高精度位置跟踪自适应增益调度滑模控制算法

影响位置跟踪精度最重要的因素之一是系统不可避免地存在内外不确定性。由于具备很强的鲁棒性,滑模控制能有效消除系统不确定性的影响,然而也会带来抖振这一顽疾。因此,有效削弱滑模控制系统的抖振是提升系统跟踪精度的关键。为此,本文提出一种误差主导的自适应增益调度算法,该算法利用等效原理准确判断系统滑动模态是否建立,并以此来调度切换函数增益值的增减;同时,为克服因利用低通滤波器获取切换函数等效输出而引起的时间延迟,在增益调度中采用误差主导的增益变化率,确保了增益调度的实时性。理论和仿真实验证明,在滑动模态建立前,该增益调度策略能加快滑模变量的收敛速度;而在滑动模态建立后,该增益调度策略能使增益值在有限时间内趋近于系统不确定的绝对值,降低了系统抖振幅值,从而获取更高的跟踪精度。直流力矩电机伺服系统位置跟踪对比实验结果表明,该增益调度方案有效,能使系统获得更高的跟踪精度。

Sliding mode control algorithm with high-precision position tracking based on adaptive gain schedule

One of the most important factors to depress the accuracy of position tracking is the internal and external uncertainties always existing in the system. Due to its strong robustness, sliding mode control can effectively eliminate the impact of uncertainties yet with the trouble named chattering. Therefore, reducing the chattering is the key to improve the accuracy of position tracking in sliding mode control system. This paper proposes an error guided adaptive gain schedule, in which the equivalent principle is employed to schedule the gain by judging whether the sliding mode is established or not. Furthermore, the changing rate of the gain is guided by the tracking error; hence the response speed can be improved by reducing the time lag produced by the low pass filter which is used to obtain the equivalent output of switching function. Theory proof and simulation results show that the gain schedule can accelerate convergence of sliding variable before sliding mode is built, and then after sliding mode is built, it can reduce the chattering by decreasing the value of gain to be close to the absolute value of uncertainty in finite time so as to improve the tracking accuracy. Moreover, the comparative experiment results of position tracking on DC torque motor servo system display that the proposed algorithm is advantageous to obtain higher tracking accuracy by scheduling the gain of switching function appropriately.