Ghommam J, Mnif F
Control and Energy Management Lab (CEM, Lab), Tunisia.
Sultan Quabous University, Oman.
ISA Trans. 2017 Mar;67:306-316. doi: 10.1016/j.isatra.2017.01.015. Epub 2017 Jan 23.
The inverted pendulum is considered as a special class of underactuated mechanical systems with two degrees of freedom and a single control input. This mechanical configuration allows to transform the underactuated system into a nonlinear system that is referred to as the normal form, whose control design techniques for stabilization are well known. In the presence of time delays, these control techniques may result in inadequate behavior and may even cause finite escape time in the controlled system. In this paper, a constructive method is presented to design a controller for an inverted pendulum characterized by a time-delayed balance control. First, the partial feedback linearization control for the inverted pendulum is modified and coupled with a state predictor to compensate for the delay. Several coordinate transformations are processed to transform the estimated partial linearized system into an upper-triangular form. Second, nested saturation and backstepping techniques are combined to derive the control law of the transformed system that would complete the design of the whole control input. The effectiveness of the proposed technique is illustrated by numerical simulations.
倒立摆被视为一类特殊的欠驱动机械系统，具有两个自由度和一个控制输入。这种机械结构允许将欠驱动系统转化为一种被称为标准型的非线性系统，其稳定化控制设计技术是众所周知的。在存在时间延迟的情况下，这些控制技术可能导致性能不佳，甚至可能使受控系统出现有限时间逃逸。本文提出了一种构造性方法，用于设计具有时滞平衡控制特性的倒立摆控制器。首先，对倒立摆的部分反馈线性化控制进行修改，并与状态预测器相结合以补偿延迟。通过进行几次坐标变换，将估计的部分线性化系统转化为上三角形式。其次，将嵌套饱和技术和反步法相结合，推导出变换后系统的控制律，从而完成整个控制输入的设计。数值模拟验证了所提技术的有效性。
