The performances of electronic power converters have been evolving through the last decades, in an attempt to be more reliable and efficient. This has been carried out thanks to the developments of the semiconductor of power components and the new system of energy conversion. These high performances are directly linked to the converter's topology and its power electronic components.Multicell converters are currently embedded in many electric devices. Their aim is to convert an electrical energy shape (voltage /current / frequency) to another one.This new topology presents two additional advantages: the possibility of a modular construction and the possibility of using components having large diffusion.On the other hand, the following model must be simple to allow real time control and precise enough to achieve the desired behaviour. Because it's based on continuous variables and discrete variables, multicell converter modelling is claimed to be difficult [19], [20]. According to previous studies, three types of models could be found. The average model consists in calculating average value of all variables during one sampling period. Nevertheless, this model cannot represent the capacitors terminal voltage natural balancing; the harmonic model based on the decomposition in Fourier series of control signals, which determine the harmonics phase and amplitude across the switches, also determining the harmonic current of the load to determine the evolution of capacitor voltages;The instantaneous model considers all the switching over a period (discrete location The main objective of this paper is to show that the multicellular converter is very well suited for a control set-up using sliding modes and which will be demonstrated by experiment.
Problem PositionIn this section, we consider a nonlinear system whose dynamics is described by the differential system:Where:T ∈ X : represents the state vector, X ⊂ℜ n , X is a differentiablemanifold or an open subset of ℜ n .u: represents the command.f:is assumed sufficiently differentiable function, but known so uncertain.t: is the time.The system ẋ = f ( t , x ,u ) include those of the form:The problem is always to force the trajectories of the system to evolve on the sliding surfaceBeing a real-valued function sufficiently differentiable such that its ( r−1 ) first derivatives with respect to time are functions of the state x (which means they do not contain any discontinuity.) defines a submanifold of ( n−1 ) dimension called sliding surface or switching.
Sliding Mode ControlThe sliding mode control is a variable structure control can change in structure and switching between two values depending on a property specific switching logic s( x ) .The principle of sliding mode control is to constrain the system to reach a given surface called sliding surface and remain there until the balance. This control is done in two steps: the convergence towards the surface and then sliding along it ( The synthesis of sliding mode control is done in three steps:-Choice of the sliding surf...