TY - GEN
T1 - Tuning PI controller in non-linear uncertain closed-loop systems with interval analysis
AU - Alexandre dit Sandretto, Julien
AU - Chapoutot, Alexandre
AU - Mullier, Olivier
N1 - Publisher Copyright:
© Julien Alexandre dit Sandretto, Alexandre Chapoutot and Olivier Mullier; licensed under Creative Commons License CC-BY
PY - 2015/11/1
Y1 - 2015/11/1
N2 - The tuning of a PI controller is usually done through simulation, except for few classes of problems, e.g., linear systems. With a new approach for validated integration allowing us to simulate dynamical systems with uncertain parameters, we are able to design guaranteed PI controllers. In practical, we propose a new method to identify the parameters of a PI controller for nonlinear plants with bounded uncertain parameters using tools from interval analysis and validated simulation. This work relies on interval computation and guaranteed numerical integration of ordinary differential equations based on Runge-Kutta methods. Our method is applied to the well-known cruise-control problem, under a simplified linear version and with the aerodynamic force taken into account leading to a non-linear formulation.
AB - The tuning of a PI controller is usually done through simulation, except for few classes of problems, e.g., linear systems. With a new approach for validated integration allowing us to simulate dynamical systems with uncertain parameters, we are able to design guaranteed PI controllers. In practical, we propose a new method to identify the parameters of a PI controller for nonlinear plants with bounded uncertain parameters using tools from interval analysis and validated simulation. This work relies on interval computation and guaranteed numerical integration of ordinary differential equations based on Runge-Kutta methods. Our method is applied to the well-known cruise-control problem, under a simplified linear version and with the aerodynamic force taken into account leading to a non-linear formulation.
KW - Huaranteed numerical integration
KW - Non-linear ordinary differential equations
KW - PID Tuning
U2 - 10.4230/OASIcs.SynCoP.2015.91
DO - 10.4230/OASIcs.SynCoP.2015.91
M3 - Conference contribution
AN - SCOPUS:85020160869
T3 - OpenAccess Series in Informatics
SP - 91
EP - 102
BT - 2nd International Workshop on Synthesis of Complex Parameters, SynCoP 2015
A2 - Andre, Etienne
A2 - Frehse, Goran
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 2nd International Workshop on Synthesis of Complex Parameters, SynCoP 2015
Y2 - 11 April 2015
ER -