Event-Based {LQR} with Integral Action

Sylvain Durand (1, 2) , Bruno Boisseau (1, 2) , John Jairo Martinez Molina (3) , Nicolas Marchand (1) , Thibaut Raharijaoana (4)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 ISM - Institut des Sciences du Mouvement Etienne Jules Marey
3 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
4 BIOROB - Biorobotique

In this paper, a state-feedback linear-quadratic regulator (LQR) is proposed for event-based control of a linear system. An interesting property of LQRs is that an optimal response of the system can be obtained in accordance to some specifications, like the actuator limits. An integral action is also added in order to not only restrict the study to null stabilization but also to tracking. The idea is to consider an external control loop and stabilize the integral of the error between the measurement and a desired setpoint to track. However, an event-triggered integral can lead to important overshoots when the interval between two successive events becomes large. Therefore, an exponential forgetting factor of the sampling interval is proposed as a solution to avoid such problems. The whole proposal is tested on a real-time system (a gyroscope) in order to highlight its ability, the reduction of control updates and the respect to the actuator limits.

Domaines: Automatique / Robotique

Sylvain Durand, Bruno Boisseau, John Jairo Martinez Molina, Nicolas Marchand, Thibaut Raharijaoana. Event-Based {LQR} with Integral Action. ETFA 2014 - EBS 2014 - 19th IEEE International Conference on Emerging Technologies and Factory Automation - Workshop on Event-Based Systems, Sep 2014, Barcelone, Spain. 7 p. ⟨hal-01067100⟩