WO2014178673A1

WO2014178673A1 - Pulse width modulation method for controlling power converter

Info

Publication number: WO2014178673A1
Application number: PCT/KR2014/003901
Authority: WO
Inventors: 박인규
Original assignee: Park In Gyu
Priority date: 2013-05-03
Filing date: 2014-05-01
Publication date: 2014-11-06

Abstract

The present invention relates to a pulse width modulation method for controlling almost all types of switching power converters. The first purpose of the present invention is to provide a pulse width modulation method which can regulate a switching frequency while maintaining excellent characteristics of a hysteresis pulse width modulation method, and which can be easily implemented, has an excellent switching frequency regulation performance, and is applicable to 2-level, multi-level and multi-phase power converters. The second purpose of the present invention is to provide a pulse width modulation method which is capable of synchronization and which can operate even in a discontinuous current mode and can be used for an open-loop control as well as a closed-loop control, in addition to the first purpose. The first invention is mainly characterized by providing a means for detecting a switching period and adjusting an allowable band signal by subtracting the detected switching periodic signal from a reference switching periodic signal and passing the remainder through a sample compensator. The second invention is mainly characterized by reducing a carrier band signal at a constant slope with time and adding a specific step value to the carrier band signal when switching a control signal. The present inventions can be used for applications, in particular, in current control integrated circuits for pulse width modulation, power management integrated circuits or motor driving integrated circuits.

Description

【Specification】

[Name of invention]

Filth Width Modulation Method for Control of Power Converter

The present invention relates to a fill width modulation method for controlling a power converter, and more particularly, a DC-DC converter or a switching regulator such as a step-down converter, a step-up converter, a step-down converter, and the like; DC switch mode power supplies or floor electric devices such as half-bridge converters, all-bridge converters, push-pull converters, forward converters, and flyback converters; Single-phase AC-DC converters such as power factor correcting rectifiers and fill width modulation converters; Single-phase DC-AC converters such as half-bridge inverters, all-bridge inverters, push-pull inverters, fill width modulated power amplifiers, or motor drivers; Three-phase bridge inverter or three-phase electric motor driver; Three-phase bridge converter; Polyphase-bridge inverters or polyphase motor drivers; It relates to a fill width modulation method for the control of almost all switched (or stationary) power converters, including polyphase-to-bridge converters.

Background Art

Switching power converter

Power conversion is to convert the power supplied to the required power. This power conversion is necessary in almost all cases of power use, from small powers of several W or less to large powers of several MW or more.

One of the important goals of power conversion is to increase power efficiency by reducing power loss. Switching power converters (hereinafter referred to as power converters) use a switch which is a lossless control element as a means to achieve high efficiency. Lossless switches are ideal, and some real state switching and switching losses occur in real semiconductor switching devices such as diodes and transistors.

A switch is a device that is not capable of continuous control but only on-off control (or switching). The power converters can thus be selectively controlled to only a limited level of voltage or current output depending on the respective circuit configuration and switching of the switches.

The most widely used are two-level converters. DC-DC converters or switching regulators such as step-down converters, step-up transformers, step-down converters, and the like; DC switch mode power supplies such as half-bridge converters, all-bridge converters, push-pull converters, forward converters, and flyback converters; Power factor correcting rectifier; Single-phase DC-to-AC converters such as half-bridge inverters, push-pull inverters, field width modulated power amplifiers, or motor drivers, etc. Belongs to level translator. _,

Multi-level converters have better output quality than two-level converters, but the circuit configuration is more complex. Widely used full bridge inverters and neutral point clamp (NPC) transducers are the typical multi-level transducers as three-level transducers.

Multi-phase transducers can be configured by connecting two-level transducers or multi-level transducers in multiple phases. Three-phase bridge converter is a representative polyphase converter. Full-bridge inverters can also be seen as two-level two-phase converters. DC-DC interleaved converters are also multiphase converters. Polyphase converters are mainly used to drive polyphase motors or generators. Control of power converters ^''

Another important goal of power conversion is to increase accuracy by reducing errors. In the early days of power conversion technology, mainly open loop control was used. Since then, closed-loop control has become increasingly known to increase accuracy and acuity.

Closed loop control is possible, but linear feedback control is typical. Linear feedback control is a control in which an error signal obtained by subtracting an output signal from a reference output signal is an input signal through a linear compensator. Examples of linear compensators include proportional compensators, proportional-integral compensators, and proportional-integral- derivative compensators. Linear feedback control has the advantage of being easy to implement and guaranteeing results.

In general, the larger the proportional gain of the compensator, the smaller the tracking error and steady-state error. And the greater the proportional gain, the faster the transient response speed, given the prevailing pole of the system transfer function. If the dominant poles of the system transfer function are complex pairs, increasing the proportional gain does not speed up the transient response and increases the frequency of vibration. Integral gain also has the effect of reducing steady-state error. The larger the integral gain and the lower the frequency, the greater the effect, and the DC steady-state error is zero regardless of the magnitude of the integral gain. However, an increase in the order of the system is a disadvantage. Basically, it has a negative effect on the transient response rate. In a condition where the dominant pole of the system transfer function is a real number, the larger the integral gain, the less the negative effect of the transient response rate. If the dominant poles of the system transfer function are complex pairs, increasing the integral gain does not speed up transient transients and increases the frequency of vibration. The derivative gain can be used for the purpose of speeding up the transient response when the dominant pole of the system transfer function is a complex pair. There are also many methods of designing compensators in the frequency domain. The accuracy at any frequency is proportional to the gain at that frequency above compensation. In general, the larger the gain of the compensator, the higher the asymmetry for variations in the various variables and parameters of the system. The input and output circuits of the power converter vary. However, a series inductor (or equivalent inductance) is usually connected to the output voltage terminals. (A current source converter is a pair of voltage source converters.) The control outputs also vary. For example, in the case of a switching regulator, a switch mode power supply, a fill width modulated power amplifier, the voltage of the filter capacitor may be the control output, and in the case of the motor driver, the motor speed may be the control output. However, it is known that the performance of the control methods including the current control of the series inductor in the minor loop is excellent. Recently, a so-called ripple-based voltage control method that uses the equivalent series resistance of the filter capacitor has also attracted attention. Although the control outputs of compensators and the types of compensators vary, the fill width modulation methods can usually be applied in common. Fill width modulation method

Power converters require a fill width modulation method because they are not capable of continuous control and can be selectively controlled to only a limited level. The field width modulation method for controlling the power converter receives a reference signal (reference control signal) as an input and outputs a control signal (signal for controlling the power converter) as an output. The fill width modulation method is based on a two-level fill width modulation method and is extended to a multi-level fill width modulation method such as three-level. It also extends to the polyphase fill width modulation method. Among the pillar width modulation methods, the carrier pillar width modulation method, the hysteresis pillar width modulation method, and the fixed frequency pillar width modulation method are classical, but are still widely used. Carrier Field Width Modulation Method

The main feature of the carrier fill width modulation method is to switch the control signal by comparing the reference signal with a high frequency carrier signal. Then, the switching frequency of the control signal is equal to the frequency of the carrier signal. As a carrier signal, a triangular wave or a sawtooth wave is mainly used. The carrier fill width modulation method can be used in both open loop control and closed loop control.

The carrier spread width modulation method has been used since the early days of power conversion techniques because it could be implemented with analog circuitry. Since the development of digital technology, sampling field width modulation methods of switching periods have emerged. The spatial vector fill width modulation method of three-phase DC-AC power converter is a representative example. However, as time delays due to sampling of switching cycles are known to adversely affect closed loop control, the role of real-time comparative carrier field width modulation without time delays becomes important again. Real-time comparison carrier field width modulation method is based on analog implementation, but switching the sampling period Much shorter than this can be implemented digitally.

The application of carrier fill width modulation to closed loop current control, such as direct-to-dc converters, switching regulators, or power factor corrected rectifiers, is commonly referred to as average current mode control. Application to closed loop control of DC-AC inverters or AC-DC converters is often referred to as the suboscillation method or the ramp comparison method.

The main advantage of the carrier fill width modulation method is that the switching frequency can be kept constant. On the other hand, in closed loop control, the biggest disadvantage is that there is a limit to the amount of gain of the compensator. This is because of the multiple crossing problem that occurs when the slope of the reference signal is greater than the slope of the carrier signal (see Non-Patent Document 4-7). The slope of the reference signal becomes large in proportion to the proportional gain of the compensator or the gain in the high frequency region, thus limiting the magnitude of the gain. In practice, however, the limit of this gain is often less than the desired or required value. As a result, it is not possible to speed up the transient quick speed sufficiently and it is impossible to sufficiently reduce the tracking error and the steady state error. It is also a disadvantage to precisely tune the compensator's gain. Another disadvantage is the inability to increase the asymmetry of variations in the parameters and parameters of the system.

Sampling or using filters to suppress switching ripples included in the reference signal does not help increase the compensator's gain. This is because vibrations and divergence occur because of sampling or delays in the filter. Hysteresis Field Width Modulation Method

The hysteresis field width modulation method is also called an allowable band, bang-bang, or sliding mode field width modulation method. Hysteresis The fill width modulation method is characterized in that the control signal is switched by comparing the hysteresis of the reference signal with a certain allowable band. The hysteresis field width modulation method can be used only in closed loop control.

The hysteresis field width modulation method has excellent characteristics in terms of transient quiescent speed, steady state error, and adaptability. However, the problem is that the switching frequency is not constant and varies greatly with the variation of various variables and parameters of the system. If the switching frequency is not constant, the switching power loss in the semiconductor switching element is not constant, which makes the heat dissipation and protection of the semiconductor switching element difficult. Difficulties also arise with filters and electro-magnetic compatibility (EMC) to suppress switching ripple. Another disadvantage is that it does not work properly when discontinuous current mode occurs. And because of the inability to synchronize, the performance is poor in a multiphase AC converter, and the harmonic neutralization in a multiphase DC interleaved converter Not applicable is also a big disadvantage. Fixed Frequency Field Width Modulation Method

Another fill width modulation method for closed loop control is a fixed (or constant) frequency pulse width modulation method. Also called peak current mode control. In the fixed frequency field width modulation method, the control signal is switched by a hysteresis comparison between a reference signal and a zero signal, and the control signal is switched at a certain period of time. The advantage is that the switching frequency is constant, synchronized, and operates in discontinuous current mode. Basically, however, there is an offset error of half the switching ripple. Also, if the duty ratio is greater than 0.5, it is unstable and low harmonics are generated. The addition of a compensating gradient wave stabilizes even when the duty ratio is greater than 0.5. However, the larger the slope, the larger the offset error tracking error and the steady state error. Increasing the integration gain or adding a design compensator in the frequency domain often cannot reduce the error significantly. It is also necessary to precisely run the slope and integral gains of the compensating gradient wave, and the disadvantage of not being able to sufficiently increase the asymmetry for the fluctuations of various variables and parameters of the system.

. The fixed frequency field width modulation method with the compensation slope wave is similar to the closed loop Lobni carrier field width modulation method. The gradient of the compensating gradient wave acts as the inverse of the proportional gain. The only difference is that hysteresis comparison is used. The proportional gain can be made larger because there is no multi-crossing problem, but there is a disadvantage that a large offset error occurs-allowable band control hysteresis field width modulation method

As a method for solving the switching frequency variation problem of the hysteresis field width modulation method, the allowable band control hysteresis field width modulation methods described in Patent Document 1, Non-Patent Document 1, and Non-Patent Document 2 are notable. These methods provide a means to detect the switching frequency, and subtract the switching frequency signal detected from the reference switching frequency signal and adjust the allowable band signal through a compensator.

Tolerant band controlled hysteresis field width modulation methods have the advantage that the switching frequency is regulated while maintaining the superior characteristics of the hysteresis field width modulation method. However, it is not very easy to implement and the switching performance of the switching frequency is not satisfactory. Essentially, detecting the switching frequency is not easy, and because the switching frequency and the allowable band are inversely related in nature. (Patent Document 1) US 6348780 Bl (David Grant) 2002. 2. 19.

(Non-Patent Document 1) KANG, B. J .; LIAW, C. M. 'Robust hysteresis current-controlled PWM scheme with fixed switching frequency', IEE Proc. Electr. Power Appl., Vol. 148, No. 6, 2001, p 503-512.

(Non-Patent Document 2) HUERTA, SC; ALOU, P .; OLIVER, JA; GARCIA, O .; COBOS, JA; ABOU-ALFOTOUH, AM 'Nonlinear control for dc— dc converters based on hysteresis of the Cout current with a frequency loop to operate at constant frequency ', IEEE Transactions on Industrial Electronics. Vol. 58, No. 3, 2011, p 1036-1043.

(Non-Patent Document 3) MOHAN, N .; UNDELAND, T. M .; ROBBINS, W. P. Power Electronics: Converters, Applications, and Design, John Wiley & Sons, 1989, ISBN 0-471-50537-4.

(Non-Patent Document 4) DIXON, L. 'Average current mode control of switching power supplies', Unitrode application note, 1990.

(Non-Patent Document 5) BROD, D. M .; NOVOTNY, D. W. 'Current control of VSI-PWM Inverter', IEEE Transactions on Industry Applications. Vol. 21, No. 4, 1985, p 562-570.

(Non-Patent Document 6) HOLTZ, J. 'Pulsewidth modulation for electronic power conversion', Proceedings of the IEEE. Vol. 82, No. 8, 1994, p 1194-1214. (Non-Patent Document 7) KAZMIERKOWSKI, M. P .; MALESANI, L.'Current control techniques for three-phase voltage-source PWM converters; a survey ', IEEE Transactions on Industrial Electronics. Vol. 45, No. 5, 1998, p 691 703.

(Non-Patent Document 8) YU, F .; LEE, FC; MATTAVELLI, P. Ά small signal model for average current mode control based on describing function approach ', in IEEE Energy Conversion Congress and Exposition Conference Record, 2011, p 405- 412.

(Non-Patent Document 9) REDL, R .; SUN, J, 'Ripple-based control of switching regulators' an overview', IEEE Transactions on Power Electronics. Vol. 24, No. 12, 2009, p 2669-2680.

[Detailed Invention] [Technical Challenges] ^■

The main object of the present invention is a prior art allowable band control hysteresis ^' pill width modulation method To improve or overcome the shortcomings of the law

The first object of the present invention is to maintain the excellent characteristics of the hysteresis field width modulation method, switching frequency is easy to implement, easy to implement, excellent switching performance of the switching frequency, 2-level, multi-level, and It is to provide a pulse width modulation method that can be applied to a polyphase power converter.

The second object of the present invention is to maintain the excellent characteristics of the hysteresis pulse width modulation method, the switching frequency is regulated, easy to implement, the switching performance is excellent, the synchronization is possible, even in the discontinuous current mode It is intended to provide a fill width modulation method that operates and can be used in open loop control as well as closed loop control and can be applied to two-level, multi-level, and multiphase power converters.

Technical Solution

The present invention is largely two kinds. The first invention achieves the first object, and the second invention achieves the second object.

In this specification, in order to more clearly describe the features of the present invention, an example described in MATLAB, which is a computer programming language, is also provided. The symbols in parentheses in the description of the feature are variables or values in the MATLAB description.

In this specification, in order to more clearly disclose the present invention, MATLAB simulation program examples are presented. In the program, the inductance is a forward Euler numerical model, and values such as frequency and voltage are some kind of per unit value. While changes to various settings of running the program ^"look can be understood in more detail the present invention. General features of the first invention

The general features of the first invention can be described as follows.

A control method for a power converter, comprising: a field width modulation method of receiving a reference signal and outputting a control signal to an output;

Providing an allowable band signal and a timer signal;

Setting a reference switching period; ^'

Increasing the timer signal by a constant slope over time; And switching the control signal through the hysteresis comparison between the reference signal and the allowed band signal, subtracting the timer signal from the reference switching period, adjusting the allowed band signal through a sampling compensator, and zeroing the timer signal. Made by hand; .

The pulls width modulation method comprising a. Features of the Two-Level Fill Width Modulation Method Embodiment of the First Invention

The characteristics of the two-level fill width modulation method embodiment of the first invention can be described as follows.

1. A fold width modulation method for controlling a two-level power converter that can be selectively controlled at two levels, the control signal s being output to a reference signal vr as an input;

Providing an allowable band signal (vb) and a timer signal (vt);

Setting the reference switching period Ts and the integral gain Ki;

Increasing the timer signal (vt) with a constant phaser over time; When the control signal (s) is at a high level (1) and the reference signal (vr) is less than the negative value of the allowable band signal (vb), change the control signal (s) to a low level (0) , Multiplying the integral gain (Ki) by the value obtained by subtracting the timer signal (vt) from twice the reference switching period (Ts), and adding the allowed band signal (vb) to the timer signal (vt). To make; And

Changing the control signal (s) to a high level (1) when the control signal (s) is at a low level (0) and the reference signal (vr) is greater than the allowable band signal (vb);

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language. vb = 0.2; vt = 0.0;

fs = 100; Ts = l / fs; Ki = 3;

vt = vt + dt;

if s == l && vr <-vb s = 0;

vb = vb + Ki * (2 * Ts-vt) ;, vt = 0; end

if s == 0 && vr> vb s = l; end Features of the Multi-Level Fill Width Modulation Method Embodiment of the Invention

The features of the multi-level fill width modulation method embodiment of the first invention can be described as follows.

For control of multi-level power converters, which can be selectively controlled in three or more levels, a spread that receives a reference signal (vr) as an input and outputs a control signal (s) and a level control signal (ss) as outputs. A width modulation method;

Raise allowable band signal (vb), delayed allowable band signal (vcl), and timer signal (vt) To do;

Setting a reference switching period (Ts), an integral gain (Ki), and a band margin (bm); Increasing the timer signal (vt) with a constant slope over time; 때에 when the control signal s is at a high level (1) and the reference signal vr is less than the negative value of the allowable band signal vb, the control signal s is changed to a low level (0) and Changing the delayed allowed band signal (vd) to the allowed band signal (vb) and multiplying the integral gain (Κί) by the value obtained by subtracting the timer signal (vt) from the reference switching period (Ts). Adding to the allowed band signal (vb) and making the timer signal (vt) zero;

When the control signal (s) is at a low level (0) and the reference signal (vr) is greater than the allowable band signal (vb), changing the additive control signal (s) to a high level (1);

The level control signal ss when the control signal s is at a high level (1) and the reference signal vr is greater than a value obtained by adding the third margin bm to the allowable band signal vb. Changing to the upper level; And

The level control when the control signal s is at a low level (0) and the reference signal vr is less than the negative value of the delayed allowed band signal (vd) minus the band margin (bm) Changing signal ss to lower level;

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language. vb = 0.1; vd = vb; vt = 0.0;

fs = 100; Ts = l / fs; Ki = 2; bm = 0.01;

vt = vt + dt;

if s == l && vr <-vb s = 0; vd = vb;

vb = vb + Ki * (Ts-yt); vt = 0; end

if s == 0 && vr> vb s = l; end

if s == l && vr> vb + bm ss = ss + 1; end

if s == 0 && vr <ᅳ vd bm ss = ss l; end Features of the Polyphase Pill Width Modulation Method Embodiment of the Invention

The characteristics of the polyphase pillar width modulation method embodiment of the first invention can be described as follows.

In the field width modulation method for controlling a multi-phase power converter in which the number of phases (N) is two or more, receiving a reference signal (vr) as an input and outputting a control signal (s) as an output for each phase (m). ; Providing a permit band signal vb and a timer signal vt for each phase; Setting the reference switching period Ts and the integral gain Ki;

For each phase (m), increasing the timer signal (vt) with a constant creeper over time;

For each phase m, the control signal s is at a high level (1) and the reference signal

When (vr) is smaller than the negative value of the allowed band signal (vb), the control signal (s) is changed to a low level (0) and the timer signal (vt) at twice the reference switching period (Ts). Multiplying the integral gain Ki by the subtracted from) to add to the allowed band signal vb, and make the timer signal vt zero; And

For each phase m, the control signal s is at a low level (0) and the reference signal

changing the control signal (s) to a high level (1) when (vr) is greater than the allowed band signal (vb);

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language.

N = 3; vb = 0.1 * ones (N, l); vt = zeros (N, l);

fs = 100; Ts = l / fs; Ki = l;

for m = l: N

vt (m) = vt (m) + dt;

if s (m) == l && vr (m) <-vb (m) s (m) = 0;

vb (m) = vb (m) + Ki * (2 * Ts— vt (m)); vt (m) = 0; end

if s (m) == 0 && vr (m)> vb (m) s (m) = l; end

end Features of First Embodiment Polyphase Single Band Pill Width Modulation Method

The features of the polyphase single band fill width modulation method embodiment of the first invention can be described as follows.

A control method for controlling a multi-phase power converter in which the number of phases N is two or more, wherein for each phase m, a field width modulation method of receiving a reference signal vr as an input and outputting a control signal s as an output;

Providing an allowable band signal vb, a timer signal vt, and a switching number signal ns; Setting the reference switching period Ts and the integral gain Ki;

Increasing the timer signal (vt) with a constant slope over time; For each phase m, the control signal s is at a high level (1) and the reference signal when (vr) is less than the negative value of the allowed band signal (vb), changing the control signal (s) to a low level (0) and increasing the switching number signal (ns) by one;

For each phase m, when the control signal s is at a low level (0) and the reference signal vr is greater than the allowable band signal vb, the control signal s is set to a high level (1). ) And increasing the switching number signal ns by one; And

^'When the switching number signal ns doubles the number N of phases, the integral gain Ki is multiplied by two times the reference switching period Ts minus the timer signal vt. Adding to the allowed band signal (vb), making the timer signal (vt) zero, and making the switching number signal (ns) zero;

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language.

N = 3; vbO.l; vt = 0; ns = 0;

fs = 100; Ts = l / fs; Ki = l;

vt = vt + dt;

for m = l: N

if s (m) == l && vr (m) <-vb s (m) = 0; ns = ns + 1; end

if s (m) == 0 && vr (m)> vb s (m) = l; ns = ns + 1; end

end

if ns == 2 * N vb = vb + Ki * (2 * Ts-vt); vt = 0; ns = 0; end General features of the second invention

The general features of the second invention can be described as follows.

A control method for a power converter, comprising: a field width modulation method of receiving a reference signal as an input and outputting a control signal to an output;

Providing a carrier band signal;

Setting a slope and a step value of the carrier band signal;

Decreasing the carrier band signal with the slope over time; And

Switching the control signal through the hysteresis comparison of the reference signal and the carrier band signal, and adding the stem value to the carrier band signal;

Field width modulation method comprising a. Features of a Two-Level Fill Width Modulation Method Embodiment of the Second Invention The features of the 2 ᅳ level spread width modulation method embodiment of the second invention may be described as follows.

Providing a carrier band signal vc;

Setting a slope (a) and a step value (b) of the carrier band signal (vc);

Reducing the carrier band signal (vc) to the slope (a) over time; And

When the control signal s is at a high level (1) and the reference signal (vr) is smaller than the negative value of the carrier band signal (vc), the control signal (s) is changed to a low level (0) and Adding the step value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), and the Adding the stem value (b) to the carrier band signal (vc);

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language. vc = 0.1;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / K _P ; b = a * Ts;

vc = vc-a * dt;

if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end Features of the Multi-Level Pill Width Modulation Method Embodiment of the Second Invention

The features of the multi-level fill width modulation method embodiment of the second invention can be described as follows.

For control of multi-level power converters, which can be selectively controlled in three or more levels, a field receiving a reference signal (vr) as an input and sending a control signal (s) and a level control signal (ss) as outputs A width modulation method; ,

Providing a carrier band signal vc;

Setting a slope (a), a stem value (b), and a band margin (bm) of the carrier band signal (vc); Reducing the carrier band signal (vc) to the phase (a) over time;

When the control signal s is at a high level (1) and the reference signal (vr) is smaller than the negative value of the carrier band signal (vc), the control signal (s) is changed to a low level (0) and Adding the step value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), and the Adding the step value (b) to the carrier band signal vc;

The level control signal ss when the control signal s is at a high level (1) and the reference signal vr is greater than a value obtained by adding the band margin bm to the carrier band signal vc. Changing to the upper level; And

The level control signal when the control signal s is at a low level (0) and the reference signal vr is less than a negative value of the carrier band signal vc minus the band margin bm. changing (ss) to the lower level;

. Field width modulation method comprising a.

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts; bm = 0;

vc = vc ᅳ a * dt;

if s == l && vr <ᅳ vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end

if s == l && vr> vc + bm ss = ss + 1; end

if s == 0 && vr <-vc-bm ss = ss 一 1; end Features of the Polyphase Pill Width Modulation Method of the Second Embodiment

The characteristics of the polyphase pillar width modulation method embodiment of the second invention can be described as follows.

For control of a multi-phase power converter in which the number of phases (N) is two or more, each phase

In the field width modulation method of receiving the reference signal (vr) with respect to (m) and outputting the control signal (s) as an output;

Providing a carrier band signal vc for each phase m;

Setting the group (a) and the stem value (b) of the carrier band signal (vc); . For each phase m, reducing the carrier band signal vc to the tilt 71 (a) over time; And

For each phase m, when the control signal s is at a high level (1) and the reference signal vr is smaller than the negative value of the carrier band signal vc, the control signal s is Change to low level (0) and add the step value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), Adding the step value (b) to the carrier band signal (vc);

Field width modulation method comprising a.

The following is an example of using the above features in the MATLAB language.

N = 3; vc = 0.2 * ones (N, l);

fs = 100; Ts = l / fs; Kp = 30; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

for m = l: N

vc (m) = vc (m) -a * dt;

if s (m) == l && vr (m) <-vc (m)

s (m) = 0; vc (m) = vc (m) + b;

elseif s (m) == 0 && vr (m)> vc (m)

s (m) = l; vc (m) = vc (m) + b; end

end Features of the Polyphase Single Band Fill Width Modulation Method of the Second Embodiment

The features of the multiphase single band fill width modulation method embodiment of the second invention can be described as follows.

For the control of a multi-phase power converter in which the number of phases (N) is two or more, for the phase width modulation method in which a reference signal (vr) is input to each phase (m) and a control signal (s) is output as an output. In;

Providing a carrier band signal vc and an auxiliary control signal sa;

Setting a slope (a) and a step value (b) of the carrier band signal (vc); Reducing the carrier band signal vc over time _and accordingly to the slope (a);

For each phase m, the auxiliary control signal sa is at high level (1). The control signal (s) is at high level (1) and the reference signal (vr) is the carrier band signal (vc). Negative When smaller than the value, changes the control signal s to a low level (0); Otherwise, when the auxiliary control signal sa is low level (0) and the control signal s is low level (0) and the reference signal vr is greater than the carrier bend signal vc, Changing the control signal (s) to a high level (1); And

When the auxiliary control signal sa is at a high level (1) and the control signal s of all phases is at a low level (0), ^' the step value (b) is added to the carrier band signal vc, and the Change auxiliary control signal sa to low level (0); When the auxiliary control signal sa is at a low level (0) and the control signal s of all phases is at a high level (1), the step value (b) is added to the carrier band signal vc, and the auxiliary Changing the control signal sa to the high level 1;

The spread width modulation method comprising a.

The following is an example of using the above features in the MATLAB language.

N-3; vc = 0.2; sa = 0;

fs = 100; Ts = l / fs; Kp = 30; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

vc = vc-a * dt;

for m = l: N

if sa == l && s (m) == l && w (m) <-vc s (m) = 0;

elseif sa == 0 && s (m) == 0 && vr (m)> vc s (m) = l; end

end

if sa = l && all (s == 0) vc = vc + b; sa = 0; end

if sa == 0 && all (s == l) vc = vc + b; sa = l; end 2—Level Fill Width Modulation Method Simulation Program of First Invention

The following is an example of a MATLAB simulation program for the two-level spread width modulation method of the first invention. DC-to-AC conversion, the load is for the case of a circuit with inductance (L), resistance (R), and electromotive force (e) in series, feedback current control, and proportional compensator. 1 is an execution result. La shows the reference signal (w) and the allowable band signal (vb), FIG. Lb shows the output voltage (V), and FIG. Current (ir) and output current G) are shown. Figure 1 shows that the switching frequency is regulated with the stabilization of the allowable band signal (vb). The same is true if the initial value of the allowable band signal vb is changed, the inductance L is changed, or the electromotive force e is changed. However, if the integral gain Ki is made small, the allowable band signal vb becomes flat and the transient time for stabilizing the switching period becomes long. For reference, the program If the extension is greater than 1, you can see the results of several cycles. clear all; clc; close all

vb = 0.2; vt = 0.0; s = l;

fs = 100; Ts = l / fs; Ki = 2;

ns = l; Ns = 2;

f = 2; w = 2 * pi * f; L = 0.02; R = 0.01;

em = 0.8; Vdc = 2; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 100 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (l, NK); vbw = zeros (l, NK); vw = zeros (l, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

e = em * cos (w * t); ir = irm * cos (w * t); vr = ir-i;

%%

vt = vt + dt;

if s == l && vr <-vb s = 0;

vb = vb + Ki * (2 * Ts-vt); vt = 0; end

if s == 0 && vr> vb s = l; end

%%

if s = l v = Vdc / 2; else v = -Vdc / 2; end

i = i + l / L * (v-R * i-e) * dt;

iw (K) = i; irw (K) = ir; vrw (K) = vr; vbw (K) = vb; vw (K) = v;

end

figure ^' , hold on; axis ([l NK-1 1])

plot (vbw, 'b'); plot (-vbw, 'b'); plot (vrw, 'r');

figure; hold on; axis ([l NK ᅳ 4 4]); plot (vw, 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw.'b '); plot (iw, 'r');

end ^' Meanwhile, the following program is a modified embodiment. If the part of the above program is replaced with the next program, it is the same when the reference switching number (Ns) is 1 It is small, and when it is 2 or more, it operates similarly. vt = vt + dt;

if s == l && vr <-vb s = 0; ns = ns + 1; end

if s == 0 && vr> vb s = l; ns = ns + 1; end

if ns == Ns vb = vb + Ki * (Ns * Ts-vt); ns = 0; vt = 0; end first multi-level field width modulation method simulation program

The following is an example of a MATLAB simulation program for the multi-level spread width modulation method of the first invention. Except for the multi-level, it is the same as the two-level fill width modulation method just presented, and shows almost the same characteristics. Running with varying number of levels (NL) and magnitudes of electromotive force (em) will reveal a variety of multi-level behaviors. The presentation of execution results is omitted. clear all; clc; close all

NL = 3; vb = 0.l; vd = vb; vt = 0.0; s = 0; ss = 0;

fs = 100; Ts = l / fs; Ki = 2; bm = 0.01;

f = 4; w = 2 * pi * f; L = 0.02; R = 0.01; Vdc = 2;

em = 1.5; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (l, NK); vbw = zeros (1, NK); vw = zeros (l, NK);

for extend = l: l

for K = l: NK; t = t + dt;

e = em * cos (w * t); ir = irm * cos (w * t); vr = ir-i;

vt = vt + dt;

if s == l && vr <ᅳ vb s = 0; vd = vb;

vb = vb + Ki * (Ts-vt); vt = 0; end

if s == 0 && vr> vb s = l; end

if s == l && vr> vb + bm ss = ss + 1; end

if s == 0 && vr <-vd-bm ss = ss- l; end

if ssXNL-2) ss = (NL-2); elseif ss <0 ss = 0; end

v = (ss + s- (NL-l) / 2) * Vdc; i = i + l / L * (vR * ie) * dt;

iw (K) = i; irw (K) = ir; vrw (K) = vr; vbw (K) = vb; vw (K) = v;

end

figure; hold on; axis (f 1 NK 一 1 1])

plot (vbw, 'b'); plot (-vbw, 'b'); plot (vrw, 'r');

figure; hold on; axis ([l NK-8 8]); plot (vw.'r ');

figure; hold on; axis ([l NK-2 2]);

plot (irw, 'b'); plot (iw, 'r');

end first multiphase pillar width modulation method simulation program

The following is an example of a MATLAB simulation program for the polyphase fill width modulation method of the first invention. DC-to-three-phase neutral point ac conversion, loads for three-phase constant speed synchronous motor models, torque (T) control by current control, and proportional compensators. The switching frequency is regulated, but the harmonics are relatively large because they are not synchronized. In particular, low speed, or low modulation rate, does not show good performance due to the so-called limit cycle phenomenon. These are the inherent disadvantages of the hysteresis field width modulation method. The presentation of execution results is omitted. clear all; clc; close all

N = 3; vb = 0.1 * ones (N, l); vt = zeros (N, l); s = zeros (N, l);

fs = 100; Ts = l / fs; Ki = l;

f = 2.0; w = 2 * pi * f; L = 0.02; RO.01; Vdc = 2;

Ps = 0.4 * Vdc / (2 * pi * 4); irm = l; i = zeros (N, l);

Ks = 1000; dt = Ts / Ks; tmax = 100 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (N, NK); irw = zeros (N, NK); Tw = zeros (l, NK);

vrw = zeros (N, NK); vbw = zeros (N, NK); vw = zeros (N, NK);

vnw = zeros (N, NK);

for extend = l: l

for K = l: NK; t = t + dt;

for m = l: N; e (m, l) = w * Ps * cos (w * t− (m−l) / N * 2 * pi); end

for m = l: N; ir (m, l) = irm * cos (w * t− (m−1) / N * 2 * pi); end

vr = ir-i; for m = l: N

vt (m) = vt (m) + dt;

if s (m) == l && vr (m) <-vb (m) s (m) = 0;

vb (m) = vb (m) + Ki * (2 * Ts-vt (m)); vt (m) = 0; end

if s (m) == 0 && vr (m)> vb (m) s (m) = l; end

end

v = (s-0.5) * Vdc; vn = v-sum (v) / N;

i = i 十 l / L * (vn-R * i-e) * dt;

T = e '* i / w;

iw (：, K) = i; irw (：, K) = ir; vrw (:, K) = vr; vbw (：, K) = vb;

vw (：, K) = v; vnw (： K) = vn; Tw (K) = T;

end

m = l;

figure; hold on; axis ([l NK-1 1])

plot (vbw (m,, 'b'); plot (-vbw (m, :), 'b'); plot (vrw (m, :), V);

figure! hold on; axis ([l NK-4 4]); plot (vw (m, :), 'r');

figure; hold on; axis ([l NK-4 4]); plot (vnw (m,, 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw (m,, 'b'); plot (iw (m, :), V);

figure; hold on; axis ([l NK-3 3]); plot (Tw / Ps, 'r');

end Simulation Program of Multiphase Single Band Pill Width Modulation of First Invention The following is an example of a MATLAB simulation program for the polyphase single band fill width modulation method of the first invention. Except for using a single band signal, it is the same case as the simulation of the polyphase pillar width modulation method just presented and shows almost the same characteristics. The presentation of execution results is omitted. clear all; clcl close all ^■

N = 3; vb = 0.1; vt = 0; ns = 0; s = zeros (N, l);

fs = 100; Ts = l / fs; Ki = l;

f = 2; w = 2 * pi * f; L = 0.02; R = 0.01; Vdc = 2;

Ps = 0.4 * Vdc / (2 * pi * 4); irm = l; i = zeros (N, l);

Ks = 1000; dt = Ts / Ks; tmax = 10 OTs; NK = round (t max / dt); t = 0;

iw = zeros (N, NK); irw = zeros (N, NK); Tw = zeros (l, NK);

vrw = zeros (N, NK); vbw = zeros (l, NK); vtw = zeros (l, NK);

vw = zeros (N, NK); vnw = zeros (N, NK);

for extend = l: l

for .K = 1: NK; t = t + dt;

for m = l: N; e (m, l) = w * Ps ^{: i!} cos (w * t- (ml) / N ^: i ⁱ 2 * pi); end

for m = l: N; ir (m, l) = irm * cos (w ^{! | i} t- (ml) / N * 2 * pi); end

vr = ir-i;

vt = vt + dt;

for m = l: N

if s (m) == l && vr (m) <— vb s (m) = 0; n to s + 1; end

if s (m) == 0 && vr (m)> vb s (m) = l; ns = ns + l; end

end

if ns == 2 * N vb = vb + Ki * (2 * Ts— vt); vt = 0; ns = 0; end

v = (s ᅳ 0.5) * Vdc; vn = v-sum (v) / N;

i = i 十 1 / L * (vn— R * i-e) * dt;

T = e '* i / w;

iw (： K) = i; irw (： K) = ir; vrw (：, K) = vr; vbw (K) = vb;

vw (： K) = v; vnw (： K) = vn; Tw (K) = T; vtw (K) = vt;

end

m = l;

figure; hold on; axis ([l NK 一 1 1])

plot (vbw / b '); plot (-vbw / b '); plot (vrw (m,:), 'r');

figure; hold on; axis ([l NK-4 4]); plot (vw (m,:) / r ');

figure; hold on; axis ([l NK ᅳ 4 4]); plot (vnw (m,:), V);

figure; hold on; axis ([l NK-2 2]);

plot (irw (m, :), 'b'); plot (iw (m,:) / r,);

figure; hold on; axis ([l NK —3 3]); plot (Tw / Ps, 'r');

end Simulation program of two-level pulse width modulation method of second invention

The following is an example MATLAB prototype for the 2 ᅳ level pulse width modulation method of the second invention. DC-to-AC conversion, the load is inductance (L), resistance (R), and electromotive force (e) o This is the case for circuits in series, feedback current control, and proportional compensators. 2 is a result of execution when the proportional gain Kp is 50. FIG. 2 shows that the switching frequency is regulated with stabilization of the carrier band signal vc. The same is true even if the initial value of the carrier band signal vc is changed, the inductance L is changed, or the electromotive force e is changed.

The second invention, unlike the carrier spread width modulation method, has no limit on the size of the proportional gain Kp of the compensator, and therefore, the gain of the compensator can be increased as desired or necessary. Then, compared to the carrier fill width modulation method, an improvement effect can be obtained in almost all aspects such as transient response speed, following error and steady state error, redness for system variation, and burden of precision tuning. In addition, since there is no limit to the gain of the compensator, there is a large margin in the gain value, thereby improving the reliability, versatility, and convenience. However, if the proportional gain Kp is increased, the allowable band signal vb becomes flat and the transient time for stabilizing the switching period becomes long. However, as long as the proportional gain (Kp) is not very large, the transient time is extremely short, and it is rarely necessary to make the proportional gain (Kp) very large. In addition, the second invention can employ other compensators such as proportional-integral compensators, but in most cases the proportional compensators show good performance. clear all; clc; close all

vc = 0.3; s = 0;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

ns = 0; Ns = l; n = 7.5; tc = 0;

f = 2; w = 2 * pi * f; L = 0.02; RO.01; em = 0.8; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 100 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (l, NK); vcw = zeros (l, NK); vw = zeros (l, NK);

for extend = l: l

for K = l: NK; t = t + dt;

e = em * cos (w * t); ir = irm * cos (w * t); vr = ir one i;

%%

vc = vc-a * dt;

if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 &&vr> vc s = l; vc = vc + b; end %%

if s == l v = Vdc / 2; else v = -Vdc / 2; end

i = i + l / L * (v-R * i-e) * dt;

iw (K) = i; irw (K) = ir; vrw (K) = vr; vcw (K) = vc; vw (K) = v;

end

figure; hold on; axis ([l NK -1 1])

plot (vcw, 'b'); plot (-vcw.'b '); plot (vrw, 'r');

figure; hold on; axis ([l NK-4 4]); plot (vw, 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw, 'b'); plot (iw, 'r');

end Meanwhile, the following program is a modified embodiment. If the part of% ^< ¾ of the above program is replaced with the next program, the same operation is performed when the reference switching number (Ns) is 1, and the operation is similar when it is 2 or more, but it is not preferable. vc = vc ^to a * dt;

if s == l && vr <-vc s = 0; ns = ns + 1;

elseif s == 0 && vr> vc s = l; ns = ns + l; end

if ns == Ns vc = vc + Ns * b; ns = 0; end The following program is also a modified embodiment. If you replace the part between the above program with the following program, it works the same. if s == l as = + a; else as = 一 a; end

vc = vc + as * df,

if s == l && vr <vc s = 0; vc = ᅳ vc + b;

elseif s == 0 &&vr> vc s = l; vc = vc ᅳ b; end The following program is also a modified embodiment. If you replace the part between %% of the above program with the following program, it works the same. This embodiment is suitable for digital implementation and may be advantageous when it is necessary to synchronize the carriers in a multiphase operation. tc = tc + dt; if tc> 2 * Ts tc = tc-2 * Ts; n = n ᅳ 2; end ^{vc = ~ a * (tc-} n * Ts);

if s == l && vr <-vc s = 0; n = n + 1;

elseif s == 0 && vr> vc s = l; n = n + 1; end The following program is also a modified embodiment. If you replace the part of the above program with the following program, it works the same. This embodiment is also suitable for digital implementation, and may be advantageous when it is necessary to synchronize carriers in multiphase operation. tc = tc + dt; if tc> 2 * Ts tc = tc-2 * Ts; n = n ᅳ 2; end

if s == l as = + a; else as = -a; end

vc = as * (tc-n * Ts);

if s == l && vKvc s = 0; n = n + 1;

elseif s == 0 && vr> vc s = l; n = n + l; end Discontinuous current mode simulation program of the second invention

The following is an example of a MATLAB simulation program for verifying operation in the discontinuous current mode of the second invention. DC-to-DC conversion, loads are for circuits in series with inductance (L), resistance (R), and electromotive force (e), feedback current control, and proportional compensators. 3 shows the execution result of the program. Unlike the carrier fill width modulation method, the second invention operates in discontinuous current mode. However, in the case of discontinuous current mode, if the proportional gain (Kp) is too large, switching may not be evenly distributed. Clear all; clc; close all

vc = 0.3; s = 0;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

f = 2; w = 2 * pi * f; LO.02; R = 0.01; em = l; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 100 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (1, NK); vcw = zeros (1, NK); vw = zeros (l, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

e = em + 0.5 * cos (w * t); ir = irm * sin (w * t); if ir <0.1 ir = 0.1; end;

vr = ir ᅳ i; ^'

vc = vc one a * dt;

if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end

if s == l v = Vdc; else v = 0; end

i = i + 1 / L * (v ᅳ R * i-e) * dt; if i <0 i = 0; end

iw (K) = i; irw (K) = ir; vrw (K) = vr; vcw (K) = vc; vw (K) = v;

end

figure; hold on; axis ([l NK—1 1])

plot (vcw, 'b') i plot (vcw / b '); plot (vrw, 'r');

figure; hold on; axis ([l NK-4 4]); plot (vw / r ');

figure; hold on; axis (l NK —2 2D;

plot (irw, 'b'); plot (iw, 'r');

end Second rectifier rectifier simulation program

The following is an example MATLAB simulation program for the inverse corrected rectifier of the second invention. In the program, the current flows backwards from the electromotive force (e) to the converter and is negatively limited by the diode. The presentation of execution results is omitted. clear all; clci close all

vc = 0.3; s = 0;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

f = 2; w = 2 * pi * f, L = 0.02; RO.01; em = 1.6; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 100 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (1, NK); vc w = zero s (1, NK); vw = zeros (l, NK);

for extend = l: l

for K = l: NK; t = t + dt;

e = em * abs (cos (w * t)); ir = -irm * abs (cos (w * t)); vr = ir-i;

vc = vc—a * dt; if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end

if s == l v = Vdc; else v = 0; end

i = i + l / L * (v-R * i-e) * dt; if i> 0 i = 0; end

iw (K) = i; irw (K) = ir; vrw (K) = vr; vcw (K) = vc; vw (K) = v;

end

figure! hold on; axis ([l NK -1 1])

plot (vcw, 'b'); plot (vcw, 'b'); plot (vrw, 'r');

figure; hold on; axis ([l NK _4 4]); plot (vw.'r ');

figure; hold on; axis ([l NK-2 2]);

plot (-irw, 'b'); plot (-iw, 'r');

end Dog loop control simulation program of the second invention

The following is an example of a MATLAB simulation program for checking the operation in the open loop control of the second invention. 4 shows the execution result of the program. The second invention shows the same result as the triangular carrier spread width modulation method in open loop control. clear all; clc; close all

vc = 0; s = 0; tc = 0;

fs = 100; Ts = l / fs; Vdc = 2; a = Vdc / Ts; b = a * Ts; .

f = 2; w = 2 * pi * f;

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

vrw = zeros (l, NK); vcw = zeros (l, NK); vw = zeros (l, NK);

for K = 1: NK; t = t + dt;

vr = 0.8 * sin (w * t);

%%

vc = vc ~ a * dt;

if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end

%

if s == l v = Vdc / 2; else v = -Vdc / 2; end

vrw (K) = vr; vcw (K) = vc; vw (K) = v; end

figure; hold on; axis ([l NK -5 5]);

plot (vcw, 'b'); plot (vrw, 'r');

figure; hold on; axisd l NK -4 4]); plot (vw, 'r'); If we replace the part between ° kPlo of the above program with the following program, we can check the triangular carrier fill width modulation method. In the following program and in Fig. 4A, the symbols of the carrier signals are described as symbols of the carrier band signal vc of the present invention. tc = tc + dt; if tc> 2 * Ts tc = tc-2 * Ts; end

if Ts * l / 2 <= tc && tc <Ts * 3/2 as = + a; else as = -a; end

vc = vc + as * dt;

if vr> vc s = l; else s = 0; end The second invention shows the same result as the triangular carrier fill width modulation method when the gain of the compensator is reduced not only in the open loop control but also in the closed loop control. However, in the triangular carrier fill width modulation method, the multi-crossing problem does not occur. The second invention can be seen to extend the slope portion of the triangular carrier fill width modulation method so that no multi-crossing problem occurs regardless of the size of the compensator gain. On the other hand, although not necessary, the second invention is the same as the hysteresis field width modulation method when the gain of the compensator is infinite. Multi-level fill width modulation method simulation program of the second invention

The following is an example of the MATLAB simulation program for the 5-level fill width modulation method of the second invention. DC-to-AC conversion, loads are for circuits in series with inductance (L), resistance (R), and electromotive force (e), feedback current control, and proportional compensators. The band margin (bm) may be zero or may be given a small value. 5 shows the execution result of the program. clear all; clc; close all

NL = 5; vc = 0.1; s = 0; ss = 0;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts; bm = 0;

f = 4; w = 2 * pi * f; L = 0.02; R = 0.01; em = 3; irm = l; i = 0; Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (1, NK); vcw = zeros (l, NK); vw = zeros (l, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

e = em * cos (w * t); ir = irm * cos (w * t); vr = ir-i;

vc = vc ^to a * dt;

if s == l && vr <-vc s = 0; vc = vc + b;

elseif s == 0 && vr> vc s = l; vc = vc + b; end

if s == l && vr> vc + bm ss = ss + 1; end

if s == 0 && vr <-vc-bm ss = ss l; end

if ssXNL-2) ss = (NL-2); elseif ss <0 ss = 0; end

v = (ss + s- (NL-l) / 2) * Vdc;

i = i + l / L * (v-R * i-e) * dt;

iw (K) = i; irw (K) = ir; vrw (K) = vr; vcw (K) = vc; vw (K) = v;

end

figure; hold on; axis ([l NK 一 1 1])

plot (vcw, 'b'); plot (-vcw, 'b'); plot (vrw, 'r');

figure; hold on; axis ([l NK-8 8]); plot (vw, 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw, 'b'); plot (iw, 'r');

end Simulation of a Two-Phase Pill Width Modulation Method of the Second Invention

The following is an example of a MATLAB simulation program for the two-phase pillar width modulation method of the second invention. DC-to-AC conversion, the load is for the case of a circuit with inductance (L), resistance (R), and trapezoidal electromotive force (e) in series, trapezoidal reference current (ir), feedback current control, and proportional compensator . This embodiment is characterized by using a carrier band signal for each of the two phases. 6 shows the execution result of the program. function main

clear all; clc; close all

vc = 0.1 * [l; l]; s = [0; 0]; fs = 100; Ts = l / fs; Kp-50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

f = 4; w = 2 * pi * f; L = 0.02; R = 0.01; em = 0.8; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (2, NK); vcw = zeros (2, NK); vw = zeros (l, NK); for extend = l: l

for K = 1: NK; t = t + dt;

e = em * F (w * t); ir = irm * F (w * t);

vr (l) = ir-i; vr (2) = − vr (l);

for m = l: ²

vc (m) = vc (m) -a * dt;

if s (m) == l && vr (m) <— vc (m)

s (m) = 0; vc (m) = vc (m) + b;

elseif s (m) == 0 && vr (m)> vc (m)

s (m) = l; vc (m) = vc (m) + b; end

end

v = (s (l) -s (2) Vdc;

i = i + l / L * (v-R * i-e) * dt;

iw (K) = i; irw (K) = ir; vrw (：, K) = vr; vcw (:, K) = vc; vw (K) = v; end

figure; hold on; axis ([l NK 一 1 1])

plot (vcw (l, ^* ) b '); plot (-vcw (l,, 'b'); plot (vrw (l, :), V); figure; hold on; axis ([l NK—4 4]); plot (vw / r ');

figure; hold on; axis ([l NK-2 2]);

plot (irw / b '); plotGw / r ');

end; end

function y = F (thl)

a = pi / 8; th = mod (thl, 2 * pi); ^'

if th <a y = l / a * th; elseif th <pi— a y = l;

elseif th <pi + a y = −l / a * (th-pi);

elseif th <2 * pi 一 ay = -l; else y = l / a * (th 一 2 * pi); end end Simulation Program for Two-Phase Single Band Pill Width Modulation of the Second Invention The following is an example of a MATLAB simulation program for the two-phase single band fill width modulation method of the second invention. This embodiment is characterized by using a two-phase common single carrier band signal. Only the shape of the carrier bend signal vc is different, and the execution result of the program is shown in FIG.

Same as 6. function main

clear all; clc; close all

N = 2; vc = l / 10; s = zeros (N, l); sa = 0;

fs = 100; Ts = l / fs; Kp = 50; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

f = 4; = 2 * pi * f; L = 0.02; R = 0.01; emO.8; irm = l; i = 0;

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (l, NK); irw = zeros (l, NK);

vrw = zeros (2, NK); vcw = zeros (1, NK); vw = zeros (l, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

e = em * F (w * t); ir = irm * F (w * t); vr (l) = ir-i; vr (2) = − vr (l);

%%

vc = vc ~ a * dt;

for m = l: N

if sa == l && s (m) == l && vr (m) < vc s (m) = 0;

elseif sa == 0 && s (m) == 0 && vr (m)> vc s (m) = l; end

end

if sa = l && all (s == 0) vc = vc + b; sa = 0; end

if sa == 0 && all (s == l) vc-vc + b; sa = l; end

%%

v = (s (l) -s (2)) * Vdc;

i = i + l / L * (v-R * i-e) * dt;

iw (K) = il irw (K) = ir; vrw (：, K) = vr; vcw (K) = vc; vw (K) = v;

end

figure; hold on; axis ([l NK 1 1]) plot (vcw, 'b'); plot (-vcw, 'b'); plot (vrw (l,, 'r')-.

figure; hold on; axis ([l NK-4 4]); plot (vw, 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw, 'b') ^' . plot (iw, 'r') ^' >

end; end

function y = F (thl)

a = pi / 8; th = mod (thl, 2 * pi);

if th <a y = l / a * th; elseif th <pi-a y = l;

elseif th <pi + a y = ᅳ l / a * (th ᅳ pi);

elseif th <2 * pi-a y = —l; else y = l / a * (th-2 * pi); end

end Meanwhile, the following program is a modified embodiment. If you replace the part between% of the above program with the following program, it works similarly. vc = vc-a * dt;

. for m = l: N

if s (m) == l && vr (m) <-vc s (m) = 0; vc = vc + b / 2;

elseif s (m) == 0 && vr (m)> vc s (m) = l; vc = vc + b / 2; end

end On the other hand, two-level two-phase converters are equivalent to three-level converters. Thus, a three-level fill width modulation method may be used. Multiphase Pill Width Modulation Method Simulation Program of Second Invention

The following is an example of the MATLAB simulation program for the polyphase fill width modulation method of the second invention. DC-to-three-phase neutral point ac conversion, loads are for three-phase constant speed synchronous motor models, torque (T) control by current control, and proportional compensators. 7 shows the execution result of the program. 7A shows the modulation reference signal (vr) and the carrier signal (vc) of the first phase, FIG. 7B shows the DC axis neutral point of the first phase-the reference phase voltage (V), and FIG. 7C shows the neutral point of the AC phase of the first phase-the reference phase voltage ( vn), FIG. 7D shows the reference current (ir) and the output current (0) of the first phase, and FIG. 7E shows the generated torque (T).

The multi-phase pillar width modulation method of the second invention not only causes the switching frequency to be regulated, but also is ^' synchronized, so that harmonic generation is relatively low. And low speed instant change There is no limit cycle even when tuning is low. However, if the proportional gain Kp is too large, the polyphase may not be synchronized and may operate similar to the hysteresis field width modulation method, or the polyphase may be undesirably synchronized. Therefore, it is necessary to make the proportional gain Kp not too large. Instead, it is desirable to add an integral gain to further reduce the error. clear all; clc; close all

N = 3; vc = 0.2 * ones (N, l); s = zeros (N, l);

fs = 100; Ts = l / fs; Kp = 30; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

3-f = 2; w = 2 * pi * f; L = 0.02; R = 0.01;

Ps = 0.4 * Vdc / (2 * pi * 4); irm = l; i = zeros (N, l);

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (N, NK); irw = zeros (N, NK); Tw = zeros (l, NK);

vrw = zeros (N, NK); vcw = zeros (N, NK);

vw = zeros (N, NK); vnw = zeros (N, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

for m = l: N; e (m, l) = w * Ps * cos (w * t− (m−l) / N * 2 * pi); end

for m = l: N; ir (m, l) = irm * cos (w * t− (m−l) / N * 2 * pi); end

vr = ir-i;

for m = l: N

vc (m) = vc (m) -a * dt;

if s (m) == l && vr (m) <-vc (m)

s (m) = 0; vc (m) = vc (m) + b;

elseif s (m) == 0 && vr (m)> vc (m)

s (m) = l; vc (m) = vc (m) + b; end

end

v = (s-0.5) * Vdc; vn = v-sum (v) / N;

i = i + l / L * (vn-R * i-e) * dt; T = e '* i / w;

iw (： K) = i; irw (： K) = ir; vrw (：, K) = vr; vcw (：, K) = vc;

vw (:, K) = v; vnw (：, K) = vn; Tw (：, K) = T;

end m = l;

figure ^' , hold on; axis ([l NK -1 1])

plot (vcw (m,, 'b'); plot (-vcw (m,, 'b'); plot (vrw (m, :), 'r');

figure; hold on; axis ([l NK-4 4]); plot (v \ y (m, :), 'r');

figure! hold on; axis ([l NK-4 4]); plot (vnw (m, :), 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw (m,, 'b'); plot (iw (m,, 'r');

figure; hold on; axis ([l NK-3 3]); plot (Tw / Ps, 'r');

end Simulation program of polyphase single band fill width modulation method of the second invention The following is an example of a MATLAB simulation program for the polyphase single band fill width modulation method of the second invention. Except for the use of a single band signal, it is the same case as the polyphase fill width modulation method presented earlier, and shows almost the same characteristics. The presentation of execution results is omitted. clear all; dc; close all

N = 3; vc = 0.2; s = zeros (N, l); sa = 0;

fs = 100; Ts = l / fs; Kp = 30; Vdc = 2;

a = Vdc / Ts / Kp; b = a * Ts;

f = 2; w = 2 * pi * f; L = 0.02; R = 0.01;

Ps = 0.4 * Vdc / (2 * pi * 4); irm = l; i = zeros (N, l);

Ks = 1000; dt = Ts / Ks; tmax = 50 * Ts;

NK = round (t max / dt); t = 0;

iw = zeros (N, NK); irw = zeros (N, NK); Tw = zeros (l, NK);

vrw = zeros (N, NK); vcw = zeros (l, NK);

vw = zeros (N, NK); vnw = zeros (N, NK);

for extend = l: l

for K = 1: NK; t = t + dt;

for m = l: N; e (m, l) = w * Ps * cos (w * t— (m—l) / N * 2 * pi); end

for m = l: N; ir (m, l) = irm * cos (w * t− (m−l) / N * 2 * pi); end

vr = ir ᅳ i;

vc = vc-a * dt;

for m = l: N if sa == l && s (m) == l && vr (m) <-vc s (m) = 0;

elseif sa == 0 && s (m) == 0 && vr (m)> vc s (m) = l; end

end

if sa = l && all (s == 0) vc = vc + b; sa = 0; end

if sa == 0 && all (s == l) vc = vc + b; sa = l; end

v = (s-0.5) * Vdc; vn = v-sum (v) / N;

i = i + l / L * (vn-R * i-e) * dt; T = e '* i / w;

iw (:, K) = i; irw (：, K) = ir; vrw (：, K) = vr; vcw (K) = vc;

vw (:, K) = v; vnw (： K) = vn; Tw (：, K) = T;

end

m = l;

figure! hold on; axis ([l NK-1 1]);

plot (vcw, 'b'); plot (vcw, 'b'); plot (vrw (m, :), 'r');

figure; hold on; axis ([l NK-4 4]); plot (vw (m, :), 'r');

figure ^' , hold on; axis ([l NK-4 4]); plot (vnw (m, :), 'r');

figure; hold on; axis ([l NK-2 2]);

plot (irw (m,, 'b'); plot (iw (m,, 'r');

figure; hold on; axis ([l NK-3 3]); plot (Tw / Ps, 'r');

end

[Favorable effect]

Prior allowed band control hysteresis Field width modulation methods are characterized by providing a means for detecting the switching frequency, subtracting the detected switching frequency signal from the reference switching frequency signal and adjusting the allowed band signal through a compensator. While the preceding methods maintain the excellent characteristics of the hysteresis field width modulation method, the switching frequency is legulated, but the implementation is not very easy and the switching performance of the switching frequency is not satisfactory. Essentially, detecting the switching frequency is not easy, and because the switching frequency and the allowable band are inversely related in nature.

The first invention feeds back the allowable band with a switching period rather than switching frequency. The main feature is to provide a means for detecting the switching period, and to adjust the allowed band signal by subtracting the switching period signal detected from the reference switching period signal and going through a sampling compensator. The switching period is the inverse of the switching frequency. However, the switching cycle can be detected accurately every cycle with a simple timer. In addition, the switching period and the allowable band are proportional in nature. Therefore, the first invention is based on the preceding methods. Compared to this, it is easy to implement and the regulation performance of switching frequency is satisfactory. The first invention can be applied to two-level, multi-level, and multiphase power converters.

However, the first invention has the disadvantage that synchronization is not possible, does not operate in discrete current mode, and cannot be used in open loop control.

The second aspect of the present invention is to reduce the carrier bend signal with a constant phase over time, and to add a constant step value to the carrier band signal when switching the control signal. Adjusting the carrier band signal in this way is very easy to implement. And basically, the second invention has not only the excellent characteristics of the hysteresis field width modulation method but also the excellent characteristics of the carrier field width modulation method. That is, synchronization is possible and can be used for open loop control as well as closed loop control. The second invention works even in discontinuous current mode. And can be applied to two-level, multi-level, and polyphase power converters.

The second invention, unlike the carrier spread width modulation method, has no limit on the size of the proportional gain of the compensator and thus the gain of the compensator can be increased as desired or necessary. Then, compared with the carrier pulse width modulation method, an improvement effect can be obtained in almost all aspects such as transient quiescent speed, following error and steady state error, redness to system variation, and burden of precision tuning. In addition, since there is no limit to the gain of the compensator, there is a large margin in the gain value, and thus an effect of improving reliability, generality, and convenience can be obtained. (This improvement is particularly beneficial in power management integrated circuits and motor-drive integrated circuits.) However, increasing the proportional gain results in longer transients that flatten the allowable band signal and stabilize the switching cycle. Lose. However, unless the proportional gain is very large, the transient time is extremely short, and it is rare that the proportional gain needs to be very large. In addition, in the second invention, other compensators such as proportional-integral compensators can be employed, but in most cases, proportional compensators show good performance.

In the second aspect of the invention, when the gain of the compensator is reduced, the same results as in the triangular carrier fill width modulation method are obtained. However, in the triangular carrier fill width modulation method, the multi-crossing problem does not occur. The second invention can be seen to extend the slope portion of the triangular carrier fill width modulation method so that no multi-crossing problem occurs regardless of the size of the compensator gain. On the other hand, the second invention is the same as the hysteresis field width modulation method when the gain of the compensator is infinite. The second invention includes a triangular carrier spread width modulation method and a hysteresis field width modulation method at both ends of the compensator gain are one theoretical proof of the superiority of the second invention.

【Brief Description of Drawings】 1 is a simulation example of the two-level fill width modulation method of the first invention. 2 is a simulation example of the two-level fill width modulation method of the second invention. 3 is a simulation example of the discontinuous current mode of the second invention.

4 is a simulation example for the open loop control of the second invention.

5 is an example simulation for the multi-level fill width modulation method of the second invention. 6 is a simulation example of a two-phase pillar width modulation method of the second invention. 7 is a simulation example of the polyphase fill width modulation method of the second invention.

[Best form for implementation of the invention]

The invention is capable of a wide variety of implementations and variations. Although important embodiments and variations have been described as examples, it is unreasonable to describe all embodiments and modifications in the specification and the claims. For example, the slope and step values of the carrier band signal may be nonlinear or variable for the purpose of limiting the size of the switching ripple or dispersing the frequency spectrum of the switching ripple. For example, it is also possible to alternate between two types of inclination and step value of a carrier band signal. Therefore, any implementation or modification having key features of the present invention is intended to be understood as equivalents of the present invention.

Best Modes for Carrying Out the Invention The embodiments described above are examples. However, the second invention is a better form than the first invention. Therefore, in the claims, the second invention is described first.

[Industrial availability]

The present inventions can be implemented and used in an analog or digital manner. The present inventions can be implemented and used in discrete circuits or integrated circuits. The present invention may be used in a control integrated circuit, a power management integrated circuit, or a motor driving integrated circuit before the fill width modulation. In addition, the present invention can be used in all power converters or devices including the power converter.

Claims

[Range of request]

[Claim 1]

A pulse width modulation method for controlling a power converter, the method comprising: receiving a reference signal as an input and outputting a control signal to an output;

Providing a carrier band signal;

Setting a slope and a stem value of the carrier band signal;

Decreasing the carrier band signal with the slope over time; And

Switching the control signal through a hysteresis comparison between the reference signal and the carrier band signal and adding the step value to the carrier band signal;

Field width modulation method comprising a.

[Claim 2]

CLAIMS 1. A pulse width modulation method for controlling a two-level power converter that can be selectively controlled in two levels, the method comprising: receiving a reference signal vr as an input and outputting a control signal s as an output;

Providing a carrier band signal vc;

Setting a phase (a) and a step value (b) of the carrier band signal (vc);

Reducing the carrier bend signal (vc) to the slope (a) over time; And

When the control signal s is at a high level (1) and the reference signal (vr) is smaller than the negative value of the carrier band signal (vc), the control signal (s) is changed to a low level (0) and Adding the stem value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), and the Adding the step value (b) to the carrier band signal vc;

Field width modulation method comprising a.

[Claim 3]

It can be selectively controlled in three or more levels - level as for the control of the power converter, receiving a reference signal (vr) as input to export the control signal (s) and the level control ^signal, call (ss) to the output A fill width modulation method;

Providing a carrier band signal vc;

Setting a slope (a), a step value (b), and a band margin (bm) of the carrier band signal (vc);

Reducing the carrier band signal (vc) to the slope (a) over time Thing;

When the control signal s is at a high level (1) and the reference signal (vr) is smaller than the negative value of the carrier band signal (vc), the control signal (s) is changed to a low level (0) and Adding the step value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), Adding the step value (b) to the carrier band signal (vc);

When the control signal (s) is large, the high level (1) and the reference signal (vr) is the carrier-band signal, the band margin (bm) to (vc) than the value, the level control signal _(ss) Changing to the upper level; And

The level control signal when the control signal s is at a low level (0) and the reference signal vr is less than a negative value of the carrier bend signal vc minus the band margin bm. changing (ss) to the lower level;

Field width modulation method comprising a.

[Claim 4]

Providing a carrier band signal vc for each phase m;

Setting a slope (a) and a step value (b) of the carrier band signal (vc);

For each phase m, reducing the carrier band signal vc to the tilt 71 (a) over time; And

For each phase m, when the control signal s is at a high level (1) and the reference signal vr is smaller than the negative value of the carrier band signal vc, the control signal s is Change to low level (0) and add the step value (b) to the carrier band signal (vc); Otherwise, when the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the control signal s is changed to a high level (1), Adding the stem value (b) to the carrier band signal (vc);

Field width modulation method comprising a.

[Claim 5]

Providing a carrier band signal vc and an auxiliary control signal sa; Setting a phase (a) and a step value (b) of the carrier band signal (vc); Reducing the carrier band signal (vc) to the slope (a) over time;

For each phase m, the auxiliary control signal sa is at high level (1) and the control signal (s) is at high level (1) and the reference signal vr is of the carrier band signal vc. When less than a negative value, changes the control signal s to a low level (0); Otherwise when the auxiliary control signal sa is at a low level (0) and the control signal s is at a low level (0) and the reference signal vr is greater than the carrier band signal vc, the Changing control signal (s) to high level (1); And

When the auxiliary control signal sa is at a high level (1) and the control signal s of all phases is at a low level (0), the step value (b) is added to the carrier band signal vc, and the auxiliary Change the control signal sa to a low level (o); When the auxiliary control signal sa is at a low level (0) and the control signal s of all phases is at a high level (1), the step value (b) is added to the carrier band signal vc, and the auxiliary Changing control signal sa to high level 1;

Field width modulation method comprising a.

[Claim 6]

Providing an allowable band signal and a timer signal;

Setting a reference switching period;

Increasing the timer signal by a constant slope over time; And switching the control signal through the hysteresis comparison between the reference signal and the allowed band signal, subtracting the timer signal from the reference switching period, adjusting the allowed band signal through a sampling compensator, and zeroing the timer signal. Made by hand;

Field width modulation method comprising a.

[Claim 7]

A control method for a two-level power converter that can be selectively controlled at two levels, comprising: a field width modulation method of receiving a reference signal vr and outputting a control signal s as an output;

Providing an allowable band signal (vb) and a timer signal (vt);

Setting the reference switching period Ts and the integral gain Ki;

Increasing with a constant slope according to the timer signal (vt) roll time; When the control signal s is at a high level (1) and the reference signal vr is smaller than a negative value of the allowable band signal vb, replace the control signal s with a low level (0), The integral gain Ki is multiplied by the value obtained by subtracting the timer signal vt from twice the reference switching period Ts, and added to the allowed band signal vb, and the timer signal vt is zero. To make; And

Field width modulation method comprising a.

[Claim 8]

For control of multi-level power converters, which can be selectively controlled in three or more levels, a field receiving a reference signal (vr) as an input and sending a control signal (s) and a level control signal (ss) as outputs A width modulation method;

Providing a allowed band signal (vb), a delayed allowed band signal (vcl), and a timer signal (vt);

Setting a reference switching period (Ts), integral gain (Ki), and band margin (bm); Increasing the timer signal (vt) with a constant slope over time; When the control signal s is at a high level (1) and the reference signal vr is less than a negative value of the allowable bend signal vb, change the control signal s to a low level (0), The delayed allowed band signal (vd) is replaced with the allowed band signal (vb), and the reference gain period (Ts) is obtained by subtracting the timer signal (vt) by the integral gain Ki to multiply the allowed band. Adding to signal vb and making said timer signal vt zero;

When the control signal s is at a high level (1) and the reference signal vr is larger than the allowance band signal vb plus the band margin bm, the level control signal ss is upwards. Switching to a level; And

The level control when the control signal s is at a low level (0) and the reference signal vr is less than the negative value of the delayed allowed band signal (vd) minus the band margin (bm) Changing signal ss to the lower level;

Field width modulation method characterized in that it comprises a.

[Claim 9]

A control method for controlling a multi-phase power converter in which the number of phases N is two or more, wherein, for each phase m, a field width modulation method of receiving a reference signal vr as an input and outputting a control signal s as an output; Providing a permit band signal vb and a timer signal vt for each phase; Setting the reference switching period Ts and the integral gain KD;

For each phase m, increasing the timer signal vt with a constant slope over time;

When (vr) is smaller than the negative value of the allowable band signal vb, change the control signal s to a low level (0), and at twice the reference switching period Ts, the timer signal (vt) Multiplying the integral gain Ki by the subtracted), and adding it to the allowable band signal vb and making the timer signal vt zero; And

Pulse width modulation method comprising a.

[Claim 10]

A fill width modulation method for receiving (m) a reference signal (vr) as an input and outputting a control signal (s) as an output;

Increasing the timer signal (vt) with a constant slope over time; For each phase m, when the control signal s is at a high level (1) and the reference signal vr is smaller than the negative value of the allowed band signal vb, the control signal s is Changing to a low level (0) and increasing the switching number signal ns by one;

When the switching number signal _ns becomes twice the number N of the phases, the timer signal vt is multiplied by the integral gain Ki by double the value at twice the reference switching period Ts. Adding to the allowed band signal (vb), making the timer signal (vt) zero, and making the switching number signal (ns) zero;

Field width modulation method comprising a.