GENERAL NONLINEAR CONTROL LAW FOR DC-DC SYMMETRIC SWITCHING CONVERTERS Seddik BACHA zyxwvut FEDCBA (*) , Azzam HASSAN (") , Marc BRUNELLO (*) (*> : Laboratoire dElectrotechnique de Grenoble , URA-CNRS 355 (") : Laboratoire dAutomatique de Grenoble , URA-CNRS 628 ENSIEG/INPG, BP 46 - 38402 Saint Martin d'H2res - France. ------ zyxwv LKJIH Abstract - zyxwvutsr IHGFEDCB I n this paper a general nonlinear control law of the family of DC-DC symmetric switching converters is given. Global asymptotic stability of this law zyxwvuts GFEDCBA is proved. We undeline not only the non sensivityt of this control law with respect to the load and voltage supply variations but the facility of its implementation on a real process as well. Simulation and practical results presented at the end show the powerful1 and the effiiency of the models and the control law. zyxwvutsrqp EDCBA I- INTRODUCTION Thanks to the operating switches, Power Electronic switching converters have naturally a variable framework. The exact converter models are govemed by differential equations with discontinuous Right Hand Side (R.H.S), they are a particular case of Variable Structure Systems (VSS). Despite the fact that this system is piece- wise linear the global behavior remains nonlinear and entails difficulties that proceed from modelling and control. We can divide the problem into two parts : -Finding output value can be reached zyxwvuts as fast as possible -The robustness of the control law against the load or supply variations be ensured. Knowing that many chnstraints impede the using of the VSS tools and in order to simplify the analysis of these devices, it is more interesting to transform the original discontinuous system to get a continuous one. For this, the study of the average behavior is adequate. First of all, we give the mathematical models used to establish the control law for the familly of DC-DC symmetric switching converters (SSC). The models are issued from previous works [2.3]. The general ideas are largely explained in [ 11. the validity and the usefulness of these obtained models are shown in [2.3,4]. Secondly we give the,control law which is applied to the converter rectifier, so this control law can be applied to the familly of DC-DC SSC. The aim of this control law is to keep the output of the converter at a preselected value.and this, as independant as possible from the load and supply variations (robustness). A stability analysis is given and the global asymptotic stability is proved. Finally, we give some simulations and practical results which show its powerfull and robustness. I1 BASIC STRUCTURES The converter in Fig.1 comprises a voltage inverter (or a current inverter ), (h). attacking a current rectifier (or a voltage rectifier), (d), CL7803-1243-W3SO3.00 0 1993 EEE through an intermediate alternative stage, (c). the whole set-up running with a supply, (a), driving a load (e). (a) (b) (d (d) (e) (a) supply, (b) inverter, (c) intermediate circuit, (d) rectifier, (e) load Fig. 1: General structure Choise of basic converters (rectifier and inverter) as well as their switches depends on the way power is transmitted (one direction or two) and on other technico-economic factors : e.g. the rectifier may be full-bridge or half-bridge, with diodes or controlled ZCS or ZVS Given u1 and u2 the switching functions which govem respectively the inverter and the rectifier, ul and u2are discrete functions belonging to the set { -1 ; + I ). In the exemple of the series resonant converter (SRC) in Fig.2 : - the inverter output voltage is described by : e(t) = E.ul(t) - the rectifier input voltage by : s(t) = Vco.u2 I 1 I I I I 1 I I I 1 I 1 I +E -E +vcc -vco . . . I 1 I I I I 1 I 1 I I I I t s(t) I I I I I I t 6 !j-+fI I j I I I I I I I I I Fin. 2 : Switchinn times conuol (SRC) - I iL-hnk cumcnt, c(t)-output voltage inverter, s(t)-input voltage rectifi E-Voltage supply, Vco- In the kind of DC-DC SSC converters, adjustment of power transfer is carried out by controlling switching times of rectifier and inverter switches. Several means of adjusting these moments may he considered (fig 2) : -adjusting switching frequency (OS). 222