基于线性单级倒立摆的LQR和NMPC控制方法对比研究  

Comparison Study of LQR and NMPC Control Methods Based on Linear Single-Stage

作　　者：邵红福 杨坤 Hongfu Shao;Kun Yang(School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai;Xi’an Xidian High Voltage Switch Operating Mechanism Co.,Ltd.,Xi’an Shaanxi)

机构地区：[1]上海理工大学机械工程学院,上海 [2]西安西电高压开关操动机构有限责任公司,陕西西安

出　　处：《建模与仿真》2024年第6期5826-5835,共10页Modeling and Simulation

摘　　要：针对目前欠驱动系统较成熟的控制方法对比缺乏的问题,研究线性单级倒立摆系统在全状态反馈控制下,采用线性二次型调节器(LQR)与非线性模型预测控制(NMPC)两种控制策略的效果。通过对比这两种控制方法的动态性能,评估它们在线性单级倒立摆系统中的适用性。首先,通过拉格朗日方程推导出系统的非线性数学模型,并进一步通过线性化理论假设得到系统的线性化数学模型。随后对其进行了稳定性、可控性和可观性分析。基于这些分析,设计了LQR和NMPC控制器。最后,在Matlab/Simulink中进行联合仿真实验。通过设置相同的初始条件和加权矩阵Q与R,对仿真结果的小车位移、摆动角度、小车速度、摆动角速度四个指标进行了对比分析。结果表明,LQR控制使小车在2.5s内回到初始位置,比NMPC控制快37.5%,并且位移最大超调量减少了38.7%,从-0.3522m降至-0.2160m。同时,LQR控制还缩短了摆杆达到竖直状态的时间至2.5s,比NMPC快28.6%,且摆杆角度的最大超调量从NMPC的-0.2381rad减少至-0.1050rad,降低了56%。结论指出,对于线性化后的单级倒立摆系统,LQR比NMPC更具优势,提供了更高效的控制效果,对以后欠驱动系统的控制具有一定的参考价值。To address the current lack of comparison between mature control methods for underactuated sys-tems,this study investigates the performance of Linear Quadratic Regulator(LQR)and Nonlinear Model Predictive Control(NMPC)for a linear single-stage inverted pendulum system under full state feedback control.By comparing the dynamic performance of these two control strategies,the study evaluates their applicability to the linear single-stage inverted pendulum system.First,the nonlin-ear mathematical model of the system is derived using the Lagrangian method,and subsequently,the system’s linearized mathematical model is obtained through linearization theory.Stability,con-trollability,and observability analyses are then conducted.Based on these analyses,LQR and NMPC controllers are designed.Finally,joint simulation experiments are conducted using Matlab/Sim-ulink.With the same initial conditions and weighting matrices Q and R,the simulation results for the cart displacement,pendulum angle,cart velocity,and angular velocity are compared.The re-sults indicate that LQR control returns the cart to its initial position within 2.5 seconds,which is 37.5%faster than NMPC control.Additionally,the maximum displacement overshoot is reduced by 38.7%,from−0.3522 meters to−0.2160 meters.LQR control also shortens the time required for the pendulum to reach the vertical state to 2.5 seconds,which is 28.6%faster than NMPC,and reduces the maximum pendulum angle overshoot from−0.2381 radians to−0.1050 radians,a decrease of 56%.The conclusion highlights that,for the linearized single-stage inverted pendulum system,LQR provides more efficient control compared to NMPC,offering valuable insights for the control of un-deractuated systems in the future.

关 键 词：LQR NMPC 拉格朗日方程 对比实验 

分 类 号：TP2[自动化与计算机技术—检测技术与自动化装置]