RU2746798C1 - Method for controlling nonlinear dynamic processes in single-phase voltage inverters with sinusoidal bipolar reverse modulation - Google Patents

Abstract

FIELD: converter technology.

SUBSTANCE: claimed invention relates to converter technology; it can be used in the implementation of digital control systems for single-phase inverters with sinusoidal pulse-width modulation. An algorithm for controlling nonlinear dynamics is proposed. The control pulses to the keys of the power part, consisting of a bridge inverter and an L-shaped LC filter, are supplied by a control system that includes two subsystems. The main subsystem is a standard automatic deviation control system that consists of an error calculator that calculates the difference between the task signal and the feedback signal, a feedback amplifier with a given coefficient, a regulator that amplifies the error signal with a given coefficient, the adder to one of the inputs of which a signal is sent after the controller, and to the second input of which a signal from the auxiliary control system for dynamic processes is sent, a sampling-storage device that captures the control signal at discrete times, the output signal of which is fed to the comparator, which compares this signal with the unfolding voltage coming from a specialized generator, and generates control pulses with power keys, which allows providing a high-quality sinusoidal output voltage in a wide range of variations in system parameters. The second subsystem is a control system for nonlinear dynamic processes. When calculating corrective actions at discrete moments in the control system for nonlinear dynamic processes, the values of phase variables at discrete moments in the previous period of the low-frequency process are used. Subtracting from them using subtractors of state variables at discrete moments in the current period of the low-frequency process, recorded by sampling-storage devices and scaled with specified coefficients, forms a residual vector, the components of which are multiplied by the specified coefficients. Then, the components of the residual vector are fed to the adder of the main control subsystem, which allows one to influence the error signal and ensure the stability of the required dynamic mode. The technical implementation of the proposed control system does not require the use of expensive high-performance microcontrollers and can be implemented by slightly modifying the circuit of a standard device.

EFFECT: invention is aimed at eliminating dangerous fluctuations in the output voltage that occur with a certain set of system parameters.

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Description

The claimed invention relates to converter technology and can be used in the implementation of digital control systems for single-phase inverters with sinusoidal pulse-width modulation with the possibility of eliminating dangerous fluctuations in the output voltage arising from a certain set of system parameters.

The known method IOP Conference Series: Materials Science and Engineering [1], called the method of targeting, where to stabilize unstable desired dynamic modes, it is assumed to use linear feedback.

The stabilization of the desired dynamic mode occurs due to the fact that a correction signal is added to the control signal after the voltage regulator, which is the sum of the components of the scaled residual vector, which is the difference between the vector of coordinates of a given fixed point of the desired mode fixed at discrete times and the vector of coordinates of the current operating point, also fixed at discrete times.

The disadvantages of this method include the need to use pre-calculated arrays of coordinates of fixed points of the stroboscopic display X _st1 = [x _11reƒ , x _12reƒ , x _13reƒ ,… x _1greƒ ]; X _st2 = [x _21reƒ , x _22reƒ , x _23reƒ ,… x _2greƒ ] of size equal to the multiplicity of quantization q. The first array is a set of tasks for the desired choke current at discrete moments in time during a period of low-frequency output voltage, and the second is a set of tasks for the desired voltage across the capacitor at discrete moments in time. To calculate them, fixed-point computers are used, which make serious demands on the speed of the control microcontroller, which increases the cost of the control system and makes it impossible to create devices with a high quantization rate.

The known method of the 4th IEEE Conference on Industrial Electronics and Applications (ICIEA) [2], called the method with lagging feedback, where to stabilize the unstable desired dynamic modes of inverters with sinusoidal pulse width modulation is also assumed to use continuous linear feedback.

The stabilization of the desired dynamic mode occurs due to the fact that a correction signal is continuously added to the control signal after the voltage regulator, which is the scaled difference between the current at time t and the current at time t- a , where a is the pulse-width modulation period, which allows you to provide the desired periodic mode. Moreover, this correction refers to the methods of continuous control of nonlinear dynamic processes.

The disadvantages of this method is the need to use a pure delay link in the nonlinear dynamic processes control subsystem, which can be implemented only with the use of microcontrollers. The peculiarity of the microcontroller implementation of the pure delay link classifies this system as a quasi-continuous control system. It is also obvious that when implementing a pure lag link, the requirements for the microcontroller are quite high.

The aim of the invention is to create a discrete control system for nonlinear dynamic processes in a single-phase voltage inverter to ensure its operation in the desired dynamic mode with a low amplitude of parasitic harmonics without using a pre-calculated array of coordinates of fixed points of stroboscopic display and without using a quasi-continuous control principle that imposes high requirements on the microcontroller, realizing a link of pure delay.

This problem is solved due to the fact that the control pulses to the keys of the power unit, consisting of a bridge inverter and an L-shaped LC filter, are supplied by a control system that includes two subsystems: the main subsystem, which is a standard automatic control system for deviation and consists of a calculator error, which calculates the difference between the reference signal and the feedback signal, a feedback amplifier with a given coefficient, a controller that amplifies the error signal with a given coefficient, an adder, one of the inputs of which is fed a signal after the controller, and the second - a signal from an auxiliary control system for dynamic processes , a sample-and-hold device that captures the control signal at discrete moments in time, the output signal of which is fed to a comparator, which compares this signal with the sweeping voltage supplied from a specialized generator, and generates control pulses with power switches, which allows emit high quality sinusoidal output voltage in a wide range of variation of system parameters; control system for nonlinear dynamic processes,

characterized in that the considered method, when calculating corrective actions at discrete moments in the control system of nonlinear dynamic processes, uses the values of phase variables at discrete moments in the previous period of the low-frequency process, subtraction from which using subtractors of state variables at discrete moments in time in the current period of the low-frequency process, fixed by the sampling-storage devices and scaled with specified coefficients, generates a residual vector whose components are multiplied by specified coefficients, and then the components of the residual vector are fed to the adder of the main control subsystem, which allows discrete time influence on the error signal and ensure the stability of the required dynamic mode.

The technical implementation of the proposed control system does not require the use of expensive high-performance microcontrollers and can be implemented by slightly modifying the circuit of a standard device.

The essence of the invention is illustrated by drawings, which show:

FIG. 1. Functional diagram of a converter with sinusoidal bipolar reversible modulation [3] with control of nonlinear dynamic processes.

FIG. 2. Two-parameter maps of dynamic modes of converters with sinusoidal bipolar reversible modulation without control of nonlinear dynamic processes.

FIG. 3. Two-parameter maps of dynamic modes of converters with sinusoidal bipolar reversible modulation with control of nonlinear dynamic processes.

In the control system of the converter (Fig. 1), two subsystems are distinguished: the main control subsystem (GPU), which provides regulation by the deviation of the instantaneous value of the output alternating sinusoidal voltage; a control system for nonlinear dynamic processes (NDPC), which provides corrective actions to the main control subsystem in order to stabilize the desired dynamic mode.

The GPU uses a β scaling amplifier to provide voltage feedback. The subtractor calculates the error of the output voltage U_osh, which is fed to the proportional controller with the coefficient α. The signal U is used as a reference for the output voltage._swhich changes in time according to a sinusoidal law. Control signal after controller U_at the input of the adder is fed, the second input of which receives the signal from the SUNDP, and the output signal is fed to the non-inverting input of the comparator. The scanning voltage U is applied to the inverting input of the comparator_R from the generator of the deployment voltage ГРН. Comparator output pulses U_and they control power transistors as part of a bridge converter, and control signals are fed to transistors VT2, VT3 from the output of the inverter, and a signal from the comparator is fed to the input of which.

FIG. 1 the following designations are adopted: x _{p, k, i} - the i-th phase variable at the beginning of the k-th clock interval of the p-th period of the sinusoidal control action; u _{p, k, i} - control action on the i-th phase variable at the beginning of the k-th clock interval of the p-th period of the sinusoidal control action.

The proposed control system does not use pre-calculated arrays of fixed points of stroboscopic display, as well as a pure delay link. The state variables in the form of the inductor current and the voltage across the capacitor are recorded by the sampling-storage devices UVX1 and UVX2 (Fig. 1) at discrete moments of time, after which they are scaled with coefficients β ₁ and β _2, respectively. УВХ1, УВХ2 are clocked by pulses from the clock generator ZG, which simultaneously clocks the reference voltage generator ГРН, providing synchronous operation of these devices. Blocks of delay BZ (Fig. 1) are also clocked by the master oscillator ZG and provide a delay for q-clock intervals, i.e. for the period of the output voltage, memorizing the state variables at discrete times, which reduces the requirements for the microcontroller.

Subtractors B1 and B2 calculate the deviations of the coordinates of the k-th discrete point at the p-th period of the control action from the coordinates of the k-th discrete point at the p-1-th period of the control action with multiplying the obtained differences that make up the residual vector ΔX = [Δx _{p, k , 1} , Δx _{p, k, 1} ] ^T = [Δu _{cp, k} , Δi _{Lp, k} ] ^T , by the coefficients К ₁ and К _2, respectively.

The corrective actions of the SUNDP u _{p, k, i are} determined by the expression

u _{p, k, i} = K _i β _i (x _{p-1, k, i} -x _{p, k, i} ) = K _i β _i Δx _{p, k, i} , where i = 1, 2, k = 1 , 2 ... q,

where q is the multiplicity of quantization.

Corrective actions u _{p, k, i} arriving at the main control subsystem cause a change in the coefficient Δz _{p, k} at the k-th clock interval.

To calculate the optimal coefficients K _i, it is necessary to calculate the monodromy matrix in the vicinity of the fixed point of the desired mode X * and choose such coefficients K _i at which the senior multiplier will be less than one.

To begin with, consider the mathematical description of the movements in the transducers in the form of a stroboscopic display, which is a modification of [4]

where p is the number of the iteration of the mapping of the system with an external periodic action, X _{p, k} are the values of the vector of phase variables at the beginning of the k-th clock interval of the p-th iteration of the mapping.

Let us introduce the notation

n=2… - вектор моментов коммутаций на тактовом интервале в относительном времени при этом z_k0=0, z_knk=1,

.Where

n = 2 ... is the vector of switching moments on the clock interval in relative time with z _k0 = 0, z _knk = 1,

...

The transition from absolute time t to relative z is carried out by the expression

The matrices A _i and the vector V _ABi in (2) for i = 1,2 are defined [4]

где R - активное сопротивление дросселя, L - индуктивность фильтра, С - емкость фильтра, U_вх - входное напряжение, R_н - сопротивление нагрузки.

where R is the active resistance of the choke, L is the filter inductance, C is the filter capacitance, U _in is the input voltage, R _n is the load resistance.

The switching function for the system under consideration when using the proposed control method taking into account [4] has the form

where X _k-1 is the value of the vector of phase variables at the beginning of the k-th clock interval; c ₁ = (0 1) ^T is a constant vector that determines the component of the vector of state variables involved in the expressions, U _z (z, k) = U _zt sin (ω ((k-1) a + z a )), where ω = 2πƒ _c , ƒ _c = 1 / (q a ), for k = 1… q - the signal for the output voltage.

The switching moment on the clock interval in relative time is determined on the basis of the switching manifold equation

where ξ _{p, k, n} (X, z) is the switching function corresponding to the nth switching time at the kth clock interval of the pth iteration of the mapping, which is used to determine the switching time z _{p, k, n} (switching functions are specific for each converter and will be discussed later). Moreover, as mentioned earlier, for all cases z _{p, k, 0} = 0 and z _{p, k, nk} = 1.

In order to find the optimal values of K _i, consider the mapping

which maps the vector of fixed points at discrete times at p-1 iteration of the mapping to the vector of fixed points at discrete times at the p-th iteration of the mapping.

Mapping (4) can be accomplished by iterating over mapping (1). The indicated mapping for the desired system regime linearized in a small neighborhood of a fixed point can be represented as

- матрица линеаризованной системы, рассчитанная в окрестности неподвижной точки желаемого режима (матрица монодромии). Неподвижная точка желаемого режима в рассматриваемой системе может быть найдена по методике [4].

is the matrix of the linearized system, calculated in the vicinity of the fixed point of the desired mode (monodromy matrix). The fixed point of the desired mode in the system under consideration can be found by the method [4].

Having calculated the matrix M according to expression (5) using numerical differentiation using (1) using the Nelder-Mead optimization method, one can find such values of K _i at which the modulus of the maximum eigenvalue of the matrix M will be less than one.

The proposed structure of the control system is implemented by a fairly large range of modern microcontrollers.

To analyze the effectiveness of the proposed control system, mathematical modeling was carried out, which was carried out with the following system parameters: L = 0.1 H; C = 1 μF; R = 10 ohms; R _n = 100 Ohm; α = 60; β = 0.01; U _zt = 5 V; U _rt = 10 V; a = 0.0001 s; K ₁ = -0.9; K ₂ = -0.9; β ₁ = 0.01; β ₂ = 0.1.

Was built a map of dynamic modes (Fig. 2) in the space of two parameters: the amplitude of the reference action U _zt and the input voltage. On the map, the symbols П _ij mark the areas of existence of various dynamic modes (i is the multiplicity of the cycle, typical for this area, j is the number of the area with multiplicity i on the map). For example, the area P _1,1 is the first region of existence of the desired mode with the frequency of oscillations of the output voltage equal to the frequency of the driving signal (1-cycle) with duty cycle at all clock intervals that fit the period of the driving action greater than zero and less than one. Areas П _Xj - correspond to areas of chaotic fluctuations of physical quantities (m → ∞).

Under the desired dynamic mode of pulse voltage converters with sinusoidal pulse-width modulation we mean such a mode in which the frequency of oscillations of the output voltage is equal to the frequency of the control signal, while at each clock interval on the period of the output voltage, the duty cycle must be less than one and greater than zero [4 ].

As can be seen (Fig. 2), the area of the area of the desired 1-cycle P _1.1 in the converter with bipolar reverse modulation with sinusoidal modulation without non-linear dynamics control is 39.26% of the map area. There is also an undesirable 1-cycle (P _1,2 ), where there are zero or unity duty cycle on the period of the low-frequency reference action.

Analysis of FIG. 3 shows that when using the control of nonlinear dynamic processes, the area of the area of the desired 1-cycle (P _1.1 ) increased significantly (69.14% of the area of the map) compared to the area of the area of the 1-cycle of the system without control of nonlinear dynamics (Fig. 2 ). As can be seen from Fig. fig. 3, the area of unwanted 1-cycles P _1,2 remained on the card, at which the duty cycle is greater than one at some clock intervals. This area is unrecoverable. At large values of the input voltage, areas of undesirable modes P _{x, 1} and P _4.1 are also observed.

Simulation clearly shows the effectiveness of the proposed method for controlling the nonlinear dynamics of a single-phase inverter with sinusoidal bipolar reversible modulation. The use of this control method does not require the use of high-performance control microcontrollers.

List of literature

1. Andriyanov, A.I. Nonlinear dynamics control in single-phase inverter with sinusoidal pulse-width modulation / A.I. Andriyanov, D. Yu. Mikhal'tsov // IOP Conference Series: Materials Science and Engineering, IOP Publishing Ltd. - 2016, - No. 124, P. 1-7.

2. Hsieh, F.-H. Fast-scale instability phenomena and chaotic control of voltage control single-phase full-bridge inverter via varying load resistance / F.-H. Hsieh, P.-L. Chang, Y.-S. Chen, H.-K. Wang, J.-C. Hwang // 4th IEEE Conference on Industrial Electronics and Applications (ICIEA). - Xian, China: IEEE, 2009. - P. 3422-3427.

3. Kobzev, A.B. Nonlinear dynamics of semiconductor converters / A.B. Kobzev, G. Ya. Mikhalchenko, A.I. Andriyanov, S.G. Mikhalchenko - Tomsk: Tomsk. state un-t control systems and radio electronics, 2007. - 224 p.

4. Andriyanov, A.I. Research of nonlinear dynamics of impulse voltage converters / A.I. Andriyanov. - Bryansk: BSTU, 2016 .-- 187 p.

Claims (1)

The control system is realized due to the fact that the control pulses to the keys of the power unit, consisting of a bridge inverter and an L-shaped LC filter, are supplied by a control system that includes two subsystems: the main subsystem, which is a standard automatic control system for deviation and consists of an error calculator that calculates the difference between the reference signal and the feedback signal, a feedback amplifier with a given coefficient, a regulator that amplifies the error signal with a given coefficient, an adder to one of the inputs of which a signal after the regulator is fed, and to the second, a signal from an auxiliary dynamic control system processes, a sample-and-hold device that captures the control signal at discrete moments in time, the output signal of which is fed to a comparator, which compares this signal with a scanning voltage supplied from a specialized generator, and generates control pulses with power switches, which allows provides a sinusoidal output voltage when the system parameters drift; control system for nonlinear dynamic processes, characterized in that when calculating corrective actions at discrete moments in the control system for nonlinear dynamic processes, the values of phase variables are used at discrete moments in the previous period of the low-frequency process, subtraction from which using subtractors of state variables at discrete moments in time at the current the period of the low-frequency process, fixed by the sampling-storage devices and scaled with the specified coefficients, forms a residual vector, the components of which are multiplied by the specified coefficients, and then the components of the residual vector are fed to the adder of the main control subsystem, which makes it possible to influence the error signal and ensure the stability of the required dynamic mode ...

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