Robust versus optimal control for the radius of spherical bubble in a perfect incompressible liquid, LMI optimization approach
| Autor: | Mahdi Alinaghizadeh Ardestani, Ehsan Badfar |
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| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization State-space representation Mechanical Engineering Linear matrix inequality 02 engineering and technology Linear-quadratic regulator Optimal control 01 natural sciences Controllability Nonlinear system 020901 industrial engineering & automation Control and Systems Engineering Control theory Modeling and Simulation 0103 physical sciences Observability Electrical and Electronic Engineering Robust control 010301 acoustics Civil and Structural Engineering Mathematics |
| Zdroj: | International Journal of Dynamics and Control. 8:497-507 |
| ISSN: | 2195-2698 2195-268X |
| Popis: | Control of the bubble radius is essential in many medical and industrial applications. In this paper, the nonlinear governing dynamic of single spherical bubble in a perfect incompressible liquid is introduced. In continuation, the state space form of the nonlinear dynamic is presented and then observability and controllability are checked by Lie derivative concepts and finally the linearized state space is obtained around its equilibrium point. Second part of this paper is devoted to designing control strategies for the nonlinear governing dynamics of bubble, where the ultrasonic pressure plays the role of control input and the output is radius of bubble which is intended to follow desired radius in order to prevent from bubble collapse phenomenon. A novel robust control is proposed to ensure the desired level of performance in the presence of parametric uncertainty. In this method, the stability of the closed loop system is guaranteed by Lyapunov theorem and the stabilizing gain is achieved by Linear Matrix Inequality (LMI) optimization approach. For comparison, Linear Quadratic Regulator method is selected which is a very classical approach. The optimal feedback gain is also achieved through LMI approach. Simulation results indicate the effectiveness and efficiency of the robust over optimal controller. |
| Databáze: | OpenAIRE |
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