A Two-Time-Scale Control Scheme for Fast Unconstrained Systems

Model predictive control (MPC) is a very effective approach to control nonlinear systems, especially when the systems are high dimensional and/or constrained. MPC formulates the problem of input trajectory generation as an optimization problem. However, due to model mismatch and disturbances, frequent re-calculation of the trajectories is typically called for. This paper proposes a two-time-scale control scheme that uses less frequent repeated trajectory generation in a slow loop and time-varying linear feedback in a faster loop. Since the fast loop reduces considerably the effect of uncertainty, trajectory generation can be done much less frequently. The problem of trajectory generation can be treated using either optimization-based MPC or flatness-based system inversion. As proposed, the method cannot handle hard constraints. Both MPC and the two-time-scale control scheme are tested via the simulation of a flying robotic structure. It is seen that the MPC scheme is too slow to be considered for real-time implementation on a fast system. In contrast, the two-time-scale control scheme is fast, effective and robust.