基于θ-D方法的欠驱动TORA系统非线性最优控制  

On the Nonlinear Optimal Control of TORA System Based onθ-D Approximation

作　　者：张宇[1] 李芦钰[2] 郭源博[1] 张晓华[1] ZHANG Yu;LI Lu-Yu;GUO Yuan-Bo;ZHANG Xiao-Hua(School of Electrical Engineering,Dalian University of Tech-nology,Dalian 116024;School of Civil Engineering,Dalian University of Technology,Dalian 116024)

机构地区：[1]大连理工大学电气工程学院,大连116024 [2]大连理工大学土木工程学院,大连116024

出　　处：《自动化学报》2020年第7期1401-1410,共10页Acta Automatica Sinica

基　　金：国家自然科学基金项目(51377013,51378093)资助。

摘　　要：针对TORA(Translational oscillator with rotating actuator)系统的镇定控制问题,提出一种基于θ-D方法的非线性最优控制方案.应用拉格朗日方程建立TORA系统的数学模型,为保证状态空间形式的TORA系统数学模型中状态向量系数矩阵A(x)能够分离出常值矩阵,且其能与控制位置矩阵构成可控对,采用不同于传统形式的解耦坐标变换对TORA系统进行了处理,以此为基础为TORA系统设计基于θ-D方法的非线性最优控制器,该控制方案可离线得到控制输入的显示表达式.通过数值仿真以及与基于局部线性化的线性最优控制方案进行比较,验证了所提非线性最优控制方案所具有的良好瞬态性能.A nonlinear optimal control scheme is proposed for the stabilization of TORA(Translational oscillator with rotating actuator)system based onθ-D Approximation in this article.The mathematical model of the nonlinear TORA system is derived through using the Lagrange equations.A novel coordinate transformation is adopted to make it available to isolate a constant matrix from the coefficient matrix A(x),and make the constant matrix and the input location vector a controllable pair.The proposed nonlinear optimal control method does not require excessive online computations,as the explicit expression of control input can be derived in controller design phase.Numerical analysis demonstrate the effectiveness of the proposed method and its advantage in instant performance over the linear optimal control approach based on local linearization.

关 键 词：具有旋转激励的平移振荡器 最优控制 坐标变换 非线性控制 HJB方程 

分 类 号：O231[理学—运筹学与控制论]