Embedded Files
System Dynamics and Constraints
System Dynamics and Constraints
We consider a mass-spring-damper system with redundant actuation and constraints of displacement and force magnitude. The system dynamics in the normal mode can be represented by
The constraints are imposed on the position of the mass to avoid hitting the obstacles (the orange boxes in the figure) and on the magnitudes of the actuation forces as
Figure 1 and 2 below show simulation results of two study cases with/without command range and rate limits. The case without these limits uses the mechanisms of tighting/relaxing constraints to satisfy the reconfiguration conditions. The simulations begin with both actuators working normally, followed by actuator 1 fails (being zeroed-out), and ends with both actuators failing. In both cases, the reconfiguration is successful and there is no constraint violation at any time, while the command range and rate limiting effect is visiable in the second case.
Figure 1. Set projections and state and output trajectories for the case using constraints tighting and relaxing mechanisms without command range and rate limits.
Figure 2. Set projections and state and output trajectories for the case with command range and rate limits.
Page updated
Report abuse