器之强健性能。文末则以非线性机械手臂系统为范例，进行计算机仿真，验证控制器的有效性与可行性。

Abstract: In this thesis, the multivariable robust control of nonlinear manipulator systems is based on the compute torque method and the LQG/LTR design procedure was proposed. This controller is able to handle the system that have modeling errors and external disturbances while it keeps the close-loop system robustness and satisfied the prescribed performance. In this research, the computed toque method is applied to design the proposed control law to form the main control structure by using the benefit of its feedback linearization strategy. The error dynamics of the plant is then formulated to the standard H2/H∞ control problem, which is easy to be applied by the LQG/LTR design procedure to find the optimal control gain and observer gains in the process of matching the target loop. With regard to the non-canceling nonlinear terms, the closed-loop system is formulated to the Lu’re-type problem form with sector-bounded uncertainties, which is then analyzed by the Multivariable Circle Criterion to discuss the stability and robustness. To verify the feasibility of proposed controller, one example with various external disturbances and parameter uncertainties is made and its computer simulation result shows the efficiency and feasibility of the proposed design methodology.