- Application of Variational Inequality to non-smooth mechanics and Control Theory
- Sliding Mode Control
- Numerical Integration
- Explicit Nonlinear Model Predictive Control
My PhD (manuscript here) was focused on the discrete-time version of sliding mode control, a well-known technique in the field. The term discrete-time refers here to the case when the control input (or action) changes only at some discrete time instants. The other type of controller is said to be continuous-time if the control input can change at any time instant, with no frequency constraint. The latter case is usually the one used in Control Theory, whereas the former is used almost for every implementation. Indeed, when a microcontroller is used to compute the control input, its value can only change at a given frequency. This topic is of paramount important given the ubiquity of microcontrollers in applications.
The main contribution of this research effort is the use of an implicit discretization instead of an explicit one. If you are interested in knowing more about the difference between the two methods, see this wiki page.
During my PhD, I made some contributions in the three domains of Automatic Control
Theory: Starting from the work of my advisors, I further characterize the implicitly discretized sliding mode controllers. We could show that many properties of the continuous-time version are preserved, or have very similar counterparts.
Simulation: I took part in the development in the Siconos platform, dedicated to the simulation of nonsmooth dynamical systems. I implemented an algorithm to solve Affine Variational Inequality (AVI) and I created a Control Toolbox. I'm still involved in the development of Siconos.
Experimentation: I successfully implemented the implicit sliding mode controller on two experimental setups: an electro-pneumatic actuator in IRCCyN, Nantes and an inverted pendulum locate at the CRIStAL lab, Lille. In both cases, the implicitly discretized controller outperforms the explicit one. With both setups, the classical ECB-SMC controller was used. In Nantes, the twisting controller (a second order sliding mode controller) was also implemented. See the videos page for an illustration of the effectiveness of the method. This tests were successfully and swiftly conducted thanks to the support of both labs.