JP2005157816A - Supporting device with magnetic force for performing feedback control of magnetic field - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a control constant deciding method which can facilitate the adjustment of many control constants, in a control system for performing feedback control of at least the position and attitude angle in a supporting device with magnetic force like a magnetic support weighing device used for a wind tunnel test. <P>SOLUTION: In a control device for performing the feedback control for at least the position and attitude angle of a test piece, a sensitivity function related to a transfer function concerning disturbance input through the outputs of the position and attitude angle, and a complementary sensitivity function related to a transfer function concerning a disturbance input through the output of a current fed to a coil and an electromagnet are defined. By setting the sensitivity function so that the maximum value is suppressed and the vibration frequency range is shifted to a higher frequency range, the vibration of the test piece can be suppressed relative to the disturbance. The complementary sensitivity function performs shaping for shifting to a higher frequency range according to the function. Many control constants included in the transfer function, based on the both functions, are decided as values so as to minimize an H∞ norm defined in robust control. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a magnetic force support device that supports a specimen including a metal and a magnet so as to be controllable to an arbitrary position and posture angle in the air by a magnetic force.

  When developing and designing space reciprocating aircraft such as aircraft and space shuttles, it is essential to know the dynamic characteristics that change the airflow has on the aircraft over time. When dynamic characteristics are required, for example, when the flow of airflow changes, such as gusts or turbulence of the airflow, when the characteristics of the airflow, such as density or temperature change, or by steering, There are cases where the attitude of the aircraft is changed. By knowing dynamically changing forces such as lift, drag, and moment acting on the model in response to such changes in the situation, it is possible to know the dynamic characteristics according to the position and attitude angle of the actual machine. The dynamic characteristics of the actual aircraft can contribute to the development and design of the outer shape, structural strength, engine characteristics, steering device, etc. of the wings and fuselage of the aircraft.

  Conventionally, in a wind tunnel test that tests the aerodynamic characteristics of an object with a model, it has been generally performed to support a model at a measurement part of a wind tunnel facility with a support. The body itself affects the air flow around the model. Therefore, the wind tunnel test result cannot be used as it is as the aerodynamic characteristic of the model (and thus the object). Therefore, it has been proposed to support the model with a magnetic force in a wind tunnel test. Since the support is not required by magnetically supporting the model, an aerodynamic influence on the model due to the presence of the support is removed, and an ideal wind tunnel test can be performed.

  The magnetic support system for the wind tunnel model has static or dynamic aerodynamic characteristics such as lift, drag, pitching (pitch) moment, etc. acting on the model by the airflow flowing around the model in the wind tunnel test. It is an apparatus for measuring by replacing the magnitude of the current flowing in the coil provided to generate a magnetic force that interacts with the provided magnet. By investigating the relationship between the aerodynamic force and the magnitude of the coil current and preparing correspondences such as maps, functions, and tables in advance, the aerodynamic characteristics acting on the model can be known by measuring the coil current. .

  With reference to FIG. 4, the outline | summary of a magnetic support type wind tunnel and a magnetic support apparatus is demonstrated. FIG. 4 is a perspective view showing an outline of a wind tunnel provided with a magnetic support device, and a measurement system and a control system used in the magnetic support device. A magnetic support device 20 shown in FIG. 4 is a device that floats and supports a wind tunnel model (hereinafter simply referred to as “model”) 7 formed of a nonmagnetic material such as aluminum in a desired shape in a flow of air. is there. Inside the model 7 is mounted a strong cylindrical magnet body made of a magnetized material, a coil that keeps a current flowing, such as a superconducting coil, or a permanent magnet. A magnetic force is generated in the magnet body of the model 7 by a magnetic action with a magnetic field generated by energizing a coil disposed around the measurement portion of the wind tunnel. With this magnetic force, the model 7 can be supported by levitating against gravity and aerodynamic force, and a wind tunnel test without interference by the support can be realized.

  The magnetic field for applying a force to the model includes two magnetic circuits composed of coils 22 to 25 and coils 26 to 29 as magnetic support coils, and an air-core coil 21 as a magnetic support coil disposed outside the magnetic circuit. , 30. By adjusting the currents flowing through the coils 22 to 29 of the magnetic circuit, it is possible to continuously change the strength and direction of the magnetic field in the yz plane and the rate of change in the x-axis direction in the magnetic circuit. it can. In addition, by adjusting the current flowing through the air-core coils 21 and 30, the rate of change of the strength of the magnetic field in the x-axis direction as viewed in the x-axis direction can be controlled, so that 5-axis control is possible. That is, the coils 22 to 29 of the magnetic circuit function as lift coils that apply magnetic force against the lift and pitching moment acting on the model 7, and the air-core coils 21 and 30 counteract the drag acting on the model 7. It functions as a drag-resistance coil that provides magnetic force.

  In the wind tunnel, in addition to the model 7 and the coils 21 to 30, a power supply system that drives each coil, a measurement system (an optical sensor 9 such as a camera) that measures the position and orientation of the model 7, and the position of the model 7 And a control system for controlling the posture. As shown in FIG. 4, measurement data related to the position and orientation of the model 7 detected by the optical sensor 9 serving as a measurement system is transmitted to a computer 13 such as a personal computer, and the calculation result in the computer 13 is amplified by a power amplifier 14. Then, it is sent to each coil 21-30 as a controlled command current.

  Since the magnetic support device 20 is an essentially unstable system, feedback control is always performed on the position and posture angle of the model 7. That is, a magnetic force acts on the model 7 by the command current, and as a result, a change appears in the position / posture angle that is a state variable of the model 7 as an output. The position / orientation angle of the model 7 is detected by the optical sensor 9, and the computer 13 as a control device outputs a command current according to the detected value, thereby feedback control (hereinafter simply referred to as “ This is abbreviated as “position feedback control.” (Details will be described later).

As shown in FIG. 4, the coordinate system used in the conventional control is based on the center of the wind tunnel measuring unit, the upstream direction of the flow is the x-axis (reverse drag direction), and the vertically upward direction (lift direction) is the z-axis. The axis that forms the axis and the right-handed system is defined as the y-axis, and the roll angle around the x-axis, the pitch angle around the y-axis, and the yaw angle around the z-axis are φ, θ, and ψ, respectively. In order to apply these axial magnetic forces and axial moments, coils are combined as shown in Table 1. The coil numbers shown in Table 1 correspond to the numbers given to the coils shown in FIG.

従来の位置フィードバック制御系では、軸間干渉と、ロール軸（ロール角φ）方向の運動とを考慮せず、また、ピッチ角θとヨー角ψは十分小さいとの仮定の下で、式（１）及び式（２）を各軸方向の電流について線形化し、電流入力に対する模型７の位置・姿勢角の伝達関数を求めて、模型７の位置・姿勢角についてのフィードバック制御が行われている。伝達関数Ｇｍは、模型７に内挿された磁石のｘ軸方向の磁気モーメントをＭｘ、模型７も全体質量又は慣性モーメントをｍ、単位電流当たりの磁場勾配をｈとして、式（３）で表される。

コイルの巻き数を少なくし、大きな電流を流すことにより、コイルの応答速度を向上させることができる。即ち、コイルのダイナミックスを式（４）で表される一次遅れ系で近似したとき、その時定数γが非常に小さくすることができる（一例として、５軸すべてで最大でおよそ９．６ｍｓｅｃ）。

Assuming that the magnetic moment vector held by the model 7 is M and the magnetic field strength vector around the model 7 is H, the magnetic force F and moment N acting on the model 7 are respectively expressed by the equations (1) and (2). It is.

The conventional position feedback control system does not consider the inter-axis interference and the movement in the roll axis (roll angle φ) direction, and assumes that the pitch angle θ and the yaw angle ψ are sufficiently small, 1) and Equation (2) are linearized with respect to the currents in the respective axial directions, the transfer function of the position / posture angle of the model 7 with respect to the current input is obtained, and the feedback control of the position / posture angle of the model 7 is performed. . The transfer function Gm is expressed by equation (3), where Mx is the magnetic moment in the x-axis direction of the magnet inserted in the model 7, m is the overall mass or moment of inertia, and h is the magnetic field gradient per unit current. Is done.

The response speed of the coil can be improved by reducing the number of turns of the coil and flowing a large current. That is, when the dynamics of the coil is approximated by a first-order lag system represented by the equation (4), the time constant γ can be made very small (for example, about 9.6 msec at the maximum for all five axes).

From the above equations, the state equation of the system including the model system and the coil system can be expressed by the following equations (5) to (8). However, O (vector) is a zero matrix having an appropriate dimension.

  The position feedback control of the model 7 is performed by the control system shown in FIG. Since the control system of the magnetic support device 20 is inherently unstable, feedback control is performed on the position / posture angle of the model 7 as shown as a block diagram in FIG. That is, a PI controller (proportional) in which a deviation E between a signal based on the position / posture angle Y as a current value (state variable) and each target value R of the position / posture angle in the target value setter 1 is a transfer function K. The amount of control is calculated by input to the integration controller 2). The calculated control amount is further added with a bias B by the bias applicator 3 and then converted into a continuous amount via a D / A converter (digital / analog converter) 4 to generate a command signal U. The bias B is a current value necessary for the model 7 to balance with gravity. The command signal U is amplified by the power amplifier 14 and then supplied to the coil drive system 5 including the coils 21 to 30 (see FIG. 4) of the magnetic force support device 20, and the magnetic field (transfer function Gc) generated by the coil drive system 5 is It acts on the model 7 as a coil magnetic force. The magnetic force due to the interaction between the magnetic field and the magnetic body of the model 7 and the disturbance D from the external force source 6 such as aerodynamic force and gravity act on the model 7, and as a result, the position / attitude angle Y of the model 7 is Obtained as output.

光学センサ９による模型７の位置・姿勢角の検出信号は、ノイズカットフィルタ１０を経て、更に二重位相進み要素１１を経るときに位相を進められるが、この位相の二重進みがシステムの安定性に重要な役割を果たしている。この補償された位置・姿勢角信号と目標値Ｒとの偏差ＥがＰＩ制御器２に入力される。ＰＩ制御器２の伝達関数Ｋ（ｓ）が、式（１０）に示されている。このように、磁力支持装置２０は、検出された模型７の位置・姿勢角Ｙに基づいて、模型７の位置・姿勢角についてのフィードバック制御を行っている。

The control system includes an optical sensor 9 for detecting the position / posture angle Y as the current value of the model 7. Since sensor noise n is mixed from the noise source 8 into the detected position / posture angle Y, a secondary Butterworth type noise having an appropriate cutoff frequency of about 60 Hz for noise removal and represented by a transfer function Hn. It is applied to the cut filter 10. Since the optical sensor 9 has a delay time (dead time) L of about 6 milliseconds from detection to output as the time required for charge accumulation as in the CCD sensor, information on the position / posture angle of the detected model 7 Is actually different from the instantaneous position / posture angle. Further, since the computer 13 requires time to calculate the command current U to be supplied to the coils 21 to 30 such as the coil current and the coil voltage, the position / posture angle of the model 7 further varies at the moment of applying the force. Yes. Therefore, the double phase advancer 11 whose transfer function Hp (s) is expressed by the equation (9) is used to compensate for these time delays.

The detection signal of the position / posture angle of the model 7 by the optical sensor 9 can be advanced in phase when passing through the noise cut filter 10 and further through the double phase advance element 11. This double advance of the phase is the stability of the system. Plays an important role in sex. A deviation E between the compensated position / posture angle signal and the target value R is input to the PI controller 2. The transfer function K (s) of the PI controller 2 is shown in equation (10). Thus, the magnetic force support device 20 performs feedback control on the position / posture angle of the model 7 based on the detected position / posture angle Y of the model 7.

As described above, the magnetic force support device 20 is an optical position sensor for detecting the position / posture angle of the model 7 (in this case, “position” is a broad term including the posture angle), and the model 7 is magnetized. Configuration based on one or more coils / electromagnets 21-30 for applying force, and a control device (computer 13 etc.) that calculates and outputs current values or voltage values applied to the coils / electromagnets 21-30 The apparatus is capable of holding the model 7 in the airflow at an arbitrary position and posture angle in the air by a magnetic force in the wind tunnel, and provided with a support body that contacts and supports the model 7 This is a useful device that can avoid the problem of interference between the generated support and the airflow, and also enables dynamic testing of the model 7 (see, for example, Non-Patent Document 1).
Hideo Sawada, Tetsuya Kunimasu, “Development of 60cm Magnetic Support Device for Low-Speed Wind Tunnels”, Japan Aerospace Society Proceedings, Japan Aerospace Society, May 2002, 50, 580, p. 188-195

In this way, the magnetic support device equipped with the control system that feeds back the position / posture angle detects the position / posture angle of the specimen (model) as needed, calculates the control amount based on the detected position / posture angle, By applying the obtained control amount to the coil / electromagnet, the specimen can be stably levitated. In particular, the control system using the double phase advancer and the PI controller as described in Non-Patent Document 1 is one of the control systems that can stably float the specimen, and lift the specimen. This is a practical control system in which the control constant can be easily changed even in the state where This control system has no problem when the specimen is static or when one-dimensional simple movement such as step response or heaving is performed, but the movement of the specimen at this time is out of phase with respect to the controlled variable. Has been observed. On the other hand, it has been observed that the movement of the specimen is in phase with the magnetic field formed by the coil / electromagnet. In order to detect the force acting on the specimen with high accuracy using this property, a Hall element may be provided in the magnetic force support device (for example, Non-Patent Document 2).
Hideo Sawada and three others, “Research on Magnetically Supported Balances at the Aerospace Research Institute in 1995 (STATUS OF MSBS STUDY AT NAL IN 1995)”, Third International Symposium on Magnetic Suspension Technology), (USA), p. 505-519

On the other hand, among known techniques related to a magnetic support device, a magnetic field is detected by a Hall element, a control amount is calculated based on the detected magnetic field, and an object is placed at a certain position by applying it to an electromagnet. There is a device for holding (for example, Patent Document 1 and Patent Document 2). Patent Document 1 has a description of an invention related to a magnetic bearing, while Patent Document 2 has a description of an invention related to magnetic levitation. These devices do not include an optical sensor and do not hold the specimen at an arbitrary position in the three-dimensional space.
Japanese Patent Laid-Open No. 9-25934 (page 3, FIG. 1) US Patent Application Publication No. 6154353

In such a magnetic force support device, a delay in the phase of the specimen movement relative to the control amount causes a delay in the response speed of the specimen, which is one of the factors that deteriorate the control performance. Therefore, there is a great possibility that this effect is manifested in the form of impairing the dynamic stability of the specimen, and in the worst case, an accident such as dropping or breakage of the specimen may be caused. In a magnetic support device that floats and supports the specimen by interaction with the magnetic field from the coil / electromagnet and performs position feedback control on the position and attitude angle of the specimen, the position and attitude angle of the specimen are controlled by the position.・ The magnetic field that determines the magnetic force that changes the position and posture angle as well as information on the posture angle is an important factor. In order to improve the control capability even for a high-speed flow, the present inventors have achieved results in improving the quick response by adding magnetic field feedback control to position feedback control (Non-patent Document 3). reference). Furthermore, in order to improve the control capability for high-speed flow by improving the detection speed of the magnetic field, proposals have been made to use the Hall element for feedback control (see Non-Patent Document 4).
Shinichi Suda, Hideo Sawada, Tetsuya Kunimasu, “Improvement of control performance of NIG magnetic support balance by adding magnetic field feedback circuit”, November 26, 2002, 45th automatic control federation lecture, Society of Instrument and Control Engineers, p. 373-376 Chin E. Lin and three others, “Improvement on Drag and Control Performance in NCKU Magnetic Suspension Wind Tunnel”, Proceedings of National Science Council, Republic of China, Part A: Physical Science and Engineering, Vol. 24, No. 5, 2000 , (Taiwan), pp. 330-340

  FIG. 6 is a block diagram showing another example of the control device in the magnetic force support device. In the magnetic support device shown in FIG. 6, the position feedback control for controlling the position and posture angle of the specimen is the same as the feedback control shown in the block diagram shown in FIG. The same reference numerals are given to the components, and the description thereof is omitted.

  The block diagram for feedback control in the magnetic support device shown in FIG. 6 is different in that magnetic field feedback control is further incorporated with respect to the feedback control with respect to the position / posture angle. The measurement control elements newly added for magnetic field feedback control are a hall element 12 as a magnetic sensor, a pre-filter 15, and magnetic field controllers 16 and 17. The magnetic field generated in the magnetic support device is measured by the Hall element 12. The pre-filter 15 is a control element that includes a conversion coefficient from current to magnetic field strength, converts the current into the same dimension as the output of the magnetic field controller 16, and amplifies it. The control current output from the PI controller 2 is converted by the pre-filter 15 into a magnetic field strength or an amount that is an index of the magnetic field strength, and then a difference from the output from the magnetic field controller 16 is taken. The magnetic field controller 17 amplifies the difference and converts the magnetic field strength or an amount serving as an index of the magnetic field strength into a current value corresponding thereto. After the conversion, the bias B from the bias 3 is added and output to the coil drive system 5.

  As a magnetic sensor for detecting a magnetic field generated by the coil drive system 5, the Hall element is disposed in the coils 21 to 30 with reference to the coil layout diagram of the magnetic force support device shown in FIG. The Hall element is embedded in the measurement unit wall so as not to protrude inside the measurement unit because it is arranged as close as possible to each of the coils 21 to 30 and does not disturb the airflow. The embedded position of the Hall element is preferably the center position of the coil cross section. However, for the air-core coils 21 and 30, the Hall elements are arranged at positions symmetrical with respect to the measurement point coordinate origin, such as the coil 21 at the upper right side of the drawing and the coil 30 at the lower left side of the drawing. It is installed. Further, in the wind tunnel, a Pitot static pressure tube for measuring the airflow velocity may be installed, and this Pitot tube is also provided with a Hall element for measuring a magnetic field in the x-axis direction.

ここで右辺のｈはホール素子の出力で、数字の添え字は４に示すコイル２１〜３０を０から９まで順番に番号を振り直したものである。 In order to measure the magnetic field of all five axes using the Hall element, it is necessary to use an amount independent of each axis by appropriately combining the outputs of the Hall elements. In this embodiment, the magnetic amount hx in the x-axis direction that is the main airflow direction of the wind tunnel, the magnetic amount hy in the y-axis direction that is the horizontal axis orthogonal to the x-axis direction, and the x-axis direction and the y-axis direction are orthogonal to each other. A magnetic amount hz in the z-axis direction, a magnetic amount hθ in the pitch axis θ direction around the y axis, and a magnetic amount hψ in the yaw axis ψ direction around the z axis are respectively expressed by the following equations (11): ).

Here, h on the right side is the output of the Hall element, and the numerical subscripts are obtained by renumbering the coils 21 to 30 shown in 4 in order from 0 to 9.

ここでの磁場は単位が任意であるため、電流と大きさを同じにすることで制御プログラムを簡単化することができる。即ち、式（１２）において、磁気量ｈを式（１３）に示すように電流値Ｉで置き換え、変換行列Ａとオフセット行列Ｂとを最小二乗法によって求めることができる。

Conventionally, when obtaining the magnitude of the magnetic field in each axial direction from the Hall element output, it has been obtained by the equation (11), but more generally, the transformation matrix A and the offset of the equation represented by the equation (12) There is a method for obtaining the matrix B. When the number of Hall elements is 6, the transformation matrix A is a 5 × 6 matrix, and the offset matrix B is a 5 × 1 vector.

Since the unit of the magnetic field here is arbitrary, the control program can be simplified by making the current and the magnitude the same. That is, in Equation (12), the magnetic quantity h is replaced with the current value I as shown in Equation (13), and the conversion matrix A and the offset matrix B can be obtained by the least square method.

また、式（１４）に代えて式（１５）に示すように、ピトー静圧管に配設したホール素子からの出力も利用可能である。

As an example, the change of each magnetic quantity in the equation (11) when the current in the y-axis direction is changed is shown as a graph in FIG. From FIG. 7, it can be seen that only h _y greatly changes with respect to the change in the control current in the y-axis direction, and Equation (12) can be used as an amount representing the magnetic field in the y-axis direction. It was confirmed that the other axes also corresponded to each other. Further, as an amount representing the magnetic field in the x-axis direction, not only the equation (11) but also the average value of the Hall elements arranged in the air-core coils 21 and 30 can be used as shown in the equation (14).

Further, as shown in the equation (15) instead of the equation (14), an output from the Hall element arranged in the Pitot static pressure tube can also be used.

ここで、コイル駆動系５の極、零点の大きさはａ₀ ＞ｂ₁ ＞ａ₁ となると仮定する。つまり時定数が比較的小さく、それに若干の位相遅れが付加されている形である。コイル駆動系５は式（１６）のような形であってもａ₀ が運動周波数に対して充分大きく、位相の遅れも充分小さければ実用上は問題が無い。そのためコイル駆動系５に対する改善点は、コイル駆動系５をフィードバック回路にしたときの時定数を小さくすること、かつｂ₁ ，ａ₁ の較差を小さくして位相の遅れ度合いを小さくすることの２点に絞られる。 For each control element, in addition to the above role, the frequency characteristics of each control element should be examined. As an embodiment, a case where the coil drive system 5 is expressed by a product of a primary delay element and a phase delay element will be described. Here, for the sake of simplicity, the description will be made using the lowest order such as equation (16).

Here, it is assumed that the magnitudes of the poles and zeros of the coil drive system 5 are a ₀ > b ₁ > a ₁ . In other words, the time constant is relatively small, and a slight phase delay is added thereto. Even if the coil drive system 5 has the form as shown in Equation (16), there is no practical problem as long as a ₀ is sufficiently large with respect to the motion frequency and the phase delay is also sufficiently small. Therefore, improvements to the coil drive system 5 are that the time constant when the coil drive system 5 is used as a feedback circuit is reduced, and the difference between b ₁ and a ₁ is reduced to reduce the degree of phase delay. Focused on a point.

式（１７）に示す制御系の場合、コイル駆動系５の部分の閉ループ伝達関数は、式（１８）に示すように１次／３次の伝達関数になる。

この伝達関数は２次遅れのような振る舞いをするので、コイル駆動系５の動特性を変化させ、制御系の調整を複雑にする。そのため、磁場制御器１７の伝達関数Ｋ_m は分母と分子が同次の有理関数であることが望ましく、その候補として定数、位相進み、近似微分が挙げられる。その中で最も簡単な定数でさえも時定数を小さくし、かつ位相遅れの大きさを小さくすることが可能である。さらに閉ループ化したコイル駆動系のゲインはプレフィルタ１５の伝達関数Ｆ_m で調整することが効果的であることもわかる。これは式（１８）の中で、磁場制御器１６の伝達関数Ｋ_m のゲインは分母、分子の両方に現れるのに対して、プレフィルタ１５の伝達関数Ｆ_m のゲインは分子のみに現れるからである。以上のことから、磁場フィードバック制御の制御要素は全て定数で充分で、ゲインの調整は主にプレフィルタ１５で行うことが効果的であることがわかる。 As an example, consider the case where the magnetic field controller is integral and the other elements are constants, as shown in equation (17).

In the case of the control system shown in Expression (17), the closed-loop transfer function of the coil drive system 5 is a first-order / third-order transfer function as shown in Expression (18).

Since this transfer function behaves like a second-order lag, the dynamic characteristics of the coil drive system 5 are changed, and the adjustment of the control system is complicated. Therefore, the transfer function K _m of the magnetic field controlling device 17 is desirably numerator and denominator are homogeneous rational functions, constants as a candidate, phase advance, include approximate differentiation. Even the simplest of these can reduce the time constant and the phase delay. It can also be seen that it is effective to adjust the gain of the coil drive system that is closed loop by the transfer function F _m of the prefilter 15. In Equation (18), the gain of the transfer function K _m of the magnetic field controller 16 appears in both the denominator and the numerator, whereas the gain of the transfer function F _m of the prefilter 15 appears only in the numerator. It is. From the above, it can be seen that constants are sufficient for all control elements of the magnetic field feedback control, and it is effective to adjust the gain mainly by the prefilter 15.

ここでｄｉａｇは各要素を対角要素にもつ対角行列を意味する。プレフィルタ１５の伝達関数Ｆ_m 、磁場制御器１６の伝達関数Ｋ_m とも、これを基準に調整する。 As a result of measuring the step response of the coil drive system 5 with the current in amperes as input and the magnetic field in volts as output, the output shown in equation (19) per unit current is obtained in equation (11).

Here, diag means a diagonal matrix having each element as a diagonal element. The transfer function F _{m of} the prefilter 15 and the transfer function K _m of the magnetic field controller 16 are adjusted based on this.

また、プレフィルタ１５の伝達関数Ｆ_m は、式（１９）の磁場変換行列１７の行列Ｖ_m に定数ゲインを掛けた値になる。 The transfer function of the magnetic field controller 17 takes the reciprocal of these and becomes Formula (20).

Further, the transfer function F _m of the pre-filter 15 is a value obtained by multiplying the matrix V _m of the magnetic field conversion matrix 17 of Expression (19) by a constant gain.

また、磁場フィードバックの加え合わせ点における単位は、磁場強さではなく、磁場強さの指標となる量であるホール素子出力電圧であるため、実際には磁場変換行列(磁場制御器１７に関連する)の行列Ｖ_m は対角要素が全て１の単位行列を用いた。 The gain is adjusted from the magnitude of the control current at the time of confirming the program operation before the numerical simulation and the levitation test. Actually, the transfer function F _{m of} the prefilter 15 and the transfer function K _m of the magnetic field controller 16 are expressed by the following equation (21). And given by equation (22).

In addition, since the unit at the addition point of the magnetic field feedback is not the magnetic field strength but the Hall element output voltage which is an amount serving as an index of the magnetic field strength, the magnetic field conversion matrix (related to the magnetic field controller 17 is actually used). ) Matrix V _m is a unit matrix whose diagonal elements are all one.

また、これらの伝達関数の比較を図８に示す。 At this time, as an example, for the y-axis, the coil drive system 5 transfers the transfer function Mop (s) expressed by the equation (23) in the case of the open loop to the transfer expressed by the equation (24) in the case of the closed loop. As shown in the function Mcl (s), it can be seen that the time constant is reduced and the degree of phase delay is reduced. That is, it can be seen that the phase delay of the coil drive system 5 is improved.

A comparison of these transfer functions is shown in FIG.

  When actually testing and comparing the step response of a control system that performs only conventional position feedback control and a control system that also performs magnetic field feedback, the settling time of the y-axis is 0 to 0.70 seconds. It was confirmed that the time was shortened to 40 seconds. FIG. 9 is a diagram showing a time history of the test results.

  In a magnetic support balance device, since aerodynamic force always acts as a disturbance in a wind tunnel model, it is necessary to consider not only rapid response but also robustness against disturbance. In addition, the number of parameters to be adjusted is two in the case of the PI control and the proportional gain kp and the integration time Ti in the case of only the position feedback control not including the magnetic field feedback control system (in the case of the PID control, further differentiation). Three including gain) and double phase advance (np, Tp), and these parameters exist for five axes excluding the roll axis. Since there are many parameters to be adjusted, the design is complicated with classical methods such as Bode diagrams, and with the parameter space method, it is difficult to graphically represent three or more parameters, and adjustment of control constants is very complicated. In addition, there is a problem that it is difficult to unify the control performance of each axis. In addition, when magnetic field feedback control is added to position feedback control, there is a problem that there are too many parameters to be adjusted. Further, the magnetic field feedback control system is configured only with a constant gain, but the control characteristics when using other controllers are not clarified. That is, in the control including the magnetic field feedback control, the number of parameters is not only the PI control and the double phase advance element, but also the transfer function of the prefilter that converts the current to the magnetic field strength and the magnetic field detected by the Hall element. There is also a parameter of the transfer function of the magnetic field controller that receives the strength input and controls the magnetic field. Furthermore, it is not guaranteed whether the adjusted control constant is optimal or close to it.

  Therefore, in designing a control system in a magnetic support device such as a magnetic support balance device used in a wind tunnel test, a problem to be solved in terms of facilitating adjustment of a large number of control constants using a robust control technique There is.

  It is an object of the present invention to determine whether a magnetic support device having a control system that performs feedback control on at least a position / attitude angle, such as a magnetic support balance device that supports a wind tunnel model with a magnetic force, is complicated and optimal. When designing a control system with control constants that are difficult to guarantee, control in a magnetic support device that can set a mixing sensitivity problem using a robust control technique and can reasonably determine the control constant It is to provide a constant determination method.

  In order to solve the above problems, a control constant determination method in a magnetic support device according to the present invention is a position sensor for detecting a position / attitude angle of a specimen having a metal and a magnet, and for applying a magnetic force to the specimen. Applied to the coil / electromagnet for feedback control of the position / posture angle of the specimen based on one or a plurality of coils / electromagnets and the position / posture angle of the specimen detected by the position sensor In a magnetic support device having a control device for calculating and outputting a current to be held and holding the specimen at an arbitrary position / posture angle in the air by the magnetic force, transmission from a disturbance input to the output of the position / posture angle A sensitivity function defined in relation to a function and a complementary feeling defined in relation to a transfer function from the disturbance input to the output of the current applied to the coil / electromagnet. Based on the function, the control constant the transfer function has, consists be determined to a value that minimizes the H∞ norm defined by robust control.

  According to the control constant determination method in the magnetic force support device, in the control device for performing feedback control on the position / posture angle of the specimen, the sensitivity is related to the transfer function from the disturbance input to the output of the position / posture angle. A function is defined, and a complementary sensitivity function is defined in relation to the transfer function from the disturbance input to the output of the current applied to the coil / electromagnet. Based on the sensitivity function thus determined and the complementary sensitivity function, the control constant of the transfer function is determined as a value that minimizes the H∞ norm defined by the robust control. Robust control is a control mode that exhibits strong characteristics against such fluctuations when the identification of the dynamic characteristic model is uncertain or when there is a random disturbance. In the present invention, paying attention to the fact that the magnetic support device is easily exposed to parameter fluctuations and disturbances, applying a robust control to the feedback control system used in the control device, a sensitivity function determined from the feedback control system and Based on the complementary sensitivity function, a large number of control constants included in the control elements constituting the feedback control system can be reasonably determined.

  In the method for determining a control constant in the magnetic force support device, a weight function for performing shaping for suppressing the maximum value of the sensitivity function and shifting to the high frequency side, and a weight function for performing shaping for shifting the complementary sensitivity function to the high frequency side are provided. The H∞ norm can be determined for the sensitivity function and the complementary sensitivity function that are respectively defined and shaped by the weight functions. As for the sensitivity function, it is possible to suppress the vibration of the model against disturbances in a higher frequency range than before by applying a shaping that suppresses the maximum value and shifts to the high frequency side as a whole using a weight function. Become. In addition, the complementary sensitivity function corresponds to the fact that a high-frequency component is required for the control current by shaping the whole shift to the high frequency side according to the shaping of the sensitivity function.

  In the control constant determination method in the magnetic force support device, the control device includes a magnetic sensor that detects a magnetic field formed by the coil / electromagnet, and a magnetic field that controls the coil / electromagnet based on the magnetic field detected by the magnetic sensor. And a feedback control for the magnetic field based on the magnetic field detected by the magnetic sensor simultaneously with the feedback control for the position / attitude angle of the specimen, and the feedback control for the magnetic field. The sensitivity function and the complementary sensitivity function when performing the above are obtained by replacing the transfer function of the magnetic field when performing only the feedback control for the position / attitude angle with the transfer function of the entire feedback control system for the magnetic field. Can be determined. When the control device performs feedback control on the magnetic field, since the feedback control on the magnetic field is performed inside the feedback control on the position / posture angle, the transfer function of the magnetic field when performing only the feedback control on the position / posture angle. Corresponds to the transfer function of the entire feedback control system for the magnetic field. Therefore, the sensitivity function and the complementary sensitivity function can be easily determined in the magnetic force support apparatus that performs feedback control on the magnetic field by replacing the transfer functions in the corresponding relationship.

  According to the control constant determination method of the present invention, in a magnetic support device including a control system that performs feedback control on at least a position and a posture angle, such as a magnetic support balance device that supports a wind tunnel model with magnetic force, Since the method is used to set the mixed sensitivity problem and the control constant of the control element is determined as a value that minimizes the H∞ norm, there are a large number of complicated control constants that are difficult to guarantee whether they are optimal or not. It is possible to rationally determine the control constant when designing the control system. In addition, since a robust control method is used, it is guaranteed that the determined control constant is optimal or sufficiently close thereto.

感度関数Ｓ（ｓ）は、外乱入力から位置出力までの伝達関数に関連した関数である。また、相補感度関数は、外乱入力から制御電流出力までの伝達関数に関連する関数である。図６に示すような位置フィードバック制御に加えて磁場フィードバック制御をも行う制御系においては、式（２５）及び式（２６）の中で、磁場の伝達関数Ｇｃ（ｓ）が式（２７）で示す伝達関数Ｇ’ｃ（ｓ）に置き換えられる。

Next, a method for determining a control constant using the method of robust control according to the present invention in the magnetic force support device will be described with reference to examples. In the control system including only the position feedback control shown in FIG. 5, the sensitivity function S (s) and the complementary sensitivity function T (s) of the system are defined as shown in equations (25) and (26), respectively.

The sensitivity function S (s) is a function related to the transfer function from the disturbance input to the position output. The complementary sensitivity function is a function related to the transfer function from the disturbance input to the control current output. In a control system that also performs magnetic field feedback control in addition to position feedback control as shown in FIG. 6, the transfer function Gc (s) of the magnetic field is expressed by equation (27) in equations (25) and (26). It is replaced with the transfer function G′c (s) shown.

  1 and 2 are frequency response diagrams showing an example of a sensitivity function and a complementary sensitivity function. Frequency is taken on the horizontal axis, and magnitude (gain) is taken on the vertical axis. A graph indicated by a dotted line in the figure shows a control system case as shown in FIG. 5 that does not include magnetic field feedback control. Moreover, the graph shown with a continuous line has shown the case of the control system containing magnetic field feedback control as shown in FIG. The thick lines indicate the weighting functions Ws (s) and Wt (s) for shaping. According to the sensitivity function S (s) shown in FIG. 1, it is shown that a vibration of about several tens of Hz appears greatly in the model against disturbances having various frequencies. Therefore, by suppressing the maximum value for the sensitivity function S (s) and shifting the whole to the high frequency side, disturbance having a frequency in a range including a higher frequency region than that of the conventional control system is achieved. On the other hand, it is possible to suppress the vibration of the model. Correspondingly, since the control current requires a higher frequency component, it is necessary to shift the complementary sensitivity function T (s) to the high frequency side as a whole.

この発明による制御定数の決定方法によれば、ロバスト制御理論から、ベクトルＰ（ｓ）を式（３０）に示すように定義するとき、その絶対値を最小化するように各制御要素に現れる制御定数を決定する。

ここで、絶対値‖Ｐ（ｓ）‖∞は、ロバスト制御では、Ｈ∞ノルムと称される量であり、Ｐ（ｓ）が１次元の場合には、そのゲインの最大値となり、多次元の場合には、最大特異値となる。ロバスト制御の理論から、‖Ｐ（ｓ）‖∞が小さければその制御系は良い制御性Ｗを備えているということが言える。 The weighting functions Ws (s) and Wt (s) are functions for shaping the sensitivity function S (s) and the complementary sensitivity function T (s) while suppressing the maximum value and shifting the whole to the high frequency side. , Respectively, are set as shown in the equations (28) and (29).

According to the control constant determining method of the present invention, when the vector P (s) is defined as shown in the equation (30) from the robust control theory, the control appearing in each control element so as to minimize the absolute value thereof. Determine the constant.

Here, the absolute value ‖P (s) ‖∞ is a quantity called H∞ norm in the robust control, and when P (s) is one-dimensional, it becomes the maximum value of the gain, and is multidimensional. In this case, the maximum singular value is obtained. From the theory of robust control, it can be said that if ‖P (s) ‖∞ is small, the control system has good controllability W.

As a result of several trials, in the case of a control system having only position feedback control as shown in FIG. 5, the transfer function K (s) of the PI controller 2 and the transfer function Hp ( s) was determined as shown in Equation (31) and Equation (32), respectively.

ここで、重み関数Ｗｓ（ｓ），Ｗｔ（ｓ）は、両方の制御系に対して式（３７）、式（３８）に示すような共通した形に設定された。

図３には、模型位置の時間変化を示す数値シミュレーションの結果が示されている。図３に示すように、従来の位置フィードバック制御のみの制御系と、磁場フィードバック制御も行う制御系とでは、外乱に対しての揺動には大きな差は見受けられなかったが、その大きさは非常に小さく抑えることが期待できる。 In the case of a control system including not only position feedback control but also magnetic field feedback control as shown in FIG. 6, the transfer function K (s) of the PI controller 2 and the transfer function of the double phase advancer 11 Hp (s) and the transfer functions Km (s) and Hm (s) of the magnetic field controllers 16 and 17 of the magnetic field feedback control system are expressed by the equations (33), (34), (35), and ( 36).

Here, the weighting functions Ws (s) and Wt (s) are set in a common form as shown in the equations (37) and (38) for both control systems.

FIG. 3 shows the result of numerical simulation showing the time change of the model position. As shown in FIG. 3, there was no significant difference in the oscillation with respect to the disturbance between the conventional control system only for position feedback control and the control system that also performs magnetic field feedback control. It can be expected to be very small.

  In this way, in a magnetic support device that is susceptible to disturbance including various frequencies, by applying a robust control technique, the control constant of the control element can be automatically and efficiently adjusted to an optimum or close state. You can make a decision. This determination method is very efficient when there are a large number of control constants. Further, although there are five (or six) support axes for the model, it is easy to unify control performance for all axes. Furthermore, an optimal control constant can be obtained for a given control performance requirement (weight function).

It is a diagram which shows an example of the sensitivity function used with the control constant determination method in the magnetic support apparatus by this invention. It is a diagram which shows an example of the complementary sensitivity function used with the control constant determination method in the magnetic support apparatus by this invention. It is a graph which shows the result of the numerical simulation which shows the time change of the model position in the control system which only performs position feedback control, and the control system which also performs magnetic field feedback control. It is a perspective view which shows the outline | summary of the measurement system used for a magnetic support type wind tunnel, a magnetic support device, and a magnetic support device, and a control system. It is a figure which shows an example of the control block of the magnetic support apparatus which performs only position feedback control. It is a block diagram which shows an example of the control apparatus of the magnetic support apparatus which performs position feedback control and magnetic field feedback control. It is a graph which shows the change of each magnetic quantity at the time of changing the electric current of a y-axis direction. It is a figure which shows the comparison of the transfer function in the case of an open loop and a closed loop about the y-axis of the coil drive system of a magnetic support apparatus. It is a graph which shows the step response of the control system which performs only position feedback control, and the control system which also performs magnetic field feedback.

Explanation of symbols

1 Target value setter 2 PI controller (transfer function K)
3 Bias Applicator 4 D / A Converter 5 Coil Drive System 7 Wind Tunnel Model 8 Noise Source 9 Optical Sensor (Delay Time L) 10 Noise Cut Filter (Transfer Function Hn) 11 Double Phase Leader (Transfer Function Hp) 12 Hall Element (magnetic sensor)
13 Computer 14 Power Amplifier 15 Prefilter (Transfer Function F _m ) 16 Magnetic Field Controller (Transfer Function K _m )
17 Magnetic field controller (transfer function H _m )
20 Magnetic support device 21, 30 Air-core coil 22-29 Coil x, y, z Coordinate axis constituting right-handed system φ Roll angle θ Pitch angle φ Yaw angle Y Position / Attitude angle R Target value E Deviation B Bias D Disturbance U Command Signal N Sensor noise
Mg Magnetic field transfer function hx hy hz hθ hψ Magnetic quantity Mop Transfer function when coil drive system 5 is open loop Mcl Transfer function when coil drive system 5 is closed loop S (s) Sensitivity function T (s) Complementary sensitivity function Ws (s), Wt (s) Weight function

Claims (3)

  A position sensor for detecting a position / attitude angle of a specimen having a metal and a magnet, one or a plurality of coils / electromagnets for applying a magnetic force to the specimen, and the specimen detected by the position sensor A control device for calculating and outputting a current applied to the coil / electromagnet in order to perform feedback control on the position / posture angle of the specimen based on the position / posture angle of the specimen; In a magnetic support device that holds an arbitrary position / posture angle in the air, a sensitivity function determined in relation to a transfer function from a disturbance input to the output of the position / posture angle, and an application from the disturbance input to the coil / electromagnet The control constant of the transfer function based on a complementary sensitivity function determined in relation to the transfer function up to the output of the current to be output is defined by robust control. Control constant determining method in the magnetic support device consists in determining the value that minimizes the norm.   A weighting function that performs shaping to suppress the maximum value of the sensitivity function and shift to the high frequency side and a weighting function that performs shaping to shift the complementary sensitivity function to the high frequency side are respectively defined, and shaped by each of the weighting functions. The method for determining a control constant in a magnetic force support device according to claim 1, wherein the H∞ norm is determined for the sensitivity function and the complementary sensitivity function.   The control device includes a magnetic sensor that detects a magnetic field formed by the coil / electromagnet, and a magnetic field controller that controls the coil / electromagnet based on the magnetic field detected by the magnetic sensor, and the control unit includes: Simultaneously with the feedback control for the position / attitude angle, the feedback control for the magnetic field is performed based on the magnetic field detected by the magnetic sensor, and the sensitivity function and the complementary sensitivity when performing the feedback control for the magnetic field. The function is defined by substituting the transfer function of the magnetic field when performing only the feedback control for the position / attitude angle with a transfer function of the entire feedback control system for the magnetic field. The control constant determination method in the magnetic support apparatus of description.

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