ON THE POSSIBILITY OF COMBINED CONTROL SYNTHESIS FOR TRANSIENT PROCESSES RATE IN FREQUENCY SYNTHESIZER, WORKING IN WIDE BAND
Vladimir I Goryunov · 2007
The procedure of combined control synthesis for frequency synthesizer under reference generator frequency, counter indexes, defining working basic and output frequency, and filter structure, using the main thesis of control theory for nonlinear systems with discrete time, is described. The possibility of using of geometrical imaginations, based on corresponding point mapping dependence on parameter, is noted. It is known, that satisfactory spectral and dynamical characteristics achievement for frequency synthesizers (FS) under fine size, energetic and other indexes of their construction is possible only when using hybrid phase synchronization systems (PSS), combining the main advantages of digital (the direct synthesis method) and pulse PSS [1]. For the purposes of optimal FS characteristics achievement the elaboration of FS structure control algorithm, allowing to use different partial methods for FS fast-action increase [2]. In current paper the synthesis procedure for combined control under reference generator frequency, indexes of counters, determining basic working and input FS frequency, and filter structure is presented. Pointed control elements choice is conditioned by their determining influence on fast-action of transient processes, arising in FS under frequency switching over fixed band. Pointed problem solving became possible only after preliminary studies, as a result of which it was a success: 1) to work out mathematical apparatus, allowing to make automatic the process of obtaining information on transient processes duration under switching of control parameter [3]; 2) to prove by means of worked out dynamical characteristics analysis methods, that under finite switch band size FS fast-action is limited [4]; 3) to show analytically and by numerical experiment, that the minimal transient process duration under FS switching over fixed frequency band is achieved when using proportionalintegrating filter (PIF) with parameters, being functions of switch band size [5]. It is necessary to mention, that the methods of synthesis of control action on tunable generator (TG) in FS by means of counter index switching through intermediate values row is known for a long time [6]. But such control opportunities research over the whole band is yet absent. It is obviously connected with the fact, that FS, constructed on the base of pulse-phase control hoop, is the essentially nonlinear system [7], so synthesizer controllability analysis under all possible switching over fixed frequency band by counter index commutation leads, according to Kalman theorem analog in the theory of nonlinear systems with discrete time controllability [8], to nonlinear functional equations solution problem. In view of formulated problem complexity on the fist stage of quasi-optimal control synthesis problem it is assumed permissible control rang to be continuous. In order to realize the opportunities of qualitative analysis and to give the basis for numerical-analytical synthesis methods all the studies are executed under consequent complication of FS mathematical model (MM). On each research stage the evaluation of discreteness parameter influence on transient processes duration is done. It is known [2], that practical realization of frequency putting methods, using optimal control theory requires complicated counting operations even in the case of the low order filters using. General statements of control theory for linear discrete systems [8] prompt, that for transient processes duration decrease we ought to decrease filter order and, maybe, even give its using up for the time of tuning process. Also it is shown [2], that the analogous statement on filter dimension role in frequency switching process duration forming for linear characteristics of FS elements remains without linearizing procedure over control (that is over counter index) for difference equations. So the main possibilities of synthesizer frequency control by counter index commutation is especially interesting. Non-filter FS scheme dynamics is described by circle point mapping [12]: ) 1 (mod )) ( ( g 0 0 τ ξ α τ τ + = ) 1 0 ( 0 ≤ < τ , (1) where 0 τ , τ are the moments of preceding and following pulses appearance at counter output, g(y) is the generator control characteristic, ) ( τ ξ – synchronizing signal, α – non-dimensional counter index. Let 0 α be counter index value, from which switching is carried out, n α – new counter index value, corresponding to new frequency, tr α – intermediate counter index value, corresponding to control process. Stationary values n * 0 ,τ τ τ = , corresponding to α = 0 α , n α are to satisfy the