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Section: New Results
Control design and co-design
Energy-aware networked control
Participants : C. Canudas de Wit [Contact person] , F. Garin, N. Cardoso de Castro, D. Quevedo [U. Newcastle] .
We have considered an event-based approach to energy-efficient management of the radio chip in the sensor node of a wireless networked control system. Indeed the radio is the main energy consumer, and intermittent data transmission allows one to reduce the use of the radio. While the existing literature in the control community on event-based control only addresses policies using two radio modes (transmitting/sleep), our work follows some considerations on the radio chip modes well-known in the communication networks literature, and introduces various radio-modes: different ‘idle’ non-transmitting modes, where only part of the radio chip is switched off (thus consuming more energy than ‘sleep’, but allowing for faster transition to transmission), and various transmitting modes, with different power levels. We propose an event-based radio-mode switching policy, which allows to perform a trade-off between energy saving and performance of the control application; to this end, a switched model describes the system, taking into account control and communication. The optimal switching policy is computed using dynamic programming, considering a cost either over an infinite time-horizon (see [36] ) or over a finite receding horizon (joint work with D. Quevedo, Univ. Newcastle, Australia, described in a paper in preparation).
Adaptive control strategy based reference model for spacecraft motion trajectory
Participants : H. Fourati [Contact person] , Z. Samigulina [Kazakh National Technical University] , O. Shiryayeva [Institute of Informatics and Control Problems] .
In aerospace field, the economic realization of a spacecraft is one of the main objectives which should be accomplished by conceiving the optimal propulsion system and the best control algorithms. Our work focuses on the development of a viable Adaptive Control Approach (ACA) for Spacecraft Motion Trajectory (SMT), see [19] . The proposed strategy involves the nonlinear mathematical model of SMT expressed in the central field, which is linearized by the Taylor expansion, and the second Lyapunov method to offer a high rate and unfailing performance in the functioning. The adaptive control system is composed of the cascade of adaptation loop and feedback control loop. When the spacecraft deviates from its reference trajectory model, the ACA acts on the control system to correct this deviation and follow the optimal reference trajectory. Therefore, when the states of the adjustable model are different from its reference values, then the error signal is provided as an input to the adaptation law, which contains the adaptation algorithm. The output will be the state variable feedback control matrix which will be used to calculate the new control law vector. The efficiencies of the linearization procedure and the control approach are theoretically investigated through some realistic simulations and tests under MATLAB. The steady state errors of control between the reference model and the adjustable model of SMT converge to zero. This work is described in [20] .
Control design for hydro-electric power-plants
Participants : C. Canudas de Wit [Contact person] , S. Gerwig, F. Garin, B. Sari [Alstom] .
We have initiated a collaboration with Alstom on collaborative and resilient control of hydro-electric power-plants, with the CIFRE PhD thesis of Simon Gerwig. The first goal of this research is to improve performance of a hydro-electric power-plant outside its design operation conditions, by adaptive cancellation of oscillations that occur in such an operation range. Indeed, current operation of power-plants often requires to operate on a variety of conditions, often different from the ones initially considered when designing the plant. At off-design operation pressure, the hydraulic turbine exhibits a vortex rope below the runner. This vortex generates pressure fluctuations after the turbine and can excite the hydraulic pipes. Indeed the water is compressible and the pipe walls elastic, so the system can oscillate. The goal is to damp these pressure oscillations as they create vibrations in the system and can lead to damages. Our first contribution has been to model the effect of the vortex rope on the hydraulic system as an external perturbation source acting on pipes. The pipes themselves are described with equations taking into account water compressibility and pipe-wall elasticity. The resulting model is nonlinear with hyperbolic functions in the equations (analogous to high-frequency transmission lines), from which we obtain a suitably linearized model.
Controller for switched linear systems
Participants : H. Fourati [Contact person] , Djamel. E. C. Belkhiat [U. Setif] , D. Jabri [U. Setif] .
We designed a robust output feedback tracking controller for a class of Switched Linear Systems (SLS) subject to external disturbances [23] . The proposed synthesis approach, based on a descriptor redundancy formulation, allows to avoid of the crossing terms appearance between the switched Proportional-Derivative (PD) controller's and the switched system's matrices. Using the multiple Lyapunov functional methods, a robust output feedback tracking performance has been formulated in terms of set of Linear Matrix Inequality (LMI). The effectiveness of the proposed synthesis procedure has been illustrated by a numerical example [24] .