Jerk Limited Time Optimal Control of Flexible Structures

Abstract

This paper addresses the problem of designing jerk limited time-optimal control profiles for rest-to-rest maneuvers of flexible structures. The variation of the structure of the jerk profile as a function of the permissible jerk is studied. An optimal control problem is formulated which includes constraints to cancel the poles corresponding to the rigid body and flexible modes of the system and to satisfy the boundary conditions of the rest-to-rest maneuver. The proposed technique is illustrated on the benchmark Floating Oscillator problem where the jerk profile is parameterized as a bang-off-bang or bang-bang profile.

Smooth control over jerk with displacement constraint

“…‘Bang-off-bang’ controls result naturally from exercising additional constraints. Muenchhof and Singh 36 studied controls in which jerk is applied until the point that acceleration reaches ‘the saturation level’, at which time the jerk is turned off. ‘Numerical results show that accepting a small increase in the final time, the jerk can be reduced considerably’.…”

Alternative definitions of energy for power meters in non-sinusoidal systems

“…Moreover, the jerk is employed in vibration control [39,40], minimum energy consumption, and trajectory optimization of cars, hard drives, cranes, and spatial and flexible arm robots [35,41]. Also the jerk is employed in electromagnetic gun systems in which the jerk is: ''proportional to the product of the current and the time rate of change of current'' [42].…”

Zero-phase velocity tracking of vibratory systems with actuation constraints

“…Some attempts of integrating smooth trajectory generation with derivatives limitation and vibrations cancellation have been proposed in the literature, see e.g. Muenchhof and Singh (2003); Biagiotti and Melchiorri (2012); Besset and Béarée (2017). In general,…”