JPH01297399A - Attitude controller for artificial satellite - Google Patents

Attitude controller for artificial satellite

Info

Publication number
JPH01297399A
JPH01297399A JP63127092A JP12709288A JPH01297399A JP H01297399 A JPH01297399 A JP H01297399A JP 63127092 A JP63127092 A JP 63127092A JP 12709288 A JP12709288 A JP 12709288A JP H01297399 A JPH01297399 A JP H01297399A
Authority
JP
Japan
Prior art keywords
attitude
satellite
yaw
roll
coordinate system
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
JP63127092A
Other languages
Japanese (ja)
Other versions
JP2685225B2 (en
Inventor
Shinichiro Ichikawa
市川 信一郎
Masaya Ho
蜂 正弥
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.)
Toshiba Corp
National Space Development Agency of Japan
Original Assignee
Toshiba Corp
National Space Development Agency of Japan
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 Toshiba Corp, National Space Development Agency of Japan filed Critical Toshiba Corp
Priority to JP63127092A priority Critical patent/JP2685225B2/en
Publication of JPH01297399A publication Critical patent/JPH01297399A/en
Application granted granted Critical
Publication of JP2685225B2 publication Critical patent/JP2685225B2/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Landscapes

  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

PURPOSE:To secure the high precision of the attitude precision by obtaining the attitude control signal by converting the attitude error of a satellite dynamics to the values on the coordinate system of a developed structure body such as solar battery paddle and converting said signal to the values on the coordinate system of the satellite dynamics and controlling the attitude of the satellite dynamics. CONSTITUTION:In the application to a satellite dynamics 12 in which a developed structure body 11 is arranged in rotatable ways around the pitch (Y) axis of the satellite body 10 of an artificial satellite, a roll detecting sensor 13 and a yaw detecting sensor 14 for detecting the roll attitude error around the roll (X) axis of the satellite dynamics 12 and the yaw attitude error around a yaw (Z) axis are installed. The output signals of the sensors 13 and 14 are inputted into the first coordinate conversion part 16, and converted to the values on the coordinate system of the developed structure body 1, and outputted into the Xp and Zp control calculation parts 17 and 18. The roll and yaw control signals in the coordinate system are obtained and sent into the second coordinate conversion part 19, and converted to the values on the coordinate system of the satellite dynamics 12, and the drive control for an actuator 15 for attitude drive is carried out.

Description

【発明の詳細な説明】 [発明の目的コ (産業上の利用分野) この発明は、例えば太陽電池・9ドル等の展開構造物を
搭載してなる人工衛星の姿勢制御装置に関する。
DETAILED DESCRIPTION OF THE INVENTION [Objective of the Invention (Industrial Application Field) This invention relates to an attitude control device for an artificial satellite equipped with a deployable structure such as a solar battery.

(従来の技術) 近時、人工衛星においては、大型化と共に、姿勢制御の
高精度化の促進が図られている。ところで、このような
人工衛星にあっては、その大型化にともなって展開構造
物の柔軟化の増加を招くために、その姿勢制御系の制御
バンド幅内に該展開構造物の固有振動数が含まれるとい
う問題を有する。そこで、制御方式としては、低次振動
モードを開ループ制御特性の位相に対して一18o。
(Prior Art) Recently, in addition to increasing the size of artificial satellites, attempts have been made to increase the precision of attitude control. By the way, in such artificial satellites, as the size of the satellite increases, the flexibility of the deployable structure increases, so the natural frequency of the deployable structure must be within the control bandwidth of the attitude control system. It has the problem of being included. Therefore, as a control method, the phase of the open-loop control characteristic of the low-order vibration mode is -18°.

から十分余裕金とって制御系を作るいわゆる位相安定に
より安定化を図シ、かつ、開ループ制御特性のゲインに
対して零dBから十分余裕をとって制御系を作るいわゆ
る高次振動モードのrイン安定化が採用されている。
Create a control system with sufficient margin from In-stabilization is employed.

第3図はこのような制御方式による人工衛星の姿勢制御
装置を示すもので、例えば第4図に示すような衛星本体
10のピッチ(Y)軸回りに太陽電池パドル等の展開構
造物11f回転自在に配設した衛星ダイナミクス12に
適用した場合を代表し゛て説明する。すなわち、衛星ダ
イナミクス12は、そのロール(X)軸回りのロール姿
勢誤差及びヨー(Z)軸回りのヨー姿#+誤差がロール
検出センサ13及びヨー検出センサ14によシ検出され
る。このロール及びヨー検出センサ13,14はそのロ
ール及びヨー姿勢誤差信号をロール及びヨー制御イ=号
演算部1.2に出力する。すると、このロール及びヨー
制御信号演算部1,2はそれぞれロール及びヨー制御イ
改号を求めて、姿勢駆動用のアクチュエータ15を駆動
制御する。これにjシ、アクチュエータ15は、その衛
星ダイナミクス12の姿勢を匍]@する。
FIG. 3 shows an attitude control device for an artificial satellite using such a control method. For example, as shown in FIG. A case where the method is applied to satellite dynamics 12 freely arranged will be explained as a representative example. That is, in the satellite dynamics 12, the roll attitude error around the roll (X) axis and the yaw attitude #+ error around the yaw (Z) axis are detected by the roll detection sensor 13 and the yaw detection sensor 14. The roll and yaw detection sensors 13 and 14 output their roll and yaw attitude error signals to the roll and yaw control number calculation unit 1.2. Then, the roll and yaw control signal calculation units 1 and 2 determine the roll and yaw control signals, respectively, and drive and control the attitude drive actuator 15. In response to this, the actuator 15 changes the attitude of the satellite dynamics 12.

ところが、上記人工衛星の姿勢制御装置では、その構成
上、第5図に示すように、衛星本体10のX軸及びZl
ltlに対して展開構造物1ノのX、軸及び2.軸が対
応しなくなると、X及びz軸回りとも、第6図に示すよ
うに、面内(I P )m動モードと面外(OF)振動
モードが混在して、展開構造物の振動モードが密状態と
なるため、低次振動モードの位相安定/高次蚕動モード
のゲイン安定を図ることが困難となるという問題を有し
ている。このため、その設計裏作が非常に煩雑なうえ、
姿勢制御精度の低下を招くと共に、姿勢制御の安定化が
困難となるという問題を有する。これは、特に、衛星の
大型化に伴う展開構造物11の柔軟化の増加と共に、高
姿勢制御の要請に対応することが困難となる。
However, in the above-mentioned attitude control device for an artificial satellite, due to its configuration, as shown in FIG.
X, axis and 2 of the deployed structure 1 relative to ltl. When the axes no longer correspond, the in-plane (I P ) m-motion mode and the out-of-plane (OF) vibration mode coexist around the X and Z axes, as shown in Figure 6, resulting in the vibration mode of the deployed structure. is in a dense state, which poses a problem in that it is difficult to stabilize the phase of the low-order vibration mode/stabilize the gain of the high-order peristaltic mode. For this reason, the design process is extremely complicated, and
This poses a problem in that attitude control accuracy decreases and it becomes difficult to stabilize attitude control. This makes it difficult to meet the demands for high attitude control, especially as the deployment structure 11 becomes more flexible as the satellite becomes larger.

係る事情は、衛星本体1oのY軸に対して展開構造物1
1の回転軸を傾斜して配置するように構成した場合にお
いても、同様の問題を有するものである。
This situation is such that the deployable structure 1
A similar problem occurs even when one rotational axis is arranged at an angle.

(発明が解決しようとする問題点) 以上述べたように、従来の人工衛星の姿勢制御装置では
、展開構造物の駆動モードの高密度化を防ぐことが困難
であった。
(Problems to be Solved by the Invention) As described above, in the conventional attitude control device for an artificial satellite, it is difficult to prevent the drive modes of the deployable structure from becoming denser.

この発明は上記の事情に鍮みてなされたもので、展開構
造物の振動モードの分離化するようにして、設計裏作の
簡略化を図ると共に、姿勢制御の高精度化及び安定化を
実現し得るようにした人工衛星の姿勢制御装置を堤供す
ることを目的とする。
This invention was made in consideration of the above circumstances, and by separating the vibration modes of a deployable structure, it is possible to simplify the design process and achieve high precision and stability of attitude control. The purpose of this project is to provide an attitude control system for artificial satellites.

[発明の構成コ (問題点を解決するための手段) この発明による人工衛星の姿勢制御装置Itは、アクチ
ュエータを介して姿勢制御される衛星ダイナミクスの姿
勢誤差を検出する検出手段と、この検出手段の姿勢誤差
信号を展開構造物の座標系に変換して姿勢制御信号を求
め、この姿勢制御信号を前記衛星ダイナミクスの座標系
に変換して前記アクチュエータを駆動制御する制御手段
とを備えて構成したものである。
[Structure of the Invention (Means for Solving Problems)] An artificial satellite attitude control device It according to the present invention includes a detection means for detecting an attitude error in satellite dynamics whose attitude is controlled via an actuator, and this detection means. and a control means for converting the attitude error signal into the coordinate system of the deployed structure to obtain an attitude control signal, and converting the attitude control signal into the coordinate system of the satellite dynamics to drive and control the actuator. It is something.

(作 用) 上記構成によれば、姿勢制御信号は衛星ダイナミクスか
ら検出した姿勢誤差(M号を、展開構造物の座標系に変
換して、その変換した姿勢誤差信号から姿勢制御値を求
め、これを衛星ダイナミクスの座標系に変換することに
よシ生成される。これにより、姿勢制御信号には展開構
造物の振動モードが例えば面外モードと面内モードに分
離でき、各々のモードに対して1次モードが位相安定、
2次モード以上がゲイン安定と安定化が図れる。従って
、設計裏作の簡略化が図れると共に、姿勢制御の高精度
化及び安定化の向上が図れる。
(Function) According to the above configuration, the attitude control signal converts the attitude error (M) detected from the satellite dynamics into the coordinate system of the deployed structure, calculates the attitude control value from the converted attitude error signal, It is generated by converting this to the satellite dynamics coordinate system.As a result, the vibration mode of the deployed structure can be separated into, for example, an out-of-plane mode and an in-plane mode, and a The first mode is phase stable,
Gain stability and stabilization can be achieved in the second-order mode and above. Therefore, it is possible to simplify the design process and improve the precision and stability of attitude control.

(実施例) 以下、この発明の実施例について、図面を参照して詳細
に説明する。
(Example) Hereinafter, an example of the present invention will be described in detail with reference to the drawings.

第1図はこの発明の一実施例に係る人工衛星の姿勢制御
装置1tfc示すもので、前記第4図に示すような衛星
本体10のピッチ(Y)軸回、9に展開構造物1ノを回
転自在忙配設した衛星ダイナミクスノ2に通用した場合
を代表して説明する。但し、第1図中では、従来の第3
図と同一部分について、同一符号を付して、その説明に
ついては省略する。
FIG. 1 shows an attitude control system 1tfc for an artificial satellite according to an embodiment of the present invention, in which a deployable structure 1 is placed at the pitch (Y) axis axis 9 of the satellite main body 10 as shown in FIG. A case will be explained as a representative case where it is applicable to satellite dynamics No. 2 which is rotatably arranged. However, in Figure 1, the conventional third
The same parts as those in the figures are given the same reference numerals, and the description thereof will be omitted.

すなわち、衛星ダイナミクス12は、そのロール(X)
軸回シのロール姿勢i差及びヨー(Z)軸回りのヨー姿
勢誤差がロール検出センサ13及びヨー検出センサ14
により検出される。このロール及びヨー検出センサ13
,14はそのa−ル及びヨー姿勢誤差信号を第1の座標
変換部16に出力する。この第1の座標変換部16は入
力したロール及びヨー姿勢誤差信号を の座標変換を行って、展開構造物1ノの座標系(X軸、
Y軸、Z 軸)に変換してX、及び2.制p     
 p      p 御演算部17.18に出力する。このX、及び2゜制御
(iI算郡部1718は座標糸(x、軸、Yp軸。
That is, the satellite dynamics 12 has its role (X)
The roll attitude i difference of the axis rotation and the yaw attitude error around the yaw (Z) axis are detected by the roll detection sensor 13 and the yaw detection sensor 14.
Detected by This roll and yaw detection sensor 13
, 14 outputs the roll and yaw attitude error signals to the first coordinate conversion section 16. This first coordinate conversion unit 16 performs coordinate conversion of the input roll and yaw attitude error signals, and converts the input roll and yaw attitude error signals into the coordinate system (X axis,
Y axis, Z axis) and X, and 2. control p
p p Output to the control calculation units 17 and 18. This X and 2° control (iI calculation section 1718 is the coordinate thread (x, axis, Yp axis.

2、軸)におけるロール及びヨー制御信号を求めて第2
の座標変換部19に出力する。この第2の座標交換部1
9は入力した座標系(X、軸、Y、軸。
2. Determine the roll and yaw control signals for the second axis
output to the coordinate conversion section 19. This second coordinate exchange section 1
9 is the input coordinate system (X, axis, Y, axis.

2、軸)におけるロール及びヨー制御信号を、の座標変
換を行って、再び上記衛星ダイナミツク12(DPJ!
!標系(X@、Y軸、2軸)に変換して姿勢駆動用のア
クチュエータ15に出力する。これにより、アクチュエ
ータ15は、その衛星ダイナミツク12の姿勢を制御す
る。
The roll and yaw control signals in the satellite dynamics 12 (DPJ! axis) are transformed again into the satellite dynamics 12 (DPJ!
! It is converted into a standard system (X@, Y axis, 2 axes) and output to the actuator 15 for attitude drive. Thereby, the actuator 15 controls the attitude of the satellite dynamics 12.

このように、上記人工衛星の姿勢制御装置は衛星ダイナ
ミツク12から検出した姿勢誤差信号を展開構造物11
の座標系に変換して、その変換した姿勢誤差信号から姿
勢制御値を求め、これを衛星ダイナミツク12の座標系
に変換することによシ生成される姿勢制御信号でアクチ
ュエータ15を駆動制御するように構成した。これKよ
シ、展開構造物11の振動モードが1例えば、第2図に
示すよう釦、面外(OP)モードと面内(IP)モード
とが分離され、各々位相安定(位相特性について一18
0’から十分に位相余裕をとることで安定させる制御方
式)、ゲイン安定(ゲイン特性に対してOdBから十分
にゲイン余裕をとることで安定させる制御方式)の構成
を容易にしている。従って、従来のようK、展開構造物
1ノの振動モードが面内及び面外モードが直なシ密状態
(第6図参照)になるおそれのあるものに比して、可及
的に設計製作性の簡略化が図れると共に、姿勢制御の高
精度化及び安定化の向上が図れる。
In this manner, the satellite attitude control device transmits the attitude error signal detected from the satellite dynamics 12 to the deployed structure 11.
The attitude control value is obtained from the converted attitude error signal, and the actuator 15 is driven and controlled by the attitude control signal generated by converting this into the coordinate system of the satellite dynamics 12. It was configured as follows. In this case, when the vibration mode of the deployable structure 11 is one, for example, as shown in FIG. 18
A control method that stabilizes the gain characteristic by taking a sufficient phase margin from 0') and gain stability (a control method that stabilizes the gain characteristic by taking a sufficient gain margin from OdB) is facilitated. Therefore, compared to the conventional structure in which the vibration mode of the deployed structure 1 is in a tight state where the in-plane and out-of-plane modes are straight (see Fig. 6), the design is as simple as possible. Manufacturability can be simplified, and posture control can be highly accurate and stabilized.

なお、上記実施例では、展開構造物11の回転軸(Y、
軸)を衛星ダイナミツク12のyp軸に対応させるよう
に構成した場合で説明したが、この配置構成に限ること
なく、適用可能である。よって、この発明は上記実施例
に限ることなく、その他、この発明の要旨を逸脱しない
範囲で檀々の変形を実施し得ることは勿論のことである
In addition, in the above embodiment, the rotation axis (Y,
Although a case has been described in which the configuration is such that the axis (axis) corresponds to the yp axis of the satellite dynamics 12, the present invention is not limited to this arrangement and is applicable. Therefore, it goes without saying that the present invention is not limited to the embodiments described above, and that various modifications can be made without departing from the spirit of the invention.

[発明の効果] 以上詳述したように、この発明によれば、展開構造物の
振動モードの分離化するようにして、設計表作の簡略化
を図ると共に、姿勢制御の高精度化及び安定化を実現し
得るようにした人工衛星の姿勢制御装置を提供すること
ができる。
[Effects of the Invention] As described in detail above, according to the present invention, the vibration modes of a deployable structure are separated, thereby simplifying the design table, and improving the precision and stability of attitude control. It is possible to provide an attitude control device for an artificial satellite that can realize the

【図面の簡単な説明】[Brief explanation of the drawing]

第1図はこの発明の一実施例に係る人工衛星の姿勢制御
装置を示すブロック図、第2図は第1図の姿勢制御信号
における展開構造物の振動モート0を示す図、第3図は
従来の人工衛星の姿勢制御装置を示すブロック図、第4
図及び第5図はこの発明の適用される人工衛星を示す図
、第6図は第3図の従来の人工衛星の姿勢制御装置の姿
勢制御信号における展開構造物の振動モードを示す図で
ある。 10・・・衛星本体、1ノ・・・展開構造物、12・・
・衛星ダイナミツク、13・・・ロール検出センサ、1
4・・・ヨー検出センサ、15・・・アクチュエータ、
16・・・2glの座標変換部、11X、制御演算部、
18・・・2.制御演算部、19・・・第2の座標変換
部。 出願人代理人  弁理士 鈴 江 武 彦第5図 第6図
FIG. 1 is a block diagram showing an attitude control device for an artificial satellite according to an embodiment of the present invention, FIG. 2 is a diagram showing vibration mode 0 of the deployable structure in the attitude control signal of FIG. 1, and FIG. Block diagram showing a conventional attitude control device for an artificial satellite, No. 4
5 and 5 are diagrams showing an artificial satellite to which the present invention is applied, and FIG. 6 is a diagram showing the vibration mode of the deployed structure in the attitude control signal of the conventional artificial satellite attitude control device shown in FIG. 3. . 10... Satellite main body, 1... Deployment structure, 12...
・Satellite dynamics, 13...Roll detection sensor, 1
4... Yaw detection sensor, 15... Actuator,
16...2gl coordinate transformation unit, 11X, control calculation unit,
18...2. Control calculation unit, 19... second coordinate transformation unit. Applicant's agent Patent attorney Takehiko Suzue Figure 5 Figure 6

Claims (1)

【特許請求の範囲】[Claims] 展開構造物を搭載してなる人工衛星の姿勢制御装置にお
いて、アクチュエータを介して姿勢制御される衛星ダイ
ナミクスの姿勢誤差を検出する検出手段と、この検出手
段の姿勢誤差信号を前記展開構造物の座標系に変換して
姿勢制御信号を求め、この姿勢制御信号を前記衛星ダイ
ナミクスの座標系に変換して前記アクチュエータを駆動
制御する制御手段とを具備したことを特徴とする人工衛
星の姿勢制御装置。
In an attitude control device for an artificial satellite equipped with a deployable structure, there is provided a detection means for detecting an attitude error in satellite dynamics whose attitude is controlled via an actuator, and an attitude error signal of the detection means that is used to determine the coordinates of the deployable structure. 1. An attitude control device for an artificial satellite, comprising: control means for converting the attitude control signal into a coordinate system of the satellite dynamics to obtain an attitude control signal, and converting the attitude control signal into a coordinate system of the satellite dynamics to drive and control the actuator.
JP63127092A 1988-05-26 1988-05-26 Satellite attitude control device Expired - Lifetime JP2685225B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP63127092A JP2685225B2 (en) 1988-05-26 1988-05-26 Satellite attitude control device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP63127092A JP2685225B2 (en) 1988-05-26 1988-05-26 Satellite attitude control device

Publications (2)

Publication Number Publication Date
JPH01297399A true JPH01297399A (en) 1989-11-30
JP2685225B2 JP2685225B2 (en) 1997-12-03

Family

ID=14951383

Family Applications (1)

Application Number Title Priority Date Filing Date
JP63127092A Expired - Lifetime JP2685225B2 (en) 1988-05-26 1988-05-26 Satellite attitude control device

Country Status (1)

Country Link
JP (1) JP2685225B2 (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5850992A (en) * 1990-11-30 1998-12-22 Aerospatiale Societe Nationale Industrielle Method for controlling the pitch attitude of a satellite by means of solar radiation pressure
US6371413B1 (en) * 1994-03-30 2002-04-16 Centre National D'etudes Spatiales Artificial satellite equipped with generators of magnetic and aerodynamic moments and control process for such a satellite
KR100720654B1 (en) * 2005-12-26 2007-05-21 한국항공우주연구원 Estimation and compensation method of solar-cell misalignment inside sun-sensor

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6447699A (en) * 1987-08-18 1989-02-22 Mitsubishi Electric Corp Attitude controller for artificial satellite

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6447699A (en) * 1987-08-18 1989-02-22 Mitsubishi Electric Corp Attitude controller for artificial satellite

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5850992A (en) * 1990-11-30 1998-12-22 Aerospatiale Societe Nationale Industrielle Method for controlling the pitch attitude of a satellite by means of solar radiation pressure
US6371413B1 (en) * 1994-03-30 2002-04-16 Centre National D'etudes Spatiales Artificial satellite equipped with generators of magnetic and aerodynamic moments and control process for such a satellite
KR100720654B1 (en) * 2005-12-26 2007-05-21 한국항공우주연구원 Estimation and compensation method of solar-cell misalignment inside sun-sensor

Also Published As

Publication number Publication date
JP2685225B2 (en) 1997-12-03

Similar Documents

Publication Publication Date Title
US4746085A (en) Method for determining the earth's magnetic field and a satellite's attitude for attitude control
CA1122677A (en) Satellite guide and stabilization
US3741500A (en) A cmg fine attitude control system
US4961551A (en) Stabilization of a spinning spacecraft of arbitary shape
JPS6047159B2 (en) Satellite attitude control device
US4458426A (en) Gyroscopic apparatus
JPH06510502A (en) Measurement equipment used in attitude control of a 3-axis stable satellite, accompanying evaluation method, control system, and control method
JPS62502079A (en) Attitude control device for dual spin satellites
US3924824A (en) Cross track strapdown inertial quidance system
US5875676A (en) Non colocated rate sensing for control moment gyroscopes
JPH0420124B2 (en)
JPH081384B2 (en) Stable directional reflector
JPH01297399A (en) Attitude controller for artificial satellite
Somov Methods and software for research and design of spacecraft robust fault tolerant control systems
JP2798938B2 (en) 3-axis attitude control device
JP2004361121A (en) Space stabilizer
CN106843256B (en) Satellite control method adopting position and speed double loops
JPS6121878B2 (en)
JPS5837482B2 (en) Gyro control device
JPH0131568B2 (en)
JPH08164898A (en) Attitude control device
JPS5987513A (en) Stabilizing device in inertia space
JPS638099A (en) Attitude controller for artificial satellite
RU2196710C2 (en) Method of forming control moments on spacecraft provided with powered gyroscopes and swivel solar batteries and system for realization of this method
JPS6252475A (en) System for automatically tracking satellite

Legal Events

Date Code Title Description
R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

R250 Receipt of annual fees

Free format text: JAPANESE INTERMEDIATE CODE: R250

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

Free format text: PAYMENT UNTIL: 20070815

Year of fee payment: 10

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

Free format text: PAYMENT UNTIL: 20080815

Year of fee payment: 11

EXPY Cancellation because of completion of term