Multi-mode input shapers for eliminating residual vibrations

When an abrupt input is applied to engineering systems, residual vibrations generally occur. These residual vibrations degrade operational performance, reduce productivity, and lower control accuracy; therefore, they must be eliminated as quickly as possible. Recently, input shaping control methods, which eliminate residual vibrations by appropriately shaping the command input, have received significant attention as a means to control these vibrations. Traditional input shaping control primarily targets systems with a single vibration mode, and even when addressing two vibration modes, it has not systematically classified and handled multi-mode input shapers. In this paper, we systematically classify multi-mode vibrations and design multi-mode input shapers capable of eliminating multi-mode vibrations at once for each category. Additionally, we propose performance indices to evaluate the performance of multi-mode input shapers in cases with multiple vibration modes.