RU176670U1 - Switching voltage converter with adaptive nonlinear dynamics control system - Google Patents

Abstract

The utility model relates to power electronics and can be used in the construction of pulsed DC-DC converters with improved quality of the output physical quantity in a wide range of variation of the system parameters. The objective of the utility model is to ensure guaranteed operation of the voltage converter in the desired dynamic mode with a small amplitude of output voltage fluctuations when changing system parameters in a wide range. The power part of the converter is based on direct A step-down converter with an automatic control system consisting of a subtractor that generates an error signal, a voltage feedback amplifier, a regulator, the input of which contains an error signal, and the output signal is fed to the non-inverting input of the comparator, to the inverting input of which a signal from the generator of the deployment voltage operating synchronously with the master oscillator, which ensures stabilization of the average value of the output voltage, a nonlinear din control system is connected Ikoyi. Additionally, adaptation blocks of scaling coefficients are used, at the input of which: information on the input voltage of the converter, information on the setting action of the standard control system, the output signal of the load resistance calculation unit, the input of which is supplied by the signal from the load current sensor and the output voltage signal, which provides the calculation optimal scaling factors depending on the current system parameters, which are calculated using the Nelder-Mead method when searching for the minimum of the objective function F (K, K, ... K) = abs (max (abs (ρ (K, K, ... K))) - ρ), where ρ is the target value of the multiplier, K are the scaling factors, ρ- i-th multiplier. The technical result provided by the given set of features is the ability to provide the desired dynamic mode in a wide range of system parameters.

Description

The utility model relates to power electronics and can be used in the construction of pulsed DC-DC converters with improved quality of the output physical quantity in a wide range of variation of the system parameters.

A known voltage converter (patent No. 2552520) with a control system built on the basis of the method of direction to the target, where to ensure the desired dynamic mode, it is assumed to use an additional non-linear dynamics control system that generates corrective effects that affect the operation of the main control system.

The desired dynamic mode is achieved due to the fact that the correction signal of the nonlinear dynamics control system is added to the controller signal of the main control system, which is the sum of two differences, scaled with the given coefficients: the difference between the signal of the throttle current sensor at the time moments and the component of the stationary task vector point of the trajectory corresponding to the current of the inductor; the difference between the signal of the voltage sensor on the capacitor at time instants and the component of the reference vector to a fixed point on the path corresponding to the voltage on the capacitor, which allows the system to reach a given fixed point on the path.

The disadvantage of this method is the inability to work in a wide range of variation of the system parameters due to the non-optimal fixed scaling factors when changing the system parameters in a wide range, which can lead to the implementation of undesirable dynamic modes.

The objective of the utility model is to ensure the guaranteed operation of the voltage converter in the desired dynamic mode with a small amplitude of fluctuations in the output voltage when changing system parameters in a wide range.

This problem is solved due to the fact that the power part of the converter, made on the basis of a direct step-down converter with an automatic control system, consists of a subtractor that generates an error signal, a voltage feedback amplifier, a regulator, the input of which contains an error signal, and the output signal is fed to the non-inverting input of the comparator, to the inverting input of which a signal is supplied from the generator of the developing voltage operating synchronously with the master generator, which ensures it stabilizes the average value of the output voltage, a nonlinear dynamics control system is connected, characterized in that it additionally uses adaptation blocks for scaling coefficients, the input of which is supplied: information about the input voltage of the converter, information about the setting action of the standard control system, the output signal of the load resistance calculation unit, the input of which receives a signal from the load current sensor and the output voltage signal, which ensures the calculation of optimal m scaling coefficients depending on the current system parameters, which are calculated using the Nelder-Mead method when searching for the minimum of the objective function F _nd (K ₁ , K ₂ , ... K _n ) = abs (max (abs (ρ _i (K ₁ , K ₂ , ... K _n ))) - ρ _st.get) , where ρ _st.get - the target value of the multiplier, K _i - scaling factors, ρ _i - i-th multiplier.

The technical result provided by the given set of features is the ability to provide the desired dynamic mode in a wide range of system parameters.

The essence of the utility model is illustrated by drawings, which depict:

FIG. 1. Functional diagram of the converter.

FIG. 2 Diagram of 1-cycle multiplier modules.

FIG. 3. Module diagram of the senior 1-cycle multiplier.

In FIG. 1 is a functional diagram of a pulse converter, the description of which is given in [patent No. 2552520]. To improve the quality of non-linear dynamics control indicators, an adaptation block (BA) of the control algorithm parameters K _{i has} been introduced into the control system for the changing parameters of the control object, which most often include: input voltage U _I , load resistance R _n and reference voltage U _s .

In FIG. 1, the following notation is adopted: R is the active resistance of the inductor, L is the inductance of the inductor, C is the capacitance of the capacitor, R _n is the load resistance, U _in is the input voltage, (β ₁ , β ₂ are scale factors, β is the voltage feedback coefficient , U _s - reference voltage, U _and - impulses for controlling the power switch, U _y - control signal, U _p - sweep sawtooth voltage, OSU - main control system, RMSS - control system for nonlinear dynamics, SRN - generator of unfolding voltages, ЗГ - master generator, "==" - computer radiator, UVX, UVX1, UVX2 - sampling-storage devices, BHT1, BHT2 - calculators of the components of the fixed point of the display vector, BA - adaptation unit, UM1, UM2 - multipliers, K1, K2 - proportionality coefficients calculated by the adaptation unit, BCH - resistance calculator load, _Ush is the error of the main control system, VD is the power diode, VT is the power transistor, x _2z , x _1z are the components of the task vector on the fixed point of the 1-cycle, x _2k , x _1k are the components of the feedback vector for state variables in discrete time instants, Δx _2k , Δx _1k - components in vector deviation of the current mode point from the given, u _k1 , u _k2 - corrective action.

The method of adapting the coefficients K _i to the changing parameters of the system is as follows.

The direct step-down voltage converter is described by a system of differential equations with dimension two. The classical automatic control system with feedback on the average output voltage of direct converters operating in discontinuous current mode is described by a stroboscopic display of the form [Kobzev, A.V. Nonlinear dynamics of semiconductor converters / A.V. Kobzev, G.Ya. Mikhalchenko, A.I. Andriyanov, S.G. Mikhalchenko - Tomsk: Tomsk, state. University of Control Systems and Radio Electronics, 2007. - 224 s]

; i_L - ток дросселя; u_с - напряжение на конденсаторе; z_k1, z_k2 - моменты коммутации в относительно времени на k-том тактовом интервале; X_x-1 - вектор переменных состояния системы в начале k-го тактового интервала;

- вектор.Where

; i _L is the inductor current; u _s - voltage across the capacitor; z _k1 , z _k2 - switching times in relation to time on the k-th clock interval; X _x-1 is the vector of system state variables at the beginning of the k-th clock interval;

- vector.

When using the ISC, additional control actions u _ik are introduced, which are determined by corrective functions of the form [1]

Then the stroboscopic display for the ACS based on the ISC has the form

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

The specified increment can be found based on the expression

для импульсной САУ, описываемой СДУ n-го порядка на основе МНЦ, имеет видSwitch function

for a pulsed self-propelled guns described by an n-th order SDE based on the ISC, has the form

where c ₁ = [0; 1] is a constant vector that defines the component of the vector of state variables participating in the expression.

The stroboscopic display (3), linearized near the fixed point of the 1-cycle, can be represented as

- матрица монодромии стабилизируемого 1-цикла, Y_k-1=Х_k-1-X'.where k is the number of iterations of the map,

is the monodromy matrix of the stabilized 1-cycle, Y _k-1 = X _k-1 -X '.

The dimension of the matrix M _D depends on the order of the system of differential equations describing the operation of the device. In this case, it is necessary to choose a value of the coefficients K _i at which the leading multiplier of the matrix M _D takes a value less than unity.

The main criterion for choosing the coefficients K _i is the convergence of the stroboscopic display (3) to a stable fixed point (i.e., the 1-cycle must be stable). To analyze the local stability of the 1-cycle, the first Lyapunov method is used. As is known, the local stability of a periodic solution is determined on the basis of multipliers (ρ _i , where i = 1 ... n) of the monodromy matrix M ^* , where n is the order of the system. As follows from expression (2-5), the multipliers of the monodromy matrix depend on the coefficients K _i .

As you know, the periodic mode is stable when the modules of all the multipliers are within the unit circle on the complex plane. For the system under consideration, this condition can be written as

abs (max (ρ _i )) <1.

This means that for the stability of the desired 1-cycle, its senior multiplier must be less than unity, which requires the selection of a certain value of the coefficients K _i . For reliable operation of the converter, we introduce the concept of the margin of safety modulo the senior multiplier, which is calculated by the expression

δ = 1-ρ _st .

where ρ _st.sel - the target value of the multiplier.

The problem of finding the optimal K _i values of the coefficients can be reduced to an optimization problem. The objective function in this case will be

As can be seen from (6), the main task is to find values of the coefficients K _{i such} that the modulus of the difference between the actual value of the modulus of the senior multiplier of the 1-cycle and the target value of the modulus of the senior multiplier will be minimal.

Features of the mathematical problem of calculating the coefficients of the correction function in the case of a system described by a two-dimensional stroboscopic display for a start are considered for the special case when K _i = K ₂ = K.

In FIG. 2 presents a particular example of a diagram of 1-cycle multipliers. In the figure: the dotted line is the dependence of the multiplier modulus | ρ ₁ |; dashed line is the dependence of the multiplier | ρ ₂ |; solid line is the dependence of the modulus of the senior multiplier | ρ _max | - As can be seen from the figure, the dependence of the modulus of the senior multiplier | ρ _max | of the coefficient K is nonlinear and undergoes a discontinuity at the point K _p . So, for K <K _{p the} module of the highest multiplier | ρ _max | = | ρ ₁ |, and for K> K _{p the} module of the highest multiplier | ρ _max | = | ρ ₂ | - Obviously, in the general case, this dependence can be more complex.

In a more complicated case, K ₁ ≠ K ₂ , which complicates the task of finding the desired values of the coefficients of the CF. Schedule module senior multiplier depending on the coefficients K ₁ and K ₂ are shown in FIG. 3, where the coordinates of the minimum of the function are marked with a white dot.

Due to the complexity of the dependence of the senior multiplier on these coefficients and the possibility of the existence of discontinuities of the objective function, this mathematical problem can be attributed to the problem of optimizing convex non-differentiable functions. A number of methods have been developed to solve such problems. The analysis showed that, depending on the situation, the Monte Carlo method, subgradient optimization methods, the Nelder-Mead method, etc. can be used to search for optimal values of the coefficients K _i . The disadvantages of subgradient optimization methods include the need for a priori knowledge of the value of the objective function at the minimum, which in this case impossible. In this case, the Nelder-Mead method is used.

The search for the minimum of the objective function (8) is carried out on the intervals [K _1mim , K _1max ] and [K _2min , K _2max ] whose boundaries are set empirically. The maximum number of iterations of the optimization method is denoted by N _c .

Iterations continue until the higher multiplier module satisfies the termination condition for iterations or the number of implemented iterations is less than N _c . If the optimal values of the coefficients were not found, then these coefficients are equal to zero (refusal to use the ISC). The refusal to use the ISC in the absence of stabilization conditions for the 1-cycle with a given margin of stability will lead to the presence of undesirable dynamic modes, but it is worth noting that the problem of completely eliminating undesirable modes in the entire range of system parameters is not solved, but the maximum possible area of the desired 1- cycle. As the analysis showed, in the general case, in the systems of the class in question in certain areas of the system parameters, the mathematical problem posed above can be unsolvable and the module of the senior multiplier will remain more than unity for any value of the coefficients of the correction function in the allowable range of their values.

Obviously, the calculation of the monodromy matrix and the search for its eigenvalues in conjunction with the optimization method for finding the optimal values of the coefficients K _{i are} quite difficult to perform directly in the digital control system due to the high requirements for computing resources, therefore, it is proposed to use a neural network for microcontroller implementation of the control system . In this case

,

,

where the function ϕ _i is realized by a neural network. The calculation of the training sample for the neural network is carried out on the basis of the algorithm considered above on the instrumental computer.

Mathematical modeling of the system was carried out in order to check the operability of the algorithm. Modeling was carried out for a system with parameters: L = 0.1 H, C = 1 μF, R = 1 Ohm, R _n = 150 Ohm, α = 30, β = 0.01, U _pm = 10 V, a = 0, 0001 s

In FIG. 4 and FIG. Figure 5 shows the maps of dynamic modes under various operating conditions of the system. On the maps, symbols П _{i, j} indicate the areas of existence of various dynamic modes (i is the m-cycle characteristic of this area, j is the number of the area on the map of dynamic modes). In particular, the region P _1.1 represents the first region of existence of the main (design) mode with a frequency of ƒ = ƒ _q (1-cycle), where ƒ _q = 1 / a is the quantization frequency. The region П _{х, j} - corresponds to non-deterministic operating modes of the transducer (m → ∞).

Analysis FIG. 4 shows that without the use of the ISC, the regions of undesirable modes occupy a rather large area of the map of dynamic modes. At large input voltages and small driving influences, a chaotic regime is realized in the system (region П _{x, 2} ). With large driving influences in the entire range of input voltages, undesirable modes with a large amplitude of oscillations are realized. The area of the 1-cycle region in FIG. 4, a is 52.74% of the map area.

The use of adaptation of the parameters K ₁ and K ₂ based on the proposed algorithm (adaptation algorithm parameters: K _1min = K _2min = -3; K _1max = K _2max = 3; ρ _st.cell = 0.6, N _c = 300) allowed eliminate areas of undesired dynamic modes, which follows from FIG. 5 and speaks of its effectiveness.

Claims (1)

A pulse converter, the power part of which is based on a direct step-down converter with an automatic control system consisting of a subtractor that generates an error signal, a voltage feedback amplifier, a regulator, the input of which contains an error signal, and the output signal is fed to the non-inverting input of the comparator, on the inverting input of which receives a signal from the generator of the deployment voltage operating synchronously with the master oscillator, which ensures stabilization of the medium output voltage values, a non-linear dynamics control system is connected, characterized in that the adaptation blocks of scaling coefficients are additionally used, the input of which is supplied: information about the input voltage of the converter, information about the setting action of the standard control system, the output signal of the load resistance calculation unit, at the input which receives a signal from a load current sensor and an output voltage signal, which ensures the calculation of optimal scaling factors nt depending on the current parameters of the system, which are calculated using the Nelder-Mead method when searching for the minimum of the objective function F _nd (K ₁ , K ₂ , ..., K _n ) = abs (max (abs (ρ _i (K ₁ , K ₂ , ..., K _n ))) - ρ _{st. Purpose} ), where ρ _{st. Purpose} - target value of the multiplier, K _i - scaling factors, ρ _i - i-th multiplier.

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