Improved Transient Performance by Lyapunov -

Many control applications implemented in the industry are optimized for use in normal conditions. However, special or extreme conditions may occur, i.e. sudden changes in the environmental parameters or the controller set-points. These incidents may lead to unsatisfactory performance of the closed-loop system. A dynamic controller may, in the first place, interpret this as measurement noise to be ignored, as a result of being optimized for steady-state noise performance. Adaptive controllers are often designed in order to achieve asymptotic stability (AS) requirements, hence the transient performance may only be satisfactory for slow varying environmental parameters and controller set-points. In this thesis, a framework for improving controller performance in such situations is presented , followed by three application examples. The framework is presenting a controller strategy using a Lyapunov-based resetting mechanism , changing one or more of the controller states to a different value when an extreme situation is detected. The controller states are reset to a different value if this leads to a drop in the Lyapunov function value. An appropriately selected Lyapunov function is expected to lead to a controller with increased transient performance. In this way, the Lyapunov function is used both as a part in the controller algorithm and as a tool for proving stability for the whole controller system. The system performance may then be divided into two separate regimes, having two separate sets of specifications and tuning variables being decoupled from each other. Performance close to steady-state, being one of the regimes, is typically tuned in order to handle normal conditions. In the other regime, however, a separate part of the controller is having a fast reacting performance, triggered by sudden changes in the environmental parameters or the controller set-points. This regime is referred to as the systems transient regime. The fast reacting performance in this regime typically leads to reduced measurement noise suppressions, but if appropriately tuned, this will only be triggered when severe changes in the environmental parameters or the controller set-points is measured. In this way, the steady-state noise performance of the overall controller system may be improved, without reducing the transient performance. The main challenge encountered developing a controller using this strategy, is the search for a suitable Lyapunov function needed in the resetting strategy. One problem is to find a Lyapunov function, another is to make sure this is a suitable measure for the system's transient energy. The first problem …