Messikh Lotfi, Guechi El-Hadi, Blažič Sašo
Laboratoire d'Automatique de Skikda (LAS), Département de Génie Électrique, Faculté de Technologie, Université 20 Août 1955, BP 26, Route El-Hadaeik, Skikda 21000, Algeria.
Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia.
Sensors (Basel). 2021 Dec 29;22(1):243. doi: 10.3390/s22010243.
In this paper, a pole-independent, single-input, multi-output explicit linear MPC controller is proposed to stabilize the fourth-order cart-inverted-pendulum system around the desired equilibrium points. To circumvent an obvious stability problem, a generalized prediction model is proposed that yields an MPC controller with four tuning parameters. The first two parameters, namely the horizon time and the relative cart-pendulum weight factor, are automatically adjusted to ensure a priori prescribed system gain margin and fast pendulum response while the remaining two parameters, namely the pendulum and cart velocity weight factors, are maintained as free tuning parameters. The comparison of the proposed method with some optimal control methods in the absence of disturbance input shows an obvious advantage in the average peak efficiency in favor of the proposed SIMO MPC controller at the price of slightly reduced speed efficiency. Additionally, none of the compared controllers can achieve a system gain margin greater than 1.63, while the proposed one can go beyond that limit at the price of additional degradation in the speed efficiency.
本文提出了一种与极点无关的单输入多输出显式线性模型预测控制（MPC）控制器，用于使四阶小车倒立摆系统在期望平衡点附近稳定。为规避一个明显的稳定性问题，提出了一种广义预测模型，该模型产生一个具有四个调谐参数的MPC控制器。前两个参数，即预测时域时间和相对小车-摆锤权重因子，会自动调整以确保先验规定的系统增益裕度和摆锤的快速响应，而其余两个参数，即摆锤和小车速度权重因子，则作为自由调谐参数保持不变。在无干扰输入的情况下，将所提方法与一些最优控制方法进行比较，结果表明所提单输入多输出MPC控制器在平均峰值效率方面具有明显优势，代价是速度效率略有降低。此外，所比较的控制器均无法实现大于1.63的系统增益裕度，而所提控制器虽会导致速度效率进一步下降，但能够超越该限制。
