PROXIMATE TIME-OPTIMAL CONTROL OF 3RD-ORDER SERVOMECHANISMS

Speed is an important performance measure in many applications, such a s disk-drive head positioning and pick-and-place robotics. Since there is a limit on the magnitude of the control signal in every control sy stem, using speed as the performance measure leads to time-optimal con trollers that are bang-bang. Because they are sensitive to disturbance s, parameter variations, and unmodeled dynamics, truly time-optimal co ntrol systems are not practical and more robust proximate time-optimal controllers that give near time-optimal responses should be used. The problem of proximate time-optimal control of third-order systems is c onsidered. Two proximate time-optimal servomechanisms, PTOS3 and PTOS3 tau, are proposed for type-3 and type-2 third-order plants, respective ly. Theorems stating sufficient conditions on each system's control de sign parameters to ensure global stability are given, and it is shown that the control parameters can be adjusted to accommodate more or les s disturbances and unmodeled dynamics in the system. The approach used here to develop the controllers is that of constructing a 'slab' in 3 -dimensional state space that describes the 'switching' structure of t he control. The technique relies on 3-dimensional phase-space analysis which is rarely applied to systems of order 3 or higher. Simulation a nd experimental results demonstrate the performance of the developed a lgorithms.