JP3656286B2

JP3656286B2 - Induction heating device

Info

Publication number: JP3656286B2
Application number: JP17569395A
Authority: JP
Inventors: 聡山田
Original assignee: Meidensha Corp
Current assignee: Meidensha Corp
Priority date: 1995-07-12
Filing date: 1995-07-12
Publication date: 2005-06-08
Anticipated expiration: 2015-07-12
Also published as: JPH0927386A

Description

【０００１】
【発明の属する技術分野】
本発明は、誘導加熱初期段階における目標温度末達部分の発生がなくなるように入熱制御する誘導加熱装置に関する。
【０００２】
【従来の技術】
誘導加熱装置で被加熱物を加熱する際は、良好な品質を得るために、加熱温度が目標温度に一致するように入熱制御をしている。図６のようなパターンの加熱の場合経験的に知られた定常状態での必要電力Ｐを加熱コイルに供給して加熱している。
【０００３】
図５は従来誘導加熱装置の入熱制御部を示すもので、１は被加熱物３を加熱する加熱コイル、２は加熱コイルに必要電力を供給するインバータ（可変電源）、５０はインバータ２を制御する演算制御部で、条件設定器７で設定した被加熱物３の外径Ｄ_W，肉厚Ｔ_W，目標温度θ_S，コイル効率ηｃ、速度検出器６からのライン速度Ｓｐを取り入れ、（１）式により主演算量Ｅｏを求める主制御量演算部と、温度計４からの被加熱物温度θｒを取り入れ、ライン速度が定格速度に達すると（２）式により補正制御量△Ｅを求める補正制御量演算部５７と、主演算量Ｅｏと補正制御量△Ｅを加算してインバータ２へ制御量Ｅを出力する加算器５４から構成されている。
【０００４】
【数１】

【０００５】
ただし、Ｋｓｐ：被加熱物により決まる定数
【０００６】
【数２】
△Ｅ＝Ｋ_θ×（θｓ−θａ）／θｓ×Ｅｏ＋△Ｅ′ ……（２）
ただし、Ｋ_θ ：０を越える正の値（定数）
△Ｅ′＝前回の△Ｅの値
θａ：移動平均温度
ライン速度がスタート時から定格速度になるまで、切換器５２をＯＦＦにして補正制御量演算部５７からの補正量△Ｅ＝０として温度フィードバック制御を停止させ、主制御量Ｅｏでインバータを制御して、主制御量Ｅｏに比例した電力Ｐを加熱コイル１へ出力させる。
【０００７】
ライン速度が定格に達すると、切換器５２をＯＮにして補正制御量演算部５７で補正量△Ｅを演算し、加算器５４で主制御量Ｅｏに加算した制御量Ｅ＝Ｅｏ＋△Ｅでインバータ２を制御する。インバータ２は制御量Ｅに比例した電力Ｐを加熱コイル１へ送る。これにより移動平均温度θａが目標温度θｓに等しくなるように温度フィードバック制御される。（特願平６−２３０９４２号）
【０００８】
【発明が解決しようとする課題】
ところで、高温状態の被加熱物の輻射損失を補う加熱等被加熱物の輻射熱による加熱コイル内の温度上昇の影響が大きい場合加熱開始直後と加熱定常状態時では必要電力Ｐが異なる。このため加熱開始直後から加熱定常状態時の必要電力を供給した場合には、加熱初期段階において目標温度未達部分が発生する。
【０００９】
本発明は、従来のこのような問題点に鑑みてなされたものであり、その目的とするところは、加熱初期段階において目標温度未達部分が少なくなるように入熱制御する誘導加熱装置を提供することにある。
【００１０】
【課題を解決するための手段】
本発明は、移動する被加熱物を加熱する加熱コイルと、加熱コイルに電力を供給する可変電源と、必要電力を発生させるための主制御量を演算する主制御量演算部と、温度フィードバックの制御用の補正制御量を演算する補正制御量演算部及びその主制御量と補正制御量を加算して可変電源を制御する加算器を有する演算制御部とを備えた誘導加熱装置において、
（１）被加熱物の外径Ｄｗ、目標温度θｓ、コイル効率ηｃ、放射率εを初期設定する条件設定データと、加熱コイル内温度θｃを検出する温度検出器を設け、
主制御量演算部がこれら条件設定データ及び加熱コイル内温度から加熱コイル内温度の低い初期段階の主制御量が定常状態時の主制御量より大きくなるように主制御量Ｅｏの演算を、下記 ( ９ ) 式を用いて行うようにした。
【数９】

但し、Ｋｄ，Ｋｅは定数。
【００１１】
（２）または、被加熱物の外径Ｄｗ、目標温度θｓ、コイル効率ηｃ、初期輻射損失Ｐｓ、定常輻射損失Ｐａ、過渡時間Ｔを初期設定する条件設定データと、加熱ＯＮ／ＯＦＦスイッチと、加熱ＯＮ／ＯＦＦスイッチのＯＮ及びＯＦＦからの経過時間を出力する加熱ＯＮ／ＯＦＦタイマを設け、
主制御量演算部がこれら条件設定データ及び加熱ＯＮ／ＯＦＦタイマの時間Ｔｈから初期段階の主制御量が定常状態時の主制御量より大きくなる主制御量Ｅｏの演算を、下記（１０）式を用いて行うようにした。
【数１０】

但し、Ｋｄは定数。
【００１２】
【発明の実施の形態】
本発明の実施の形態について図面を参照して説明する。
【００１３】
実施の形態１
図１について、１は加熱コイル、２は加熱コイルに出力するインバータ（可変電源）、３は加熱コイルにより加熱される被加熱物、４は被加熱物の温度θｒを検出する温度計、４１は加熱コイル１内の温度θｃを検出する熱電対、７１は被加熱物の外径Ｄｗ，目標温度θｓ，コイル効率ηｃ，放射率εを初期設定する入力リンクデータ対条件設定器、５０は演算制御部で、データ条件設定データを転送するデータ転送部９と、主制御量演算部６０１と、補正制御量演算部５７と、演算された主制御量Ｅｏと補助制御量△Ｅとを加算してインバータ２を制御する加算器５４で構成されている。
【００１４】
主制御量演算部６０１は、データ転送部９から転送される条件設定データＤｗ，θｓ，ηｃ，ε及び熱電対４１からの温度θｃから主制御量Ｅｏを（３）式にて求めるように構成されている。
【００１５】
【数３】

【００１６】
Ｋｄ，Ｋｅ：定数
Ｋｄ×Ｄｗ：表面積
Ｋｅ×ε×｛（θｓ＋２７３）⁴−（θｃ＋２７３）⁴｝：Ｗ／ｃｍ²
Ｗ／ｃｍ²：輻射損失を補うｃｍ²当たりの必要電力
補正制御量演算部５７は従来図５のそれと同様にライン速度が定格速度に達すると被加熱物の温度を検出する温度計の温度θｒを用いて補正制御量△Ｅを演算する構成となっている。
【００１７】
次にこの装置の動作について説明する。主制御量演算部６０１は（３）式を演算して主制御量Ｅｏを出力する。
【００１８】
【数４】
Ｐ＝Ｋｄ×Ｄｗ×Ｋｅ×ε×｛(θｓ＋２７３)⁴−(θｃ＋２７３)⁴｝…（４）
必要電力Ｐは、（４）式から明らかなように、コイル内温度θｃによって変化し、θｃの値が小さい初めのうちはＰは大きく、θｃの値が小さくなるとＰは小さくな。従って（３）式による主制御量Ｅｏでインバータ２を制御すれば、コイル内温度θｃが定常状態になるまでの必要電力Ｐが大きくなる。
【００１９】
補正制御量演算部５７は従来図５の場合と同様にライン速度が定格速度に達すると（２）式の演算をして補正制御量を出力する。しかしてインバータ２はライン速度が定格に達するまでは主制御量Ｅｏのみで制御され、定格速度になると、制御量Ｅ（＝Ｅｏ＋△Ｅ）による温度フィードバック制御となる。
【００２０】
この実施の態様によれば、コイル内温度θｃが通常状態になるまでの必要電力を大きくすることができるので、加熱初期段階における目標温度未達部分の発生を抑制することができる。
【００２１】
実施の形態２
図２について、１は加熱コイル、２は加熱コイルに出力するインバータ、３は被加熱物、４は被加熱物の温度を検出する温度計、７２は被加熱物の外径Ｄｗ，目標温度θｓ、コイル効率ηｃ，初期輻射損失Ｐｓ，定常輻射損失Ｐａ，過度時間Ｔを初期設定する入力リンクデータ条件設定器、Ｓ１は加熱ＯＮ／ＯＦＦスイッチ、５０は演算制御部で、データ条件データを転送するデータ転送部９と、加熱ＯＮ信号により時間減算を開始し加熱ＯＦＦ信号により時間乗算を開始する加熱ＯＮ／ＯＦＦタイマ８０と、主制御量演算部６０２と、補正制御量演算部５７と、演算された主制御量Ｅｏと補正制御量△Ｅとを加算してインバータ２を制御する加算器５４で構成されている。
【００２２】
主制御量演算部６０２はデータ転送部９を介して入力する条件設定データＤｗ，θｓ，ηｃ，Ｐｓ，Ｐａ，Ｔとタイマ８０からの時間Ｔｈから主制御量Ｅｏを（５）式で求めるように構成されている。
【００２３】
【数５】

【００２４】
ただし、Ｐｓ：初期輻射損失
Ｐａ：定常輻射損失
Ｔ：過渡時間
Ｔｈ：加熱ＯＮ／ＯＦＦタイマからの時間
補正制御量演算部５７は従来図５のそれと同様に構成されている。
【００２５】
次に、この装置の動作について説明する。主制御量演算部６０２は、条件設定データと加熱ＯＮ／ＯＦＦスイッチＳ１のＯＮ又はＯＦＦにより出力する加熱ＯＮ／ＯＦＦタイマ８０からの時間Ｔｈから（５）式で主制御量Ｅｏを求める。この場合初期段階の輻射損失を補うｃｍ²当たりの必要電力Ｗ／ｃｍ²を図３に示すように近似し、スイッチＳ１からの加熱ＯＮ／ＯＦＦ信号により動作する加熱ＯＮ／ＯＦＦタイマ８０により必要電力Ｐを（６）式で決定し、必要電力Ｐ，コイル効率ηｃから主制御量Ｅｏを求める。
【００２６】
【数６】

【００２７】
しかして、加熱ＯＮ／ＯＦＦスイッチＳ１のＯＮ，ＯＦＦにより輻射損失を補うｃｍ²当たりの必要電力Ｐを図３又は図４に示すように変化させることができ、被加熱物温度が目標の定常状態になるまでの必要電力を大きくすることができる。
【００２８】
補正制御量演算部５７は従来図５の場合と同様にライン速度が定速に達すると補正制御量△Ｅを演算するので、インバータはライン速度が定格に達するまでは主制御量Ｅｏで制御され、定格速度では制御量Ｅ（＝Ｅｏ＋△Ｅ）による温度フィードバック制御となる。
【００２９】
この実施の態様によれば、図３又は図４に示すように加熱初期の必要電力を大きくして、目標温度未達部分の発生を制御することができる。
【００３０】
【発明の効果】
本発明は、加熱開始直後から適正な制御量を演算して必要電力を制御しているので、加熱開始直後に生ずる目標温度未達部が減少する。このため製品歩留まりが向上する。
【図面の簡単な説明】
【図１】本発明の実施の態様を示すブロック構成図。
【図２】本発明の実施の態様２に示すブロック構成図。
【図３】輻射損失を補う必要電力を示す線図。
【図４】加熱スイッチをＯＮ／ＯＦＦさせた場合の輻射損失を補う必要電力を示す線図。
【図５】従来例を示すブロック構成図。
【図６】従来必要電力パターンを示す線図。
【符号の説明】
１…加熱コイル
２…インバータ
３…被加熱物
４…温度計
６…速度検出器
７…条件設定器
４１…熱電対
５０…演算制御部
５１…温度変換器
５２…切換器
５４…加算器
５５…移動平均温度演算部
５６…判定部
５７…補正制御量演算部
５８…警報部
５９…速度変換器
６０，６０１，６０２…主制御量演算部
Ｅ…制御量
△Ｅ…補正制御量
Ｅｏ…主制御量
θｒ…検出温度
θａ…移動平均温度
θｃ…コイル内温度
θｓ…目標温度
Ｓｐ…ライン速度[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an induction heating apparatus that controls heat input so as to eliminate generation of a target temperature end portion in an initial stage of induction heating.
[0002]
[Prior art]
When the object to be heated is heated by the induction heating device, the heat input is controlled so that the heating temperature matches the target temperature in order to obtain good quality. In the case of heating in a pattern as shown in FIG. 6, necessary power P in a steady state known from experience is supplied to the heating coil for heating.
[0003]
FIG. 5 shows a heat input control unit of a conventional induction heating apparatus. 1 is a heating coil for heating an object to be heated 3, 2 is an inverter (variable power source) for supplying necessary power to the heating coil, and 50 is an inverter 2. An arithmetic control unit for controlling takes in the outer diameter D _W , the wall thickness T _W , the target temperature θ _S , the coil efficiency ηc, and the line speed Sp from the speed detector 6 set by the condition setting unit 7, The main control amount calculation unit for obtaining the main calculation amount Eo by the equation (1) and the heated object temperature θr from the thermometer 4 are incorporated, and when the line speed reaches the rated speed, the correction control amount ΔE is calculated by the equation (2). A correction control amount calculation unit 57 to be obtained and an adder 54 that adds the main calculation amount Eo and the correction control amount ΔE and outputs the control amount E to the inverter 2 are configured.
[0004]
[Expression 1]

[0005]
Where Ksp is a constant determined by the object to be heated.
[Expression 2]
ΔE = K _θ × (θs−θa) / θs × Eo + ΔE ′ (2)
However, K _θ : a positive value exceeding 0 (constant)
.DELTA.E '= previous .DELTA.E value .theta.a: the moving average temperature line speed is changed from the start to the rated speed, the switch 52 is turned off and the correction amount from the correction control amount calculation unit 57 is set as .DELTA.E = 0. The feedback control is stopped, the inverter is controlled by the main control amount Eo, and electric power P proportional to the main control amount Eo is output to the heating coil 1.
[0007]
When the line speed reaches the rated value, the switch 52 is turned on, the correction control amount calculation unit 57 calculates the correction amount ΔE, and the adder 54 adds the main control amount Eo to the inverter with the control amount E = Eo + ΔE. 2 is controlled. The inverter 2 sends electric power P proportional to the control amount E to the heating coil 1. Thus, temperature feedback control is performed so that the moving average temperature θa is equal to the target temperature θs. (Japanese Patent Application No. 6-230942)
[0008]
[Problems to be solved by the invention]
By the way, when the influence of the temperature rise in the heating coil due to the radiant heat of the heated object such as heating that compensates for the radiation loss of the heated object in a high temperature state is large, the required power P is different immediately after the start of heating and in the steady heating state. For this reason, when the necessary power in the heating steady state is supplied immediately after the start of heating, a target temperature unachieved portion occurs in the initial heating stage.
[0009]
The present invention has been made in view of such conventional problems, and an object of the present invention is to provide an induction heating apparatus that controls heat input so that a target temperature unachieved portion is reduced in the initial stage of heating. There is to do.
[0010]
[Means for Solving the Problems]
The present invention includes a heating coil that heats a moving object to be heated, a variable power source that supplies power to the heating coil, a main control amount calculation unit that calculates a main control amount for generating necessary power, and a temperature feedback In an induction heating apparatus including a correction control amount calculation unit that calculates a correction control amount for control and an operation control unit that includes an adder that controls the variable power source by adding the main control amount and the correction control amount.
(1) The condition setting data for initially setting the outer diameter Dw, the target temperature θs, the coil efficiency ηc, and the emissivity ε of the object to be heated, and the temperature detector for detecting the heating coil internal temperature θc are provided.
The operation of the main control amount Eo as the main controlled variable of lower initial stage of the main controlled variable heating coil within the temperature calculating unit from these condition setting data and the heating coil inside temperature is greater than the main control amount in the steady state, the following This is done using equation ( 9 ) .
[Equation 9]

However, Kd and Ke are constants.
[0011]
(2) or condition setting data for initially setting the outer diameter Dw, target temperature θs, coil efficiency ηc, initial radiation loss Ps, steady radiation loss Pa, and transient time T of the object to be heated; heating ON / OFF switch; A heating ON / OFF timer that outputs the elapsed time from ON and OFF of the heating ON / OFF switch is provided,
The main control amount calculation unit calculates the main control amount Eo main control amount of the initial stage from the time Th of condition setting data and heating ON / OFF timer is greater than the main control amount in the steady state, the following equation (10) It was made to use .
[Expression 10]

However, Kd is a constant.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described with reference to the drawings.
[0013]
Embodiment 1
1, 1 is a heating coil, 2 is an inverter (variable power source) that outputs to the heating coil, 3 is an object to be heated by the heating coil, 4 is a thermometer that detects the temperature θr of the object to be heated, and 41 is A thermocouple that detects the temperature θc in the heating coil 1, 71 is an input link data to condition setting unit that initially sets the outer diameter Dw, target temperature θs, coil efficiency ηc, and emissivity ε of the object to be heated, and 50 is an arithmetic control. The data transfer unit 9 for transferring the data condition setting data, the main control amount calculation unit 601, the correction control amount calculation unit 57, and the calculated main control amount Eo and auxiliary control amount ΔE are added. The adder 54 controls the inverter 2.
[0014]
The main control amount calculation unit 601 is configured to obtain the main control amount Eo from the condition setting data Dw, θs, ηc, ε transferred from the data transfer unit 9 and the temperature θc from the thermocouple 41 by the equation (3). Has been.
[0015]
[Equation 3]

[0016]
Kd, Ke: Constant Kd × Dw: Surface area Ke × ε × {(θs + 273) ⁴ − (θc + 273) ⁴ }: W / cm ²
W / cm ² : The required power correction control amount calculation unit 57 per cm ² that compensates for the radiation loss is the temperature θr of a thermometer that detects the temperature of the object to be heated when the line speed reaches the rated speed, similarly to that of FIG. Is used to calculate the correction control amount ΔE.
[0017]
Next, the operation of this apparatus will be described. The main control amount calculation unit 601 calculates the expression (3) and outputs the main control amount Eo.
[0018]
[Expression 4]
P = Kd × Dw × Ke × ε × {(θs + 273) ⁴ − (θc + 273) ⁴ } (4)
As is clear from the equation (4), the required power P varies depending on the in-coil temperature θc. P is large when the value of θc is small, and P is small when the value of θc is small. Therefore, if the inverter 2 is controlled with the main control amount Eo according to the equation (3), the required power P until the in-coil temperature θc reaches a steady state increases.
[0019]
When the line speed reaches the rated speed, the correction control amount calculation unit 57 calculates the expression (2) and outputs the correction control amount as in the case of FIG. Thus, the inverter 2 is controlled only by the main control amount Eo until the line speed reaches the rating, and when the rated speed is reached, temperature feedback control is performed by the control amount E (= Eo + ΔE).
[0020]
According to this embodiment, the power required until the in-coil temperature θc reaches the normal state can be increased, so that the occurrence of the target temperature unachieved portion in the initial heating stage can be suppressed.
[0021]
Embodiment 2
2, 1 is a heating coil, 2 is an inverter that outputs to the heating coil, 3 is an object to be heated, 4 is a thermometer that detects the temperature of the object to be heated, 72 is an outer diameter Dw of the object to be heated, and a target temperature θs , Coil efficiency ηc, initial radiation loss Ps, stationary radiation loss Pa, input link data condition setting device for initial setting of transient time T, S1 is a heating ON / OFF switch, 50 is a calculation control unit, and transfers data condition data The data transfer unit 9, the heating ON / OFF timer 80 that starts time subtraction by the heating ON signal and starts time multiplication by the heating OFF signal, the main control amount calculation unit 602, and the correction control amount calculation unit 57 are calculated. The adder 54 controls the inverter 2 by adding the main control amount Eo and the correction control amount ΔE.
[0022]
The main control amount calculation unit 602 obtains the main control amount Eo from the condition setting data Dw, θs, ηc, Ps, Pa, T input via the data transfer unit 9 and the time Th from the timer 80 by the equation (5). It is configured.
[0023]
[Equation 5]

[0024]
However, Ps: initial radiation loss Pa: stationary radiation loss T: transient time Th: time correction control amount calculation unit 57 from the heating ON / OFF timer is configured similarly to that of FIG.
[0025]
Next, the operation of this apparatus will be described. The main control amount calculation unit 602 obtains the main control amount Eo by the equation (5) from the condition setting data and the time Th from the heating ON / OFF timer 80 that is output when the heating ON / OFF switch S1 is turned on or off. In this case the required power W / cm ² per cm ² to compensate for the radiation loss of the initial stage is approximated as shown in FIG. 3, it requires power by heating ON / OFF timer 80 which operates by heating ON / OFF signal from the switch S1 P is determined by equation (6), and the main control amount Eo is obtained from the required power P and the coil efficiency ηc.
[0026]
[Formula 6]

[0027]
Thus, the required power P per cm ² that compensates for the radiation loss can be changed by turning ON / OFF the heating ON / OFF switch S1, as shown in FIG. 3 or FIG. The required power to become can be increased.
[0028]
Since the correction control amount calculation unit 57 calculates the correction control amount ΔE when the line speed reaches a constant speed as in the case of the conventional FIG. 5, the inverter is controlled by the main control amount Eo until the line speed reaches the rating. At the rated speed, temperature feedback control is performed with a control amount E (= Eo + ΔE).
[0029]
According to this embodiment, as shown in FIG. 3 or FIG. 4, the required power at the initial stage of heating can be increased to control the occurrence of the target temperature not reached portion.
[0030]
【The invention's effect】
In the present invention, the necessary power is controlled by calculating an appropriate control amount immediately after the start of heating, so that the target temperature unachieved portion that occurs immediately after the start of heating is reduced. Because of this product step remains is improved.
[Brief description of the drawings]
FIG. 1 is a block diagram showing an embodiment of the present invention.
FIG. 2 is a block diagram showing a second embodiment of the present invention.
FIG. 3 is a diagram showing required power to compensate for radiation loss.
FIG. 4 is a diagram showing required power to compensate for radiation loss when a heating switch is turned on / off.
FIG. 5 is a block diagram showing a conventional example.
FIG. 6 is a diagram showing a conventional required power pattern.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Heating coil 2 ... Inverter 3 ... To-be-heated object 4 ... Thermometer 6 ... Speed detector 7 ... Condition setter 41 ... Thermocouple 50 ... Operation control part 51 ... Temperature converter 52 ... Switch 54 ... Adder 55 ... Moving average temperature calculation unit 56 ... determination unit 57 ... correction control amount calculation unit 58 ... alarm unit 59 ... speed converters 60, 601, 602 ... main control amount calculation unit E ... control amount ΔE ... correction control amount Eo ... main control Amount θr ... Detection temperature θa ... Moving average temperature θc ... In-coil temperature θs ... Target temperature Sp ... Line speed

Claims

A heating coil that heats a moving object to be moved, a variable power source that supplies power to the heating coil, a main control amount calculation unit that calculates a main control amount for generating necessary power, and correction for temperature feedback control In an induction heating apparatus including a correction control amount calculation unit that calculates a control amount and an operation control unit that includes an adder that controls the variable power supply by adding the main control amount and the correction control amount,
Condition setting data for initially setting the outer diameter Dw, target temperature θs, coil efficiency ηc, emissivity ε of the object to be heated, and a temperature detector for detecting the heating coil internal temperature θc are provided.
The operation of the main control amount Eo as the main controlled variable of lower initial stage of the main controlled variable heating coil within the temperature calculating unit from these condition setting data and the heating coil inside temperature is greater than the main control amount in the steady state, the following (7) was performed using induction heating apparatus the target temperature not reached moiety is characterized in that so as not to occur in a heating initial stage.

However, Kd and Ke are constants.

A heating coil that heats a moving object to be moved, a variable power source that supplies power to the heating coil, a main control amount calculation unit that calculates a main control amount for generating necessary power, and correction control for temperature feedback control In an induction heating apparatus including a correction control amount calculation unit that calculates an amount and an operation control unit that includes an adder that controls the variable power supply by adding the main control amount and the correction control amount,
Condition setting data for initial setting of outer diameter Dw, target temperature θs, coil efficiency ηc, initial radiation loss Ps, steady radiation loss Pa, transient time T , heating ON / OFF switch, and heating ON / OFF switch A heating ON / OFF timer that outputs the elapsed time from ON and OFF is provided.
The main control amount calculation unit calculates the main control amount Eo main control amount of the initial stage from the time Th of condition setting data and heating ON / OFF timer is greater than the main control amount in the steady state, the following equation (8) performed using induction heating apparatus, characterized in that the target temperature not reached part was not generated in the heating initial stage.

However, Kd is a constant.