Robust and Switched Control Design for Electrical Stimulation of Lower Limbs: a Linear Analysis
Willian Ricardo Bispo Murbak Nunes1; Ricardo Gouveia Teodoro2; Rafael Augusto de Araujo3; Marcelo Augusto Assunção Sanches3; Marcelo Carvalho Minhoto Teixeira3; Aparecido Augusto de Carvalho3
1 UTFPR - Federal University of Technology - Paraná; 2 IFPR - Federal Institute of Paraná; 3 UNESP - São Paulo State University
Baixar PDF doi:10.20906/CPS/CBA2018-1399
Resumo
Functional electrical stimulation (FES) has been used to restore and aid motor functions in paraplegics, promoting better therapeutic results for its users. From experimental results, we observe that the control signal is uncertain for an operating point, because of plant uncertainties. We present an experimental setup to identify the linear model containing polytopic uncertainties, and design robust $p_{(r,\xi)}(t)$ and switched controller $p_{(\sigma,\xi)}(t)$ that compensate uncertain control signal through an adequate switching law. Results obtained from open-loop control $ p_0 $, robust controllers $ p_r(t) $ and $p_{(r,\xi)}(t)$, and switched controllers $p_{\sigma}(t) $ and $p_{(\sigma,\xi)}(t) $ are compared. These results indicate that switched controller $p_{(\sigma,\xi)}(t)$ minimizes the uncertainty in the control signal, returns the smallest time derivative value of the Lyapunov function, consequently minimizing the angular position error in steady state ($e_{ss}\approx0.20^{\circ} $) in electrically stimulated lower limbs.
Palavras-chave: Switched control; linear matrix inequalities (LMIs); rehabilitation; neuromuscular electrical stimulation