In this paper, a new parametric optimization approach to retune nonlinear controllers is proposed. It discusses the design of these controllers under temporal constraints. The formulated optimization problem is often complex; it involves nonsmooth design parameters and criteria. An efficient optimization algorithm based on the approximation of the epsilon subdifferential notion is presented. It only requires gradients which are computed using parametric sensitivity functions. The proposed approach is applied to tune a nonlinear missile autopilot. The purpose especially concerns how to appropriately apply our procedure in order to improve performance of a controlled nonlinear dynamic system. We show that the choice of the controller structure and parameters has a great effect on the validation of the temporal specifications. Simulation results are given to demonstrate the effectiveness of the proposed approach.
This paper presents a general optimization approach in automatic's field. It discusses the design and retuning of controllers as well as the validation of the general manufacturer specifications, which will be expressed by a frequency and/or temporal templates in order to be solved by a general optimization problem. This is a very complex and particular problem. It will be shown that it involves nondifferentiable functions and criteria. The resolution of this kind of problems can be difficult or impossible via gradient and all classical descent algorithms. In this study, we propose an £ subdifferential algorithm, very efficient for nonsmooth optimization. This algorithm, mixing with an exact computation of gradient based on parametric sensitivity functions, appears to be well suited to problems with nonsmooth costs and constraints. As illustration, this method will be used to retune backstepping controller for a magnetic suspension system. Simulations and comparison results are given to demonstrate the effectiveness of the proposed approach.
The purpose of this paper is to describe how the fundamental problem of linear controller design can be solved, for general specifications, by combining a theoretical result with a recent numerical nonconvex nonsmooth optimization technique. Various temporal and/or frequency design criteria and constraints can be considered. The formulated optimization problem is complex; it involves implicit and explicit design parameters and nonsmooth criteria as well. A new algorithm based only on the gradient notion is fully described. This algorithm, mixing with an exact computation of gradients based on parametric sensitivity functions, appears to be well suited for controller design and retuning. As illustration, this method is used to design an optimal PI controller for a benchmark oscillatory model and to tune a PID controller for a motor position control. Computer simulations and experimental bench results are given to demonstrate the effectiveness of the proposed algorithm.
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