Minimum Time Control of a Gantry Crane System with Rate Constraints
Minimum Time Control of a Gantry Crane System with Rate Constraints
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DOI：
10.1016/j.ymssp.2023.110120
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Adrian Stein;T. Singh
中科院分区：
文献类型：
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作者：
Adrian Stein;T. Singh
本文主要研究了在存在模态参数不确定性的情况下，门式起重机系统点对点运动的最小时间控制曲线的建立。假设起重机小车的速度是可控的，并且受到限制，提出了一个最优控制问题，以确定使系统从静止点过渡到无残余振动的终端状态的开关控制律。同时考虑了无阻尼和欠阻尼系统，研究了最优控制律的结构随最终位移的变化规律。随着刚体位移大小的增加，观察并解释了最优控制剖面中道岔的倒塌和诞生。通过强迫终端时刻的状态灵敏度为零来考虑对模态参数不确定性的稳健性。对于特定的终端位移，注意到时间最优控制轮廓与鲁棒时间最优控制合并的观察结果，并用参数最优控制轮廓的时滞滤波的零点的迁移来解释这一反直观的结果。作为与所提出的控制器的比较，分析了一种加速度约束的时间最优控制，它如预期的那样需要更大的机动时间。以一个两自由度龙门起重机系统为例，对数值研究的结果进行了实验验证，并通过实验说明了增加操纵时间对减小残余振动的权衡。
This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. As a comparison to the proposed controller, an acceleration constrained time-optimal control is analyzed which as expected demands a larger maneuver time. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.