JPH07123761A - Methods for controlling and estimating output torque of motor drive system - Google Patents

Methods for controlling and estimating output torque of motor drive system

Info

Publication number
JPH07123761A
JPH07123761A JP5292743A JP29274393A JPH07123761A JP H07123761 A JPH07123761 A JP H07123761A JP 5292743 A JP5292743 A JP 5292743A JP 29274393 A JP29274393 A JP 29274393A JP H07123761 A JPH07123761 A JP H07123761A
Authority
JP
Japan
Prior art keywords
torque
motor
shaft
load
command
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP5292743A
Other languages
Japanese (ja)
Other versions
JP3253434B2 (en
Inventor
Geihou Chin
芸峰 陳
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Toyo Electric Manufacturing Ltd
Original Assignee
Toyo Electric Manufacturing Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Toyo Electric Manufacturing Ltd filed Critical Toyo Electric Manufacturing Ltd
Priority to JP29274393A priority Critical patent/JP3253434B2/en
Publication of JPH07123761A publication Critical patent/JPH07123761A/en
Application granted granted Critical
Publication of JP3253434B2 publication Critical patent/JP3253434B2/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Landscapes

  • Control Of Electric Motors In General (AREA)

Abstract

PURPOSE:To inexpensively make a motor drive system to follow a command without vibrating the output torque of the system by estimating the output torque signal required for the control of the output torque from a speed sensor fitted to a motor without providing any torque sensor on the shaft of the motor. CONSTITUTION:At the time of making a torsion system composed of a motor 7 which drives a load 9 and elastic shaft 8 which connects the load 9 with the motor 7 to follow a command without vibrating its output torque Ts by only using a speed detector fitted to the motor 7, three stable poles which decide the response characteristic of the system are first decided. When the poles are decided to -pa, -pb, and -pc, the gain of each control loop is calculated from the poles and the machine constants rho and omegao of a plant based on formulae I, II, and III and inputted to each control block. Then a cut-off frequency omegac is appropriately decided by taking the noise condition at the actual operating time into account and the coefficient of each software observation instrument is decided from the frequency omegac and the machine constants of the plant. Finally, the calculated coefficients are respectively inputted to the software observation instruments.

Description

【発明の詳細な説明】Detailed Description of the Invention

【0001】[0001]

【産業上の利用分野】本発明は、電動機と負荷を連結す
る軸からなるねじり系において、軸トルクセンサを設け
ず電動機に取り付けられた速度センサだけを用い、ねじ
り振動を防止または抑制しかつ軸トルクを推定して得る
制御システムおよびトルクセンサレス制御アルゴリズム
に関するものである。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a torsion system consisting of a shaft for connecting a motor and a load, and uses only a speed sensor attached to the motor without providing a shaft torque sensor to prevent or suppress torsional vibration and The present invention relates to a control system obtained by estimating torque and a torque sensorless control algorithm.

【0002】[0002]

【従来の技術】ねじり系の軸トルク制御においては、従
来一般に軸に軸トルクセンサを設け、指令トルクと軸ト
ルクセンサによるトルク検出信号との偏差に基づき、何
にかの制御理論に基づいて制御しており、トルクセンサ
を設けずに軸トルク制御すること自体、従来では不可能
とされている。さらに、軸トルクセンサ方式によれば、
トルク検出信号にノイズが多く含まれ制御に使える信号
とするのに何にかの特殊な信号処理を必要とするため、
センサの値段が高く製品のコストがぐんと高くなること
はよく知られている。
2. Description of the Related Art In the axial torque control of a torsion system, an axis torque sensor is generally provided on the axis, and control is performed based on some control theory based on a deviation between a command torque and a torque detection signal from the axis torque sensor. Therefore, it has been conventionally impossible to control the shaft torque without providing a torque sensor. Furthermore, according to the shaft torque sensor method,
The torque detection signal contains a lot of noise, and some special signal processing is required to make it a signal that can be used for control.
It is well known that the price of sensors is high and the cost of products is much higher.

【0003】[0003]

【発明が解決しようとする課題】剛性の低い軸を有する
電動機駆動システムにおいて、軸にトルクセンサを設け
ず、電動機に取り付けられた速度センサから軸トルク制
御に必要とする軸トルク信号を推定し、推定されたトル
ク信号を用いて廉価で軸トルクを振動せずに指令通りに
追従させることが本発明の第1の課題である。また、軸
振動を抑制するために軸トルクの微分値などの信号もフ
ィードバックする必要があり、それらの信号も遅れずに
ソフトで確実に推定するアルゴリズムを提供することが
本発明の第2の課題である。
In a motor drive system having a shaft with low rigidity, a torque sensor is not provided on the shaft, and a shaft torque signal required for shaft torque control is estimated from a speed sensor attached to the motor, The first object of the present invention is to use the estimated torque signal to inexpensively cause the shaft torque to follow the command without vibrating. Further, in order to suppress the shaft vibration, it is necessary to feed back signals such as a differential value of the shaft torque, and it is a second object of the present invention to provide an algorithm for surely estimating these signals by software without delay. Is.

【0004】[0004]

【課題を解決するための手段】ここで、本発明の理解を
容易にするため、まずシステムの動特性分析を説明す
る。
In order to facilitate understanding of the present invention, a dynamic characteristic analysis of the system will be described first.

【0005】電動機と負荷と弾性軸を含むシステムのブ
ロックは図3のように表され、また運動方程式はよく知
られているように、式(1),(2),(3)のように
表される。図3においては、7は電動機、8は弾性軸、
9は負荷機、10はトルク発生係数である。
The block of the system including the electric motor, the load and the elastic shaft is represented as shown in FIG. 3, and the equation of motion is well known as in equations (1), (2) and (3). expressed. In FIG. 3, 7 is an electric motor, 8 is an elastic shaft,
Reference numeral 9 is a load machine, and 10 is a torque generation coefficient.

【0006】[0006]

【数1】 [Equation 1]

【0007】ただし、ωm,ωl,Ts,u,Tlはそ
れぞれ電動機7と負荷機9の速度,軸に発生する軸トル
ク,電動機に印加する制御入力,負荷に印加されている
負荷トルクであり、Jm,Dm,Ktは電動機の慣性,
粘性摩擦係数,トルク発生係数を表し、Jl,Dlは負
荷機の慣性,粘性摩擦係数を表し、Kcは軸のバネ定数
を表す。
However, ωm, ωl, Ts, u, and Tl are the speed of the electric motor 7 and the load machine 9, the axial torque generated in the shaft, the control input applied to the electric motor, and the load torque applied to the load, respectively. Jm, Dm, Kt are the inertia of the motor,
The viscous friction coefficient and the torque generation coefficient are represented, Jl and Dl represent the inertia of the load machine and the viscous friction coefficient, and Kc represents the spring constant of the shaft.

【0008】軸トルク制御で扱い易いモデルにするた
め、状態変数ωm,Ts,Tsの微分値(以下φと記
す),Tlとし、式(1),(2),(3)の運動方程
式を、つぎのような状態方程式で表す。
In order to make the model easy to handle in axial torque control, the differential equations of the state variables ωm, Ts and Ts (hereinafter referred to as φ) and Tl are used, and the equations of motion of equations (1), (2) and (3) are , Is expressed by the following equation of state.

【0009】[0009]

【数2】 [Equation 2]

【0010】ここで、系に僅かな粘性摩擦を無視し、電
動機に印加する制御入力uから、軸トルクTsまでの伝
達関数は式(8)のようになる。
Here, the transfer function from the control input u applied to the electric motor to the shaft torque Ts is given by equation (8), ignoring a slight viscous friction in the system.

【0011】[0011]

【数3】 [Equation 3]

【0012】ρoωoは、電動機係数Jm,負荷慣性J
l,軸ばね定数Kcの機械定数を使って、式(9),式
(10)と定義されるパラメータであり、それぞれ負荷慣
性が等価的に全体慣性に占める割合とねじり系共振角周
波数を表す。
Ρoωo is the motor coefficient Jm, the load inertia J
1, the mechanical constants of the axial spring constant Kc are parameters defined by the equations (9) and (10), which respectively represent the ratio of the load inertia to the total inertia and the torsion system resonance angular frequency. .

【0013】[0013]

【数4】 [Equation 4]

【0014】システムの特性を決める式(8)の分母の
特性多項式をみると、減衰係数(sにあたる係数)は0
であり、典型的な2次振動系になっていることが解か
る。実際に、粘性摩擦によって系に減衰する効果を多少
寄与するが、僅かである。
Looking at the characteristic polynomial of the denominator of the equation (8) that determines the characteristic of the system, the damping coefficient (the coefficient corresponding to s) is 0.
And it can be seen that it is a typical secondary vibration system. In fact, the viscous friction contributes somewhat to the effect of damping it in the system, but only slightly.

【0015】これより、ねじり振動を抑えるために、制
御入力から系に減衰項に相当するものを与える必要があ
る。それは軸トルクの微分値フィードバックに対応して
いる。これは、図1のようにPID制御則によるもので
あってよい。
Therefore, in order to suppress the torsional vibration, it is necessary to give a system equivalent to a damping term from the control input. It corresponds to the differential feedback of the shaft torque. This may be due to the PID control law as shown in FIG.

【0016】図1は本発明の技術思想を示すトルクセン
サレス軸トルク制御原理を表したものであり、1は制御
対象、2は速度センサ、3はソフト観測器、4は比例積
分器、5は微分ゲイン、61,62は加算器である。図1よ
り、トルク指令T*から軸トルクTsまでの伝達関数
は、式(11)になる。
FIG. 1 shows a torque sensorless shaft torque control principle showing the technical idea of the present invention. 1 is a controlled object, 2 is a speed sensor, 3 is a soft observer, 4 is a proportional integrator, and 5 is a proportional integrator. Differential gains, 61 and 62 are adders. From FIG. 1, the transfer function from the torque command T * to the shaft torque Ts is given by equation (11).

【0017】[0017]

【数5】 [Equation 5]

【0018】すなわち、微分ゲインKdは減衰項(s=
乗項)に入り、振動抑制の効果を果たしていることが解
かる。また、閉ループ系の三つの特性極は三つのゲイン
Kp,Ki,Kdで自由に調整することができる。
That is, the differential gain Kd is the damping term (s =
It is understood that the vibration suppression effect is achieved by entering the (multiplication term). Further, the three characteristic poles of the closed loop system can be freely adjusted by the three gains Kp, Ki and Kd.

【0019】前述した制御側に、軸トルクとその微分信
号をフィードバックする必要があるが、その信号は直接
に測定しないため、ここではオブザーバ理論を変形用
い、プラントの機械定数に基づいてソフト観測器を構成
することにより、電動機に印加する制御入力信号と電動
機に取り付けられた速度センサの検出信号から、軸トル
ク,軸トルク微分値,負荷トルクを推定する。
It is necessary to feed back the shaft torque and its differential signal to the control side described above, but since the signal is not directly measured, the observer theory is modified here and the soft observer is based on the mechanical constant of the plant. With the above configuration, the shaft torque, the shaft torque differential value, and the load torque are estimated from the control input signal applied to the electric motor and the detection signal of the speed sensor attached to the electric motor.

【0020】そのソフト観測器3は図2の如きものであ
る。ここで、図2は本発明によるソフト観測器の原理を
示す図である。すなわち、ソフト観測器はつぎのような
状態方程式で表される。
The soft observer 3 is as shown in FIG. Here, FIG. 2 is a diagram showing the principle of the soft observer according to the present invention. That is, the soft observer is represented by the following equation of state.

【0021】[0021]

【数6】 [Equation 6]

【0022】ただし、ωcは設計者が自由に決められる
カットオフ周波数を表し、それ以上の高周波ノイズを減
衰することを意味する。ソフト観測器出力のうち、x
b,xc,xdはそれぞれ軸トルク信号,軸トルク微分
値信号,負荷トルク信号に相当する。かようにして、観
測した信号は実際の信号に漸次収束することが保証され
る。しかも、その信号をフィードバックした場合、制御
ループに影響しないことも指摘されている。最初の初期
偏差は除いて真の信号を使った場合と完全に等価にな
る。
However, ωc represents a cutoff frequency freely decided by the designer, and means that high frequency noise higher than that is attenuated. X of soft observer output
b, xc, and xd correspond to a shaft torque signal, a shaft torque differential value signal, and a load torque signal, respectively. In this way it is guaranteed that the observed signal will gradually converge to the actual signal. Moreover, it is pointed out that the feedback of the signal does not affect the control loop. Except for the first initial deviation, it is completely equivalent to using the true signal.

【0023】[0023]

【作用】図1においては、微分ゲイン5は系に減衰項を
与え、ねじり振動を防止または抑制する役割を果たす。
トルク調整ループにおいて、比例積分器4にて比例器は
指令トルクT*に追従速度を調整し、積分器は指令追従
のオフセットをなくす役割をする。図2のソフト観測器
3において、カットオフ周波数ωcは収束のスピードを
決めるとともに、それ以上の高周波観測ノイズをカット
オフする役割をする。
In FIG. 1, the differential gain 5 gives a damping term to the system to prevent or suppress torsional vibration.
In the torque adjustment loop, the proportional integrator in the proportional integrator 4 adjusts the follow-up speed to the command torque T *, and the integrator serves to eliminate the command follow-up offset. In the soft observer 3 shown in FIG. 2, the cutoff frequency ωc plays a role of determining the speed of convergence and cutting off higher frequency observation noise.

【0024】[0024]

【実施例】さらに本発明を、具体的なシステム適用例に
て詳述する。すなわち、負荷を駆動する電動機と、負荷
と電動機を連結する弾性軸とらなるねじり系において、
電動機に取り付けられた速度検出器のみを使って、軸ト
ルクを振動させずに指令に追従させる適用においては、
まずシステム応答特性を決める三っの安定な極を決め
る。
The present invention will be described in more detail with reference to specific system application examples. That is, in the torsion system consisting of the electric motor that drives the load and the elastic shaft that connects the load and the electric motor,
In an application that uses only the speed detector attached to the electric motor to follow the command without vibrating the shaft torque,
First, determine the three stable poles that determine the system response characteristics.

【0025】例えば、−pa,−pb,−pcと決めた
とき、これらの極とプラントの機械定数であるρ, ωo
から、制御ループに各ゲインを式(17),(18),(1
9)と計算し、各制御ブロックに入れる。
For example, when -pa, -pb, -pc are determined, the mechanical constants of these poles and plant, ρ, ωo.
From the equations (17), (18), (1
9) Calculate and put in each control block.

【0026】つぎに、実際運転時のノイズ状況をみて、
カットオフ周波数ωcを適当に決め、このカットオフ周
波数とプラントの機械定数から、ソフト観測器の各係数
は決められることにより、最後に、計算した各係数をそ
れぞれソフト観測器に入れればよい。
Next, looking at the noise situation during actual operation,
The cutoff frequency ωc is appropriately determined, and each coefficient of the soft observer is determined from the cutoff frequency and the mechanical constant of the plant. Finally, each calculated coefficient may be input to the soft observer.

【0027】[0027]

【発明の効果】以上説明したように本発明によれば、ね
じり振動制御に必要とする軸トルク,軸トルク微分値に
相当する信号を、ソフト観測器により格別に推定し、あ
るいはフィードバック系を有してねじり振動を抑制し得
る安価な制御方法を提供することができる。
As described above, according to the present invention, the signals corresponding to the shaft torque and the shaft torque differential value required for the torsional vibration control are extrapolated by a software observer or a feedback system is provided. Thus, an inexpensive control method capable of suppressing torsional vibration can be provided.

【図面の簡単な説明】[Brief description of drawings]

【図1】図1は本発明の技術思想を示すトルクセンサレ
ス軸トルク制御原理を表す系統図である。
FIG. 1 is a system diagram showing a torque sensorless shaft torque control principle showing the technical idea of the present invention.

【図2】図2は本発明によるソフト観測器の原理を示す
図である。
FIG. 2 is a diagram showing the principle of a soft observer according to the present invention.

【図3】図3はねじり系制御対象ブロックを示す系統図
である。
FIG. 3 is a system diagram showing a torsion system control target block.

【符号の説明】[Explanation of symbols]

1 制御対象 2 速度センサ 3 ソフト観測器 4 比例積分器 5 微分ゲイン 7 電動機 8 弾性軸 9 負荷機 10 トルク発生係数 T* 指令トルク u 制御入力トルク Ts 軸トルク φ 軸トルク微分値推定値 ωo ねじり係共振角周波数 ωm 電動機速度 ωl 負荷機速度 Tl 負荷外乱 ωc カットオフ周波数 1 Control object 2 Speed sensor 3 Soft observer 4 Proportional integrator 5 Differential gain 7 Electric motor 8 Elastic shaft 9 Load machine 10 Torque generation coefficient T * Command torque u Control input torque Ts Axial torque φ Axial torque differential value estimated value ωo Torsional coefficient Resonance angular frequency ωm Motor speed ωl Load machine speed Tl Load disturbance ωc Cutoff frequency

【数7】 [Equation 7]

Claims (2)

【特許請求の範囲】[Claims] 【請求項1】 負荷と負荷を駆動する電動機の間を連結
する剛性の低い軸の軸トルクを振動抑制しながら指令ト
ルクに追従制御させる方法において、前記電動機に取り
付けられた速度センサの出力値を入力して軸トルクの値
とその微分値を推定して得るソフト観測手段を設けると
ともに、指令トルクと前記軸トルクの推定値との偏差を
比例積分した値に、前記推定された軸トルクの微分値を
印加することにより、トルク指令を得るようにしたこと
を特徴とする電動機駆動システムの軸トルク制御方法。
1. A method for controlling a command torque to follow a command torque while suppressing vibration of a shaft torque of a low-rigidity shaft connecting a load and a motor for driving the load, wherein an output value of a speed sensor attached to the motor is controlled. A soft observation means is provided to obtain the value of the shaft torque and its differential value by inputting, and a derivative of the estimated shaft torque is obtained by proportionally integrating the deviation between the command torque and the estimated value of the shaft torque. A shaft torque control method for an electric motor drive system, wherein a torque command is obtained by applying a value.
【請求項2】 電動機と負荷を連結する弾性軸に発生す
るねじり軸トルクとその微分値の推定方法において、前
記電動機に印加する制御入力と電動機速度センサの出力
信号とプラントの機械定数と任意に指定されるカットオ
フ周波数に基づいて次数4のソフト観測器(3)を構成
することにより、該ソフト観測器(3)の状態変数(x
b)と状態変数(xc)を軸トルクとその微分値の推定
値とすることを特徴とする電動機駆動システムの軸トル
ク推定方法。
2. A method of estimating a torsional shaft torque generated on an elastic shaft connecting a motor and a load and a differential value thereof, wherein a control input applied to the motor, an output signal of a motor speed sensor, a mechanical constant of a plant are arbitrarily set. By configuring the soft observer (3) of order 4 based on the specified cutoff frequency, the state variable (x
b) and the state variable (xc) are used as an estimated value of the axial torque and its differential value, and an axial torque estimation method for an electric motor drive system.
JP29274393A 1993-10-28 1993-10-28 Shaft torque control method and shaft torque estimation method for motor drive system Expired - Lifetime JP3253434B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP29274393A JP3253434B2 (en) 1993-10-28 1993-10-28 Shaft torque control method and shaft torque estimation method for motor drive system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP29274393A JP3253434B2 (en) 1993-10-28 1993-10-28 Shaft torque control method and shaft torque estimation method for motor drive system

Publications (2)

Publication Number Publication Date
JPH07123761A true JPH07123761A (en) 1995-05-12
JP3253434B2 JP3253434B2 (en) 2002-02-04

Family

ID=17785760

Family Applications (1)

Application Number Title Priority Date Filing Date
JP29274393A Expired - Lifetime JP3253434B2 (en) 1993-10-28 1993-10-28 Shaft torque control method and shaft torque estimation method for motor drive system

Country Status (1)

Country Link
JP (1) JP3253434B2 (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5444714A (en) * 1977-09-14 1979-04-09 Mitsubishi Electric Corp System for controlling torsional vibration of mechanical drive system
JPH01304511A (en) * 1988-06-02 1989-12-08 Seiko Instr Inc Servo controller
JPH0358106A (en) * 1989-07-27 1991-03-13 Mitsubishi Heavy Ind Ltd High speed positioning control method
JPH04275086A (en) * 1991-02-28 1992-09-30 Fuji Electric Co Ltd Controller for dynamic simulator
JPH0542878A (en) * 1991-07-09 1993-02-23 Koyo Seiko Co Ltd Power steering
JPH05111274A (en) * 1991-10-16 1993-04-30 Fuji Electric Co Ltd Control device of electric motor
JPH05168267A (en) * 1991-12-13 1993-07-02 Toyo Electric Mfg Co Ltd Tortional vibration restriction control method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5444714A (en) * 1977-09-14 1979-04-09 Mitsubishi Electric Corp System for controlling torsional vibration of mechanical drive system
JPH01304511A (en) * 1988-06-02 1989-12-08 Seiko Instr Inc Servo controller
JPH0358106A (en) * 1989-07-27 1991-03-13 Mitsubishi Heavy Ind Ltd High speed positioning control method
JPH04275086A (en) * 1991-02-28 1992-09-30 Fuji Electric Co Ltd Controller for dynamic simulator
JPH0542878A (en) * 1991-07-09 1993-02-23 Koyo Seiko Co Ltd Power steering
JPH05111274A (en) * 1991-10-16 1993-04-30 Fuji Electric Co Ltd Control device of electric motor
JPH05168267A (en) * 1991-12-13 1993-07-02 Toyo Electric Mfg Co Ltd Tortional vibration restriction control method

Also Published As

Publication number Publication date
JP3253434B2 (en) 2002-02-04

Similar Documents

Publication Publication Date Title
KR100855798B1 (en) Positioning servocontroller
US4792737A (en) Circuit for controlling the motion of a moving object
US7638965B2 (en) Motor control apparatus
JP2001273037A (en) Servo control unit
JP2004213472A (en) Control device
KR20100084671A (en) Engine bench system control system
JPH0956183A (en) Mechanical vibration detecting equipment and damping controller
JP4367058B2 (en) Motor control device
JP3274070B2 (en) Motor control method and motor control device
CN102163952B (en) Motor control device
JP2016057812A (en) Control system of power plant
JP4914979B2 (en) Motor control device and motor control method
JP3526022B2 (en) Oscillation criticality detection method for servo control system
JPH04275086A (en) Controller for dynamic simulator
WO2005064781A1 (en) Motor controller
JPH03110607A (en) Servo motor control system
JPH07123761A (en) Methods for controlling and estimating output torque of motor drive system
JP4664576B2 (en) Servo control device
JPH08278821A (en) Damping method for servo control system
US20200408631A1 (en) Controller for evaluating inertia and inertia evaluation method
JP2004177259A (en) Controller for engine tester
JP2838578B2 (en) Motor control device, disturbance load torque estimation device
JP2958600B2 (en) Motor control device
JP2798217B2 (en) High-speed positioning control method
JP3257873B2 (en) Shaft torque control method for motor drive system

Legal Events

Date Code Title Description
FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20081122

Year of fee payment: 7

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20081122

Year of fee payment: 7

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20091122

Year of fee payment: 8

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20101122

Year of fee payment: 9

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20101122

Year of fee payment: 9

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20111122

Year of fee payment: 10

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20111122

Year of fee payment: 10

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20121122

Year of fee payment: 11

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20131122

Year of fee payment: 12

EXPY Cancellation because of completion of term