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Omar Santos,Sabine Mondié 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.3
The design of a control law guaranteeing an upper bound on the performance index of linear systems with point wise and distributed delay is addressed. The control law is computed through an iterative procedure: at each step, it is the solution that minimizes the Bellman type equation obtained from plugging in the functional of complete type associated to the closed loop system of the previous step. It is shown that at each step, the closed loop system remains into the class of systems with distributed delays, the stability of the closed loop is maintained, and the guaranteed cost does not increase. The allowed continuous time varying norm bounded uncertainties guaranteeing the cost are also char-acterized. An illustrative example validates the approach.
Raúl Villafuerte,Belem Saldivar,Sabine Mondié 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.5
In this paper, the practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays and bounded perturbations is discussed. Sufficient conditions based on Lyapunov-Krasovskii functionals are derived. They are formulated in terms of the feasibility of a set of Bilinear Matrix Inequalities (BMI’s). A practical exponential estimate of the system response is also obtained. This approach is shown to be useful in the solution of an engineering problem: the elimination of the stick-slip phenomenon in the drilling process.
A Delay-based Nonlinear Controller for Nanopositioning of Linear Ultrasonic Motors
Luis Luna,Kevin López,Rubén Garrido,Sabine Mondié,Luis Cantera 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
This work introduces a delay-based nonlinear controller aimed at position control of linear ultrasonic motors (LUMs), which is termed the cascade nonlinear proportional integral retarded (CNPIR) control law. This new controller incorporates a time delay in its structure, composed of two nested loops. The inner velocity loop is regulated through an integral retarded (IR) controller that contains a time delay in its structure. The outer position loop resorts to a nonlinear proportional (NP) controller endowed by a saturation function. A tuning procedure for the CNPIR controller is also proposed, and it is based on the placement of multiple dominant roots. The inner loop is tuned by assigning a dominant triple root, whereas a method based on solving a transcendental equation allows tuning the outer loop and assigns two dominant roots. Moreover, pole dominance is assessed through the argument principle. Experimental results on a linear ultrasonic motor allow assessing the real-time performance of the proposed controller to achieve high precision and fast response in spite of the effects of inner disturbances, hysteresis, and friction phenomena.