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摘要:
为了消弱滑模控制高频抖振，提出一种新型开关切换函数，代替传统的符号函数。以多自由度串联机器人的动力学模型为研究对象，利用该新型开关切换函数，设计了一种滑模控制律，并证明多自由度机器人滑模控制系统渐近稳定。两自由度机器人滑模控制的仿真实验表明，两个关节都实现了较高的角位置和角速度跟踪精度，并且动态响应较快。同时，与采用符号函数作为开关切换函数的机器人滑模控制系统相比，有效消弱了滑模控制量的高频抖振。该新型开关切换函数具有通用性，适用于机载光电稳定平台、导弹制导等其它滑模控制系统。
Abstract:A novel switching function which replaces the sign function is presented in order to reduce high frequency chattering of the sliding model control. The dynamics model of multi-DOF serial robot manipulators is studied. A sliding control law with this novel switching function is designed and the asymptotic stability of the sliding model control of robot manipulators is proved. The simulation experiments of the sliding model control of 2-DOF robot manipulators illustrate that two links have higher angular position tracking accuracy and speed tracking accuracy. Moreover, its dynamic response is faster. The sliding model control system with the novel switching function reduces high frequency chattering effectively compared with the sliding model control system with the sign function. This novel switching function can be used on other sliding model control systems, for instance, the airborne electro-optical stabilized platform and missile guidance.
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Abstract: The high frequency chattering of the sliding model control system affects the control accuracy and increases energy consumption. It perhaps stimulates the uncertainty dynamics with the high frequency and causes the system instability. The control input discontinuity caused by the sign function is the main reason for the high frequency chattering in the sliding model control system. A novel switching function which replaces the sign function is presented in order to reduce high frequency chattering of the sliding model control. It is a special continuous power function in the neighborhood of the origin, which refrains from the high frequency chattering phenomena of the control input. When the absolute value of the error is smaller, the gain in the function is greater. When the absolute value of the error is greater, the gain in the function is smaller. Firstly, the dynamics mathematics model of multi-DOF serial robot manipulators with the parameters uncertainties and external disturbance is studied. Secondly, a multi-order sliding control law for robot manipulators with the novel switching function is constructed, and the asymptotic stability of the sliding model control system of robot manipulators is proved by using the Lyapunov function. Finally, the sine signal tracking simulation experiments of the sliding model control of 2-DOF robot manipulators with the novel switching function are conducted, which are compared with those of the sliding model control with the sign function. The desired angular position signal of link 1 and link 2 is q1d=cos(2πt) and q2d=sin(2πt) respectively. The maximum angular position tracking error of link 1 is 0.013° and that of link 2 is 0.0065° besides the original values. The maximum angular speed tracking error of link 1 is 0.46°/s and that of link 2 is 0.45°/s besides the original values. The experiment results illustrate that two links of robot manipulators obtain higher angular position tracking accuracy and speed tracking accuracy. Moreover, dynamic response of the control system is faster. The sliding model control system with the novel switching function reduces high frequency chattering effectively compared with the sliding model control system with the sign function. So the angular speed of two links has much less high frequency chattering. The novel switching function can reduce high frequency chattering phenomena of the sliding model control system which achieves better tracking performances. This switching function can be used on other sliding model control systems, for instance, the airborne electro-optical stabilized platform, numerical control machine and missile guidance, etc.
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图 6 采用符号函数的两关节角速度跟踪误差.
Figure 6. Speed tracking error of two links with the sign function.
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