On-Off Input Shaping
In general, input shaping produces a variable amplitude command signal. Unfortunately, some systems are equipped with constant-force actuators which can only be turned on or off; no amplitude control is possible. The most prominent example of this type of system is the reaction jets which are used to maneuver the Space Shuttle.
To generate shaped inputs for on-off actuators, the amplitudes of the impulses must have specific values and in a specific order. For example, if the amplitudes are 1, -2, 2, -2, 1, then convolution of the shaper with a step input will produce an on-off command profile.
It is usually a poor idea to use the above on-off profile (which is the time-optimal control) because it leads to large deflections during the move (even though there will be zero residual vibration). Additionally, it is very expensive in terms of fuel usage. To conserve fuel, while still moving very fast, use a shaper with amplitudes of 1, -1, 1, -1, -1, 1, -1, 1. With these amplitudes the shaped command will be a series of positive pulses followed by a series of negative pulses. The periods of coasting provide significant fuel savings with only a negligible loss in maneuver speed.