电动推杆轨迹跟踪积分滑模控制

Integral Sliding Mode Control for Trajectory Tracking of Electric Push Rod

摘要:

针对电动推杆在精密运动控制中面临的模型参数摄动和外部扰动等问题,本文提出一种积分滑模控制（Integral sliding mode control, ISMC）策略。首先,基于直流电机电枢方程和机械系统动力学方程,建立了电动推杆机电耦合系统动力学模型和电压-位移传递函数模型,并简化为二阶系统形式。在此基础上,设计了积分型滑模面以消除传统滑模控制稳态跟踪误差,采用指数趋近律以改善系统动态品质,并基于Lyapunov稳定性理论证明了闭环系统渐近稳定性。通过对正弦波、复杂波和衰减波轨迹跟踪控制试验,对比了所提方法与传统滑模控制（Sliding mode control, SMC）和比例积分微分（Proportional integral derivative, PID）控制算法的轨迹跟踪效果。结果表明,在跟踪正弦波轨迹时,ISMC最大误差为2.7816 mm,平均绝对误差为0.9258 mm,均方根误差为1.0935 mm;在复杂波情形下,ISMC最大误差为2.8206 mm,平均绝对误差为0.6030 mm,均方根误差为0.7369 mm;衰减波轨迹控制下ISMC最大误差为4.1097 mm,平均绝对误差为0.6093 mm,均方根误差为0.7807 mm。在控制精度方面,3种轨迹下ISMC平均绝对误差与均方根误差均为最优,稳态跟踪精度显著高于PID与SMC控制,且抗干扰性能更优,为电动推杆在复杂环境下高精度轨迹跟踪控制提供了有效方案。

Abstract:

An integral sliding mode control (ISMC) strategy was proposed to address the issues of model parameter perturbations and external disturbances faced by electric push rods in precision motion control. Firstly, based on the armature equation of the DC motor and the dynamic equation of the mechanical system, a dynamic model of the electromechanical coupling system and a voltage displacement transfer function model of the electric push rod were established and simplified into a second-order system form. On this basis, an integral sliding surface was designed to eliminate the steady-state tracking error of traditional sliding mode control, and an exponential convergence law was adopted to improve the dynamic quality of the system. The asymptotic stability of the closed-loop system was proved based on Lyapunov stability theory. Through trajectory tracking control experiments on sine waves, complex waves, and attenuated waves, the trajectory tracking performance of the proposed method was compared with traditional sliding mode control (SMC) and proportional integral derivative (PID) control algorithms. The experimental results indicated that when tracking a sinusoidal trajectory, the ISMC achieved a maximum error of 2.7816 mm, a mean absolute error of 0.9258 mm, and a root mean square error of 1.0935 mm. Under complex waveform conditions, the ISMC yielded a maximum error of 2.8206 mm, a mean absolute error of 0.6030 mm, and a root mean square error of 0.7369 mm. For the damped waveform trajectory, the ISMC attained a maximum error of 4.1097 mm, a mean absolute error of 0.6093 mm, and a root mean square error of 0.7807 mm. In terms of control accuracy, the ISMC consistently achieved the optimal mean absolute error and root mean square error across all three trajectory types. Its steady-state tracking precision was significantly superior to that of PID and SMC controllers, and it exhibited enhanced anti-disturbance capability. The research result can provide an effective solution for high-precision trajectory tracking control of electric push rods in complex environments.