Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator

Noussaiba Gasmi,Mohamed Boutayeb,Ghazi Bel Haj Frej,Mohamed Aoun,Assem Thabet

doi:10.3390/act10110303

Abstract

The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed H∞ observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results.

Highlights

Many remarkable methods have been synthesized: robust stabilization via output feedback [1,2], H∞ control for systems with uncertain parameters [3,4] and Lipschitz nonlinearities [5], finite-time control for one-sided Lipschitz nonlinear systems [6], interval observers for global feedback control [7], feedback Stabilization with nonlinear output [8] and adaptive sliding mode control with finite-time [9] and tracking problem [10]
Actuators 2021, 10, 303 results are provided. They confirm the high quality of stabilization offered by the proposed approach through a real-time implementation based on ARDUINO UNO R3 board that is used as an Digital Signal Processing (DSP) emulator through target mode (Hardware In the Loop)
By solving the Linear Matrix Inequality (LMI) given by the proposed approach, we obtain the following results with r = 2: λmin = 0.2487

Summary

Introduction

In many industrial processes, developing a perfect model to the system dynamics is crucial either to build a controller or to obtain real time information on the system for surveillance. Data errors, disconcerted parameters, environmental noise, disturbances or even the age of the system can lead to modeling errors. These errors can cause a deviation of the dynamics during surveillance or decision-making. The presence of uncertainties leads to instability, divergence or degraded controller performance. Robust uncertainty stabilization methods have been proposed to filter disturbances and uncertainties and ensure a good degree of noise sensitivity, good performance and robustness. Many remarkable methods have been synthesized: robust stabilization via output feedback [1,2], H∞ control for systems with uncertain parameters [3,4] and Lipschitz nonlinearities [5], finite-time control for one-sided Lipschitz nonlinear systems [6], interval observers for global feedback control [7], feedback Stabilization with nonlinear output [8] and adaptive sliding mode control with finite-time [9] and tracking problem [10]

Objectives

Results

Discussion

Conclusion