Analysis and Design of Hybrid Control Systems

Abstract: Different aspects of hybrid control systems are treated: analysis, simulation, design and implementation.

A systematic methodology using extended Lyapunov theory for design of hybrid systems is developed. The methodology is based on conventional control designs in separate regions together with a switching strategy.

Dynamics are not well defined if the control design methods lead to fast mode switching. The dynamics depend on the salient features of the implementation of the mode switches. A theorem for the stability of second order switching together with the resulting dynamics is derived. The dynamics on an intersection of two sliding sets are defined for two relays working on different time scales.

The current simulation packages have problems modeling and simulating hybrid systems. It is shown how fast mode switches can be found before or during simulation. The necessary analysis work is a very small overhead for a modern simulation tool.

To get some experience from practical problems with hybrid control the switching strategy is implemented in two different software environments. In one of them a time-optimal controller is added to an existing PID controller on a commercial control system. Successful experiments with this hybrid controller shows the practical use of the method.