Proximate time-optimal control of third-order servomechanisms

The problem of proximate time-optimal control of third-order systems is considered. Two proximate time-optimal servomechanisms, PTO53 and PTO53τ, are proposed for type-3 and type-2 third-order plants, respectively. Theorems stating sufficient conditions on each system´s control design parameters to ensure global stability are given, and it is shown that the control parameters can be adjusted to accommodate, more or less, disturbances and unmodeled dynamics in the system. The approach used to develop the controllers is that of constructing a `slab´ in three-dimensional state space that describe the `switching´ structure of the control. The technique relies on three-dimensional phase-space analysis, which is rarely applied to systems of order three or higher. Simulation and experimental results demonstrate the performance of the algorithms developed