RU2552520C2 - System of control of nonlinear dynamics of direct step-down voltage converter - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention relates to the field of electrical equipment and can be used in digital control systems of DC voltage converters with the function of suppression of the hazardous oscillations of output voltage occurring at a certain set of parameters of the system. In the nonlinear dynamics control system the control system consisting of the main subsystem and the control auxiliary subsystem, approximators on the basis of neural networks is connected to the power part of the converter. The converter control signal provides the stabilization of average value of output voltage. In the system the correction of error signal is provided, thus the stabilization of the design dynamic mode (1 cycle) is provided.

EFFECT: ensuring of pre-set nonlinear dynamic properties of the system and pre-set parameters of speed and accuracy of output voltage stabilization in case of refusal from parametrical synthesis.

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Description

The claimed invention relates to a conversion technique and can be used in the implementation of digital control systems for DC / DC converters with the function of suppressing dangerous fluctuations in the output voltage that occur with a certain set of system parameters.

The known method of the International Journal of Circuit Theory and Applications [1], called the method with delayed feedback, where to stabilize unstable periodic trajectories it is assumed to use feedback with a delay approximately equal to the period of the stabilized periodic mode.

The stabilization of the design mode occurs due to the fact that two correction signals are added to the control signal after the controller of the standard control system: the scaled difference between the current at stroboscopic time instants and the current at stroboscopic time instants delayed by the pulse-width modulation period; the scaled difference between the voltage at the capacitor at stroboscopic time instants and the voltage at the capacitor at stroboscopic time instants delayed by the pulse-width modulation period, which makes it possible to correct the vector of forcing actions from the point of view of the system of differential equations describing the system and to ensure the design periodic mode.

The disadvantages of the method include the difficulty in choosing the duration of the delay and the parameters of the control system, which leads to the absence of a guarantee of the correct operation of the device in a wide range of changes in its parameters.

The objective of the invention is to control the nonlinear dynamics of the system to ensure its operation in the design periodic mode with a small amplitude of oscillations in a wide range of parameters of the control system or input voltage, taking into account the possibility of working in areas of multistability.

This problem is solved due to the fact that a control system consisting of two subsystems is connected to the power part of the converter, made on the basis of a direct lowering converter, LC filter: the main subsystem, consisting of a subtractor, which forms the difference between the reference signal and the feedback signal (signal error), a scaling voltage feedback amplifier proportional to the controller, to the input of which an error signal is supplied, and the output signal is fed to the input of the comparator, to the second input of which stumbles signal from the scanning voltage generator operating synchronously with the master oscillator, that allows to generate the inverter control signal providing stabilization of the mean value of the output voltage; auxiliary control subsystem, characterized in that the method in question does not use a time delay when stabilizing the design mode, but introduces approximators based on neural networks that, using the current values of the input voltage and the load resistance, form the drive vector (inductor current and voltage capacitor) onto a fixed point of the 1-cycle display, subtracting from this a vector of feedbacks on state variables at stroboscopic time instants, obtaining sampler-storage devices using scaling amplifiers is implemented using subtractors; further, the subtraction result is amplified by scaling amplifiers and fed to the subtractor of the main control subsystem, correcting the error signal, thereby stabilizing the design dynamic mode (1-cycle).

Functional diagram of a control system (CS) by a direct step-down DC-DC converter is presented in Fig. 1.

In SU there are two subsystems:

- the main control subsystem (OPU) provides stabilization of the average value of the output voltage without taking into account nonlinear dynamic properties;

- auxiliary control subsystem (VPU) provides stabilization of the design dynamic mode (1-cycle).

The standard automatic control system with feedback on the average value of the output voltage of the pulse converter is described by the stroboscopic display function of the form [2]

, $${\text{X}}_{\text{k}}={\text{e}}^{\text{A}a}{\text{X}}_{\text{k-1}}+{\text{(e}}^{\text{A}a}{\text{-e}}^{{\text{A (1-z}}_{\text{k}}\text{)}a}{\text{) A}}^{\text{-one}}\text{B}$$

,

where the vector of state variables X = [i _L , U _c ,] ^Т , i _L is the inductor current; U _c is the voltage across the capacitor; z _k is the PWM duty cycle on the k-th clock interval; X _k-1 is the vector of system state variables at the beginning of the k-th clock interval. The matrix of parameters of system A and the vector of forcing actions B are presented in [2]. Matrix A depends on the inductance of the inductor L, the capacitance of the capacitor C, the stray resistance of the inductor R and the load resistance R _H. Vector B depends on the input voltage of the converter E ₀ and the inductance of the inductor L.

In a standard control system, a scaling amplifier with a coefficient of β is used to establish voltage feedback. Subtractor B calculates the error by the voltage _Ush , which is fed to the proportional controller with coefficient α. As a reference to the average value of the output voltage, the signal U _{s is used} . The control signal after the regulator U _y is fed to the non-inverting input of the comparator. At the inverting input of the comparator, a deployment voltage U _p is supplied from the generator of the deployment voltage of the surge voltage. The output pulses of the comparator U _and control the power transistor VT as part of the direct step-down converter.

In this case, two additional control actions ΔU _Ош1k and ΔU _Ош2k (Fig. 1), which are determined by the expressions

_Osh1k ΔU = K ₁ (U _ckz -U _ck)

ΔU _os2k = K ₂ (U _Lkз -I _Lk ),

where U _ckЗ , U _Lkз are the reference signals for the voltage across the capacitor and the inductor current, respectively, at stroboscopic time instants (fixed display point); U _ck is the scaled voltage across the capacitor at stroboscopic times; I _Lk - scaled throttle current at stroboscopic time instants.

The expression for the stroboscopic display function of the control system has the form

, $${\text{X}}_{\text{k}}={\text{e}}^{\text{A}a}{\text{X}}_{\text{k-1}}+{\text{(e}}^{\text{A}a}{\text{-e}}^{{\text{A (1- (z}}_{\text{k}}+\Delta {\text{z}}_{\text{k}}\text{)))}a}{\text{) A}}^{\text{-one}}\text{B}$$

,

where Δz _k is the increment of the duty cycle on the k-th clock interval.

The specified increment is calculated based on the expression

, $$\Delta z_k=\frac{\alpha \left(\Delta U_{\mathrm{about}w\mathrm{one}k}+\Delta U_{\mathrm{about}w2k}\right)}{U_{pm}}$$

,

where U _pm is the amplitude of the deploying voltage at the output of the surge voltage.

When implementing the considered control algorithm, the most important task is to calculate the fixed point of the stroboscopic display, which is found using the method of period equations [2]. However, when using this method, the microcontroller of the control system has to implement one of the numerical methods for solving systems of nonlinear transcendental equations, which requires quite serious computational resources. To simplify this problem, two neural networks (HC1 and HC2) were used, each of which calculates its component of the fixed-point vector of the 1-map mapping X * = [U _ckз , i _Lkз ] ^T.

The input variables of neural networks (regression factors) are parameters that can vary widely during the operation of the system. Factors used in the regression models under consideration include reference voltage U _s , input voltage E ₀ and load resistance R _n , which is calculated using the signals of the load current sensor and the output voltage sensor. This approach can significantly reduce the calculation time of a fixed point, and the achieved approximation accuracy is acceptable from the point of view of practice. In the control system under consideration, neural networks implemented a regression model of the form X * = F (P) = [f ₁ (U ₃ , E ₀ , R _n ), f ₂ (U _z , E ₀ , R _n )], where f ₁ and f ₂ - nonlinear three-parameter functions - components of the vector function F, realized by HC1 and HC2, respectively, P = [U _s , E ₀ , R _n ] ^T - vector of regression factors. The calculation of the current load resistance is carried out by the calculator block of the load resistance of the BCH.

Feedback on state variables at stroboscopic time points in the proposed system (Fig. 1) is carried out using sampling and storage devices (UVX1 and UVX2 in Figure 1). As can be seen from figure 1, the voltage at the output capacitor C and the inductor current L, scaled with the coefficients β ₁ and β _2, respectively, are stored at the beginning of each clock interval when a gating pulse is supplied to the I / O from a master oscillator, which works synchronously with the generator voltage deployment voltage. Using two subtractors (B1 and B2 in FIG. 1), the deviation of the current position of the display point from the specified one is calculated, followed by scaling with coefficients K ₁ and K _{2 of the} corresponding components of the mismatch vector ΔX = [ΔU _ck , Δi _Lk ] ^T. Calculated increment ΔU ΔU _{osh2k osh1k} and summed with the error voltage U GTC _oui causing each clock interval stabilizing design mode duty ratio increment Δz _k. When the project 1-cycle system is established, ΔU _Ош1k = ΔU _Ош2k = 0, and also Δz _k = 0.

The proposed structure of the control system is implemented by a fairly wide range of modern digital signal microcontrollers or inexpensive programmable logic integrated circuits. When using the latter, the calculation of a task on a fixed point of a 1-cycle using neural networks is greatly simplified.

In order to analyze the proposed method, computer simulation was performed, the results of which are shown in FIGS. 2, 3 in the form of dynamic mode maps showing the features of dividing the system parameter space into the stability domains of various modes. Modeling was carried out with the following system parameters: L = 0.1 H; C = 1 μF; R = 10 ohms; R _n = 100 Ohms; α = 60; β = 0.01; U _s = 5 B; U _pm = 10 B; a = 0.0001 s; K ₁ = -0.9; K ₂ = -0.9; β ₁ = 0.01; β ₂ = 0.1.

When constructing dynamic mode maps (Figs. 2, 3), a sufficiently large regulator gain α = 60 was selected, which made it possible to evaluate the capabilities of the method when the system operates in rather difficult conditions. As can be seen from figure 2, the region of the 1-cycle system without controlling the nonlinear dynamics is not simply connected and its area is relatively small.

Figure 3 presents a map of dynamic modes, the analysis of which shows that the region of the 1-cycle (P1) has increased significantly compared with the region of the 1-cycle in figure 2. In particular, with an input voltage E ₀ <1500 V, a stable 1-cycle is present in the system over the entire range of the voltage variation of the reference. At E ₀ > 500 V and at U _З > 8 B, regions of chaotic oscillations appear on the map, whose area is relatively small. The use of this control method made it possible to significantly improve the nonlinear dynamic properties of the system, while the gain of the proportional controller remained unchanged, which allowed us to preserve the given static error _Ush .

The simulation clearly shows the effectiveness of the method of controlling the nonlinear dynamics of a direct step-down voltage converter. Using this control method will allow you to abandon parametric synthesis while providing the specified nonlinear dynamic properties of the system and at the same time provide the specified performance and accuracy of the stabilization of the output voltage.

Literature

1. Batlle C. Stabilization of periodic orbits of the buck converter by time-delayed feedback / C. Batlle, E. Fossas, G. Olivar // International Journal of Circuit Theory and Applications. - 1999. - Vol. 27, No. 3. - P.617-631.

2. Kobzev, A.B. Nonlinear dynamics of semiconductor converters / A.B. Kobzev, G.Ya. Mikhalchenko, A.I. Andriyanov, S.G. Mikhalchenko - Tomsk: Tomsk, state. University of Control Systems and Radio Electronics, 2007. - 224 p.

Claims (1)

A control system implemented due to the fact that a control system consisting of two subsystems is connected to the power part of the converter made on the basis of a direct lowering converter, ZC filter: the main subsystem, consisting of a subtractor, which forms the difference between the reference signal and the feedback signal ( error signal), a scaling voltage feedback amplifier proportional to the controller, to the input of which an error signal is supplied, and the output signal is fed to the input of the comparator, to the second input otorrhea signal from the scanning voltage generator operating synchronously with the master oscillator, that allows to generate the inverter control signal providing stabilization of the mean value of the output voltage; auxiliary control subsystem, characterized in that approximators based on neural networks are introduced, which, using the current values of the reference voltage, input voltage and load resistance (calculates the load resistance calculator), form a reference vector (inductor current and voltage across the capacitor) to a fixed display point 1-cycle, subtraction from which the vector of feedbacks on state variables at stroboscopic time moments obtained at the output of sampling-storage devices using using scaling amplifiers, it is realized using subtractors, then the subtraction result is amplified by scaling amplifiers and fed to the subtractor of the main control subsystem, correcting the error signal, thereby stabilizing the design dynamic mode (1-cycle).

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