Minimum settling time control design through direct search optimization
This work provides a new optimization framework for control engineers seeking to minimize settling time directly, though it is an incremental improvement over existing indirect methods.
The authors propose a direct search optimization method to directly minimize the settling time of closed-loop control systems, addressing the non-smooth and discontinuous nature of the objective function. The approach yields controllers with improved settling time compared to existing methods that minimize related but different objectives.
The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature do not minimize directly the settling time but only related objective functions. Indeed, the settling time objective function is not only non-smooth but also discontinuous. Therefore we propose to use direct search methods, which do not use any gradient information. An important reason is a recent result that some direct search methods are guaranteed to convergence on such discontinuous objective functions. The proposed approach is self-standing but can also improve the solutions obtained with the alternatives of the literature, which lead to good solutions but suboptimal in terms of the settling time. Note also that this approach is very flexible and can be adapted to a broad range of objectives as well as nonlinear systems or controllers, as long as the time response can be simulated.