河北科技大学学报2026，Vol.47Issue(3)：250-262,13.DOI:10.7535/hbkd.2026yx03003
基于伴随函数能量优化的二级倒立摆摄动控制
Perturbation control of double inverted pendulum based on adjoint function energy optimization
摘要
Abstract
To address the performance degradation of a double linear inverted pendulum under simultaneous parameter perturbations and external disturbances,an energy-optimization-based composite control strategy was proposed.The dynamic model was firstly established using the Lagrange method.Then,the LQR weight matrices were optimized by minimizing the state-energy sensitivity integral,and the minimum energy gain was corrected by combining the terminal state deviations caused by parameter perturbations.Finally,feedforward compensation was integrated with an extended state observer to construct a composite controller based on adjoint function energy optimization and feedforward compensation(AJFC).The results show that,under about 10%structural parameter perturbations,relatively large friction uncertainty and an external input disturbance of 1 m/s,the AJFF controller reduces the second-pendulum angle by about 87.6%and the cart steady-state displacement deviation by about 89.0%compared with the nominal LQR controller,while keeping the control input energy nearly unchanged;Compared with the sliding mode controller,it achieves better overall performance in cart displacement,pendulum-angle dynamic error and steady-state accuracy;Further±30%interval parameter perturbation analysis show that the system settling time is always maintained within the range of 3～5 s,and both the settling time and ITAE index are superior to those of the nominal LQR controller.The proposed method featuring a clear structure can effectively suppress external disturbances,and is easily engineering implementated,which provides some reference for the anti-disturbance control of similar underactuated systems.关键词
控制论/二级倒立摆/伴随函数/能量优化/摄动Key words
cybernetics/double inverted pendulum/adjoint functions/energy optimization/perturbation分类
信息技术与安全科学引用本文复制引用
高婉玉,张永立,牟温宝,王晨,郭成飞..基于伴随函数能量优化的二级倒立摆摄动控制[J].河北科技大学学报,2026,47(3):250-262,13.基金项目
国家自然科学基金(62541324) （62541324）
教育部主题案例项目(ZT-2410066005) （ZT-2410066005）
