基于Kalman滤波和LQG控制的起重机控制研究  

Research on Crane Control Based on Kalman Filter and LQG Control

作　　者：魏炳胜 许安定 WEI Bingsheng;XU Anding(School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学机械工程学院,上海200093

出　　处：《重庆工商大学学报（自然科学版）》2023年第3期20-26,共7页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：针对双载荷轨道起重机在抬升重物时的消摆时间长、定位速度慢的问题,提出采用最优控制理论和卡尔曼滤波算法,设计线性高斯二次型(Linear Quadratic Gaussian, LQG)控制器并对其进行残余振动抑制。首先,运用Lagrange方程建立起重机系统的非线性动力学方程,其次,运用雅可比矩阵将非线性方程线性化,得到系统的状态空间方程;通过证明线性系统的可控性和可观性,选择合适的权函数,设计最优二次型线性调节器(Linear Quadratic Regulator, LQR)和最优状态估计器来得到LQG控制器,通过建立相关模型的Simulink控制系统仿真表明:设计的LQG控制器能有效衰减残余振动;通过与PID控制器对比分析,所提出的LQG控制器能更有效衰减残余振动幅值,振动的超调量更小,所需的稳态时间更短,验证了该控制策略的有效性和可行性。Aiming at the problems of long swing elimination time and slow positioning speed when lifting heavy objects,a Linear Quadratic Gaussian(LQG)controller based on optimal control theory and Kalman filter algorithm was proposed to suppress residual vibration.Firstly,the Lagrange equation was used to establish the nonlinear dynamic equation of the crane system.Secondly,the Jacobian matrix was used to linearize the nonlinear equation,and the state space equation of the system was obtained.By proving the controllability and observability of the linear system,selecting the appropriate weight function,and designing the optimal Linear Quadratic Regulator(LQR)and the optimal state estimator,the LQG controller was obtained.The simulation of Simulink control system with relevant models shows that the designed LQG controller can effectively attenuate the residual vibration.Compared with PID controller,the proposed LQG controller can attenuate the residual vibration amplitude more effectively,the overshoot of vibration is smaller,and the required steady-state time is shorter.The effectiveness and feasibility of the control strategy were verified.

关 键 词：起重机 振动抑制 LQR控制 卡尔曼滤波 LQG控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]