Adaptive robust controller based on integral sliding mode concept

ABSTRACT

This paper proposes, for a class of uncertain nonlinear systems, an adaptive controller based on adaptive second-order sliding mode control and integral sliding mode control concepts. The adaptation strategy solves the problem of gain tuning and has the advantage of chattering reduction. Moreover, limited information about perturbation and uncertainties has to be known. The control is composed of two parts: an adaptive one whose objective is to reject the perturbation and system uncertainties, whereas the second one is chosen such as the nominal part of the system is stabilised in zero. To illustrate the effectiveness of the proposed approach, an application on an academic example is shown with simulation results.

Keywords:

• Adaptive control
• robust control
• integral sliding mode

Acknowledgment

The authors acknowledge the support of the ANR grant CHASLIM (ANR-11-BS03-0007).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The ratio R_* is defined as, respectively for |z₁|, |z₂| and |z₃| $$\begin{array}{ccc}\hfill R_{|z_1|}& =& {\displaystyle \frac{|z_1{|}_{\tau =1ms}}{|z_1{|}_{\tau =0.1ms}}{R}_{|z_2|}=\frac{|z_2{|}_{\tau =1ms}}{|z_2{|}_{\tau =0.1ms}}}\hfill \\ \hfill R_{|z_3|}& =& {\displaystyle \frac{|z_3{|}_{\tau =1ms}}{|z_3{|}_{\tau =0.1ms}}}\hfill \end{array}$$

Additional information

Funding

ANR grant CHASLIM [grant number ANR-11-BS03-0007].