JP2008257348A - Method for designing controller for vibration reduction device, controller for vibration reduction device, and vibration reduction device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for designing a plurality of controllers for controlling corresponding vibration reductions in a plurality of frequency bands, in consideration of both control performance in terms of noise suppression, responsiveness and the like, and robust stability. <P>SOLUTION: In the design of one of the plurality of controllers, a model error is computed from an object controlled by the one controller in a state of feedback about the one controller from one or more controllers other than the one controller, and a weight function satisfying robust stability is computed with the use of the model error. This can determine the model of each divided frequency band in low dimensions to shorten the modeling calculation time and increase the modeling accuracy. The design of each band controller from the low dimensional model corresponding to the band can implement efficient control system design and low dimensional construction of the designed controllers. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention is provided in a device for reducing vibrations generated by a vibration source, and controls a plurality of controller design methods, a controller for vibration reduction devices, and a vibration reduction device for controlling the reduction of vibrations in a plurality of frequency bands, respectively. About.

As a control method for achieving excellent control performance and robust stability performance, there is a mixed H ₂ / H _∞ control method in which the control performance is evaluated by H ₂ norm and the robust stability is evaluated by H _∞ norm.

FIG. 35 is a block diagram showing a control problem. In FIG. 35, P (s) is a controlled object, y is an observation output, and u is a control input. If the transfer function matrix from the disturbance w to the frequency weighted control response Z ₂ is T _Z2w (s), and the transfer function matrix from the disturbance w to the frequency weighted control input Z ₁ is T _Z1w (s), then the mixed H ₂ / The _H∞ control problem is expressed by the following equations (1) and (2).

ここで、式（１）はＴ_Ｚ２ｗ（s）のＨ_２ノルム、式（２）はＴ_Ｚ１ｗ（s）のＨ_∞ノルムを表す。モデル誤差Δ_∞（s）に対して適切に周波数重み関数Ｗ_１（s）を与え、制振目標に対応した周波数重み関数Ｗ_２（s）を設定した上で、制御問題である式（１）、（２）を解くことにより、モデル誤差に対しロバスト安定性を有するコントローラＫ（s）が設計される。本コントローラは、ロバスト安定性を満たしつつ、制御応答（振動応答）のエネルギーを最小化できるため、振動制御における有効性が高い。

Here, Formula (1) represents the H ₂ norm of T _Z2w (s), and Formula (2) represents the H _∞ norm of T _Z1w (s). A frequency weighting function W ₁ (s) is appropriately given to the model error Δ _∞ (s), and a frequency weighting function W ₂ (s) corresponding to the vibration suppression target is set. ), (2), a controller K (s) having robust stability against model errors is designed. Since this controller can minimize the energy of control response (vibration response) while satisfying robust stability, it is highly effective in vibration control.

  As a method of performing noise control, there is an active noise control method based on feedforward control. This method is a control method in which noise characteristics are acquired by learning from a reference signal related to noise and an error signal at a measurement point where noise should be canceled by the speaker, and the noise is canceled by outputting a sound having a phase opposite to that of the noise from the speaker. . There are technical difficulties in performing acoustic control in such a control method in a wide frequency band from low frequency to high frequency. This is because modeling in a wide frequency band is not only less accurate, but also has a higher order, so that control in the high frequency region becomes difficult in terms of computational load in the control circuit. As a method for solving this problem, there is a method of configuring a noise characteristic learning and control circuit in a low frequency band and a high frequency band in the above active noise control technique. By preventing interference between the two control circuits with a filter, noise control in a low frequency band and a high frequency band is enabled (see Patent Document 1).

Japanese Patent No. 3471370

  When the noise characteristics learning and control circuit configuration method is configured separately for the low frequency band and high frequency band described above, since it is based on feedforward control, robust stability against model errors when the noise characteristics are acquired by learning It is not possible to design in consideration of safety. In addition, control other than noise control, for example, general vibration control, is mainly feedback control that considers robust stability, and the active noise control method based on the above-mentioned feedforward control controls noise suppression and speed response. It can happen that the specifications cannot be met in terms of both performance and robust stability.

  The present invention has been made in view of the above problems, and its purpose is to reduce vibrations in a plurality of frequency bands in consideration of both control performance related to noise suppression and rapid response and robust stability. It is an object of the present invention to provide a design method for a plurality of controllers, a controller for a vibration reduction device, and a vibration reduction device that perform corresponding control.

  In order to achieve the above object, in the controller design method of the vibration reduction apparatus of the present invention, a plurality of vibration reduction devices provided in an apparatus for reducing vibrations generated by a vibration source and controlling vibration reduction in a plurality of frequency bands respectively. The controller design method of claim 1, wherein for one controller of the plurality of controllers, a model error is obtained from a control target of the one controller while being fed back by one or more other controllers excluding the one controller, The one controller is designed by obtaining a weight function satisfying robust stability using the model error. Thereby, the frequency band can be divided and the model of each band can be identified in a low dimension, and the calculation time for modeling and the improvement of modeling accuracy can be achieved. And since the controller for each band is designed from a low-dimensional model corresponding to each band, it is possible to increase the efficiency of the control system design, and at the same time, the designed controller can also be configured in a low dimension. it can.

  A method for designing a plurality of controllers, which is provided in an apparatus for reducing vibrations generated by a vibration source and controls correspondingly the reduction of vibrations in a plurality of frequency bands, and includes one of the plurality of controllers. With respect to the controller, a model error is obtained from the control target of the one controller in a state fed back by all other controllers except the one controller, and a weight function satisfying robust stability is obtained using the model error, and the 1 It features the design of two controllers. As a result, even with two or more controllers, it is possible to obtain a great control effect by performing a coordinated design that considers the influence of all other controllers as an error, and it is possible to reliably stabilize the control system. .

  More specifically, the first frequency band controller for controlling the reduction of the vibration in the first frequency band and the reduction of the vibration in the second frequency band are provided in an apparatus for reducing the vibration generated by the vibration source. A second frequency band controller design method for determining a first frequency band model error from a control target of the first frequency band controller in a state where there is no second frequency band controller, A first step of designing the first frequency band controller by obtaining a first frequency weighting function satisfying robust stability using a first frequency band model error, and feedback by the first frequency band controller The frequency response under the condition is regarded as the response of the actual control target, and the second frequency band model is controlled from the control target of the second frequency band controller. A second step of determining an error and designing a second frequency band controller by determining a second frequency weighting function satisfying robust stability using the second frequency band model error; and A frequency response in a state fed back by the frequency band controller is regarded as a response of the actual control target, a new first frequency band model error is obtained from the control target of the first frequency band controller, and the first frequency weighting function is obtained. Completes the design of each controller if the first frequency band model error satisfies the robust stability against the first frequency band model error, while the first frequency weighting function is stable against the first frequency band model error. When the first frequency weight is not satisfied, the first frequency weight is set so as to satisfy the robust stability using the first frequency band model error. The number is corrected and the first frequency band controller is redesigned to go to the next fourth step. The third step and the frequency response in the state fed back by the first frequency band controller are actually controlled. A new second frequency band model error is obtained from the control target of the second frequency band controller, and the second frequency weighting function is robust against the second frequency band model error. If the second frequency weighting function does not satisfy the robust stability with respect to the second frequency band model error, the design of each controller is terminated. Redesigning the second frequency band controller by modifying the second frequency weighting function to satisfy robust stability using a band model error; Back to the third step, and a fourth step, characterized in that the controllers are designed until the controllers satisfy each other's robust stability.

  In order to achieve the above object, the controller of the vibration reducing apparatus of the present invention is characterized by being designed by the controller designing method of each of the vibration reducing apparatuses. In order to achieve the above object, the vibration reducing apparatus of the present invention is characterized by including the above controller. Thereby, the controller and vibration reduction apparatus of the vibration reduction apparatus which show said each effect can be provided.

  Embodiments of the present invention will be described with reference to the drawings. The embodiments described below do not limit the invention according to the claims, and all the combinations of features described in the embodiments are not necessarily essential to the solution means of the invention. Absent.

  The design method according to the embodiment of the present invention is effectively applied to a plurality of controllers included in the vibration reduction device. However, in order to make the explanation easy to understand, the design method is first applied to a single controller. The case will be described.

  FIG. 1 is a configuration diagram illustrating a vibration reduction apparatus including a single controller. The vibration reducing apparatus 10 includes an acceleration sensor 12 that measures vibration of a system (control target) 11, a low-pass filter 13 that removes noise in a measurement signal, and digital control for calculating a control input from the measurement signal according to a control law. The system 14 includes an actuator 15 for applying a control input to the controlled object 11. On the other hand, a measurement system for evaluating vibration characteristics by data processing includes an input / output signal and an FFT analyzer 16. This measurement system is not involved in the control of the controlled object 11 and need not be used except for data processing and vibration characteristic evaluation. A disturbance input such as an external force acts on the control target 11, and the control target 11 is excited by this disturbance input. A signal detected by the acceleration sensor 12 in the vibration reduction device 10 is transmitted via the sensor amplifier 17. The signal passes through the analog low-pass filter 13 and is input to the controller 14b that calculates the control law through the AD converter 14a. A control input signal is output from the DA converter 14 c and input to the control actuator 15 via the amplifier 18. A control force acts on the control target 11 by the actuator 15, and vibration of the control target 11 is suppressed.

2 and 3 are schematic block diagrams of the control system of the vibration reducing apparatus 10. As shown in FIG. 2, the control target 11, the disturbance w _u to be added to the control input and the disturbance w _d about external force. From FIG. 35 and FIG. 2, the transfer function from w _u to u is an evaluation index of robust stability. On the other hand, with respect to an external force disturbance w _d, it may be difficult to grasp that and precise characteristics to measure it. In this case, as shown in FIG. 3, the disturbance only as w _u, the equivalent disturbance and when w _d is applied it can be accommodated based on the idea that to act as a w _u. In this way, even without knowing the point of action and properties of the precise external force disturbance, if to grasp a rough output characteristics due to an external force, and it is reflected in the characteristics of w _u, to design the control system be able to. 3 can be regarded as a special case of FIG. 2, if a controller design method is constructed for the control system of FIG. 2, the same can be applied to FIG.

  Next, a frequency response measurement method will be described. By inputting the excitation input signal (external force disturbance) and the acceleration signal detected by the acceleration sensor 12 to the FFT analyzer 16, data processing based on the fast Fourier transform is performed in the FFT analyzer 16, and the frequency response between the input and output is changed. The result is calculated as acceleration (| acceleration / force |) and compliance (| displacement / force |). Similarly, an excitation input signal is given as a control input disturbance, an excitation force is applied to the controlled object 11 from the control actuator 15, the vibration response of the controlled object 11 is measured by the acceleration sensor 12, and the controlled input disturbance signal and the acceleration sensor are measured. The frequency response is measured by processing the 12 output signals with the FFT analyzer 16. On the other hand, when an analysis model using a finite element method or the like exists, a frequency response obtained by simulation using a computer can be used.

  Next, a frequency response curve fitting method will be described. In order to describe the model of the controlled object 11 from the measured frequency response, it is necessary to identify the mode characteristics (such as the natural frequency, natural mode, and mode damping ratio) of the controlled object 11. As a method for identifying mode characteristics by curve fitting from frequency response (acceleration, compliance, etc.), a method of experimental mode analysis represented by a partial iteration method is the mainstream. On the other hand, when an analysis model by the finite element method or the like exists, the mode characteristics are calculated by a simulation using a computer, so that these analysis results can be used regardless of the identification method.

  Next, a method for creating a model error and a frequency weight function will be described. When modeling is performed by the above-described system identification method, there is generally an error between the frequency characteristics of the model and the frequency characteristics actually obtained by measurement (in the actual system). The controller 14b in constructing the control system must be designed to have robust stability against this error.

FIG. 4 is a block diagram in which a model error is given as a multiplicative error and is described together with a position where a disturbance acts. 4, a P (s) is the control target, K (s) is the controller, delta _∞ (s) is multiplicative error of the controlled object, P ~ (s) actual control object (real system). On the other hand, in the block diagram of FIG. 35, it is possible to design a control system that guarantees robust stability by appropriately giving the frequency weighting function W ₁ (s) to the model error Δ _∞ (s). That is, a controller that satisfies the following equation (4), which is a robust stability condition based on the small gain theorem, with W ₁ (s) satisfying the following equation (3) with respect to the frequency response (σ-plot) of Δ _∞ (s): To design. A controller based on this mixed H ₂ / H _∞ control problem is designed by a numerical search method for a control problem described in the form of a linear matrix inequality (LMI).

以上のようにして設計されたコントローラは、Δ_∞（s）という誤差の範囲内で、ロバスト安定性を満たすことができる。一方、制御応答の性能（振動の低減）に関しては、Δ_∞（s）により規定されるロバスト安定条件の制約に依存する。すなわち、誤差Δ_∞（s）が対象とする周波数領域において小さければ制御応答に関して高い制御性能を達成することは可能であるが、逆に誤差が大きい場合にはその性能は劣化する。広い周波数帯域を制御する場合、単一のコントローラで制御しようとすると、多くの振動モードを含む広帯域の特性を一つのモデルで表現する必要があり、必然的にシステム同定の精度低下（モデル誤差の増加）とモデル次数の増加をもたらす。このことは、結果として制御性能の低下につながる。

The controller designed as described above can satisfy the robust stability within an error range of Δ _∞ (s). On the other hand, the performance of control response (reduction of vibration) depends on the constraint of the robust stability condition defined by Δ _∞ (s). That is, it is possible to error delta _∞ (s) to achieve a high control performance with respect to the control response smaller in the frequency domain of interest, if the error is large, the inverse performance deteriorates. When controlling a wide frequency band, if it is attempted to control with a single controller, it is necessary to represent a wideband characteristic including many vibration modes with one model, which inevitably reduces the accuracy of system identification (model error) Increase) and model order. This results in a decrease in control performance.

  Therefore, in order to solve the problem of the broadband control by the single controller described above, a vibration reduction apparatus configured by robustly coordinating a plurality of controllers for each band will be described.

  FIG. 5 is a configuration diagram illustrating a vibration reducing apparatus including a plurality of controllers according to an embodiment of the present invention. The vibration reducing apparatus 20 includes a low-frequency band controller and a high-frequency band controller connected in parallel to form a wide-band controller, and the basic components other than the low-frequency band controller 21 and the high-frequency band controller 22 are configured. Since the configuration is the same as that of FIG. 1, the same reference numerals are given and the description thereof is omitted. Here, the controllers 21 and 22 for each frequency band are designed to satisfy the robust stability specification so as not to cause instability due to interference with the controllers 22 and 21 for other frequency bands.

  Next, a robust cooperative design method for the low frequency band controller 21 and the high frequency band controller 22 will be described.

FIG. 6 is a block diagram of a control system in which two controllers for a low frequency band and a high frequency band are coupled in parallel. Here, K _L (s) is a low frequency band controller, and K _H (s) is a high frequency band controller. In the feedback control system, since both controllers interfere with each other, it is necessary to perform a coordinated design of both controllers in consideration of robust stability. Therefore, a robust control system is designed by regarding the characteristic change due to feedback control by one controller as a model error in the other controller design. Here, the frequency characteristic of the feedback control system by each controller can be predicted from the designed controller and the frequency response obtained by measurement.

  The following shows the process of a collaborative design method that should ensure robust stability in a parallel coupled control system of multiple controllers.

  FIG. 7 is a block diagram in which the model error of the low frequency band controller is given as a multiplicative error and expressed together with the position where the disturbance acts, FIG. 8 is a block diagram fed back by the low frequency band controller, and FIG. FIG. 10 is a block diagram in which the model error of the high frequency band controller is given as a multiplicative error and is described together with the position where the disturbance acts. FIG. 10 is a block diagram fed back by the high frequency band controller.

<Step 1>: When there is no high frequency band controller in FIG. 7 (K _H (s) = 0), using the low frequency band control target P _L (s) and the model error Δ _∞ (s), 5) is given so that W _∞L (s) is satisfied, and the low frequency band controller K _L (s) is designed to satisfy the robust stability.

<ステップ２>：低周波数帯域コントローラＫ_Ｌ（s）でフィードバックしたシステムＰ~（s）をＫ_Ｌ（s）と（計測した）実システムＰ~（s）から次式（６）により表す（図８参照）。

<Step 2>: expressed by the following equation of a low frequency band controller K _{L (s)} system and feedback P ~ (s) and K _{L (s)} (measured) real system P ~ (s) (6) ( (See FIG. 8).

ここで、Ｐ~（ｊω）が計測された周波数応答に対応するので、式（２）の周波数応答を実システムの応答とみなした上で、高周波数帯域制御対象Ｐ_Ｈ（s）とのモデル誤差Δ_∞Ｈ（s）を次式（７）から求める。

Here, since P˜ (jω) corresponds to the measured frequency response, the frequency response of Equation (2) is regarded as the response of the real system, and then the model with the high frequency band control object P _H (s). The error _Δ∞H (s) is obtained from the following equation (7).

そして、高周波数帯域制御対象Ｐ_Ｈ（s）とモデル誤差Δ_∞Ｈ（s）を用い、次式（８）となるようにＷ_∞Ｈ（s）を与え、ロバスト安定性を満たすように高周波数帯域コントローラＫ_Ｈ（s）を設計する（図９参照）。

Then, using the high frequency band control target P _H (s) and the model error Δ _∞H (s), W _∞H (s) is given so as to satisfy the following equation (8), and high stability is satisfied so as to satisfy the robust stability. The frequency band controller K _H (s) is designed (see FIG. 9).

<ステップ３>：高周波数帯域コントローラＫ_Ｈ（s）でフィードバックしたシステムＰ~_Ｌ（s）をＫ_Ｈ（s）と（計測した）実システムＰ~（s）から次式（９）により表す（図１０参照）。

<Step 3>: The system P to _L (s) fed back by the high frequency band controller K _H (s) is expressed by the following equation (9) from K _H (s) and the (measured) real system P to (s). (See FIG. 10).

この周波数応答を実システムの応答とみなした上で低周波数帯域制御対象Ｐ_Ｌ（s）とのモデル誤差Δ_∞Ｌ（s）を次式（１０）から求める。

The model error Δ _∞L (s) with respect to the low frequency band control target P _L (s) is obtained from the following equation (10) after regarding this frequency response as the response of the actual system.

もし、低周波数帯域周波数重み関数Ｗ_∞Ｌ（s）がΔ_∞Ｌ（s）に対しロバスト安定性（次式（１１））を満たしていれば終了する。そうでなければ、低周波数帯域制御対象Ｐ_Ｌ（s）とモデル誤差Δ_∞Ｌ（s）を用い、次式（１２）を満たすようにＷ_∞Ｌ（s）を修正した上で低周波数帯域コントローラＫ_Ｌ（s）を再設計し、ステップ４に行く（図７参照）。

If the low frequency band frequency weighting function _W∞L (s) satisfies the robust stability (the following equation (11)) with respect to _Δ∞L (s), the processing ends. Otherwise, a low frequency band control target P _{L (s)} and using the model error Δ _{∞L (s),} a low frequency band on a modification of the W _{∞L (s)} so as to satisfy the following equation (12) redesign the controller _{K L} (s), go to step 4 (see FIG. 7).

<ステップ４>：ステップ２の手順と同様に、低周波数帯域コントローラＫ_Ｌ（s）でフィードバックしたシステムＰ~_Ｈ（s）の周波数応答をＫ_Ｌ（s）と計測した（実システムＰ~（s））周波数応答から計算し、それを実システムの応答とみなした上で高周波数帯域制御対象Ｐ_Ｈ（s）とのモデル誤差Δ_∞Ｈ（s）を求める。もし、高周波数帯域周波数重み関数Ｗ_∞Ｈ（s）がΔ_∞Ｈ（s）に対しロバスト安定性（次式（１３））を満たしていれば終了する。そうでなければ、高周波数帯域制御対象Ｐ_Ｈ（s）とモデル誤差Δ_∞Ｈ（s）を用い、次式（１４）を満たすようにＷ_∞Ｈ（s）を修正した上で高周波数帯域コントローラＫ_Ｈ（s）を再設計し、ステップ３に戻る（図９参照）。

<Step 4>: Similar to the procedure in Step 2, the frequency response of the system P to _H (s) fed back by the low frequency band controller K _L (s) was measured as K _L (s) (actual system P to ( s)) A model error Δ _∞H (s) with respect to the high frequency band control object P _H (s) is obtained after calculating from the frequency response and considering it as a response of the real system. If the high frequency band frequency weighting function W _∞H (s) satisfies the robust stability (the following equation (13)) with _respect to Δ _∞H (s), the processing ends. Otherwise, using the high frequency band control object P _H (s) and the model error Δ _∞H (s), and correcting W _∞H (s) to satisfy the following equation (14), the high frequency band The controller K _H (s) is redesigned and the process returns to Step 3 (see FIG. 9).

ここで、本設計プロセスにおける設計終了条件は次式（１５）のとおりである。すなわち、低周波数帯域用コントローラと高周波数帯域用コントローラがそれぞれ互いにロバスト安定性を満たすときに設計終了となる。ここで、式（１５）の最左項は行列Δ_∞Ｌ（ｊω）の最大特異値を示し、次式（１６）（尚、＊は複素転置行列）の最大固有値を表す。Ｗ_∞Ｌ（ｊω）、Δ_∞Ｈ（ｊω）およびＷ_∞Ｌ（ｊω）の最大特異値についても同様である。

Here, the design end condition in this design process is as shown in the following equation (15). That is, the design ends when the low frequency band controller and the high frequency band controller satisfy the robust stability of each other. Here, the leftmost term of Expression (15) represents the maximum singular value of the matrix Δ _∞L (jω), and represents the maximum eigenvalue of the following Expression (16) (where * is a complex transpose matrix). The same _{applies to} the maximum singular values of W _∞L (jω), Δ _∞H (jω), and W _∞L (jω).

図１１は、ステップ１からステップ４をフロー図にしたものである。このフロー図におけるプロセスは、上記終了条件を満たすまでコントローラの設計を繰り返すことを示している。上記プロセスにより設計されたそれぞれのコントローラは、お互いの干渉に対しロバスト安定性を満たすことになる。なお、低周波数帯域コントローラが無い場合（Ｋ_Ｌ（s）＝０）に、高周波数帯域制御対象Ｐ_Ｈ（s）とモデル誤差Δ_∞（s）を用い、Ｗ_∞Ｈ（s）を与え、ロバスト安定性を満たすように高周波数帯域コントローラＫ_Ｈ（s）を設計し、以降も設計する方法であっても良い。また、ステップ２〜ステップ４において、Ｋ_Ｌ（s）（もしくはＫ_Ｈ（s））でフィードバック制御したときの実システムＰ~_Ｈ（s）（もしくはＰ~_Ｌ（s））の周波数応答として、制御実験による実測データを用いても構わない。

FIG. 11 is a flowchart of steps 1 to 4. The process in this flow diagram indicates that the controller design is repeated until the termination condition is satisfied. Each controller designed by the above process will satisfy the robust stability against mutual interference. When there is no low frequency band controller (K _L (s) = 0), the high frequency band control object P _H (s) and the model error Δ _∞ (s) are used to give W _∞H (s), The high frequency band controller K _H (s) may be designed so as to satisfy the robust stability, and the design method may be used thereafter. In Steps 2 to 4, the frequency response of the actual system P _H (s) (or P _L (s)) when feedback control is performed with K _L (s) (or K _H (s)) Actual measurement data from a control experiment may be used.

  Furthermore, even when the number of controllers is three or more, the controllers can be designed in the same steps. In other words, the controller in the initial state is set to 0, and the controller is designed according to the above steps so as to satisfy the robust stability in a state where the controller in each band is fed back by all the controllers in other bands. For example, when the number of controllers is 3, it is as follows. Controller 1 designs all other controllers as 0. The controller 2 feeds back the controller 1 and designs the controller 3 as 0. The controller 3 is designed with the controllers 1 and 2 fed back. Thereafter, the controller is designed in the order of the controllers 1, 2, and 3 in accordance with this design step until the redesign becomes unnecessary.

  As described above, according to the method of robust co-design of a plurality of controllers for each band, it is possible to identify each band model in a low dimension by dividing the frequency band, and the calculation time for modeling Shortening and improved modeling accuracy. Since the controller for each band is designed from a low-dimensional model corresponding to each band, the efficiency of the control system design is improved, and at the same time, the designed controller is configured in a low dimension. Higher design efficiency can be expected to shorten the design period and thereby reduce costs. Furthermore, since the controller can be configured in a low dimension, errors in numerical calculation in controller design are small, and it can be said that the reliability of the designed controller is high. The wideband controller used in the actual system is a combination of low-dimensional controllers for each band connected in parallel, so the computational efficiency is significantly higher than a single controller designed directly from a large-scale model for wideband. It can be improved. The basis for this can be understood from the fact that the number of multiplications per sample in a digital control system is approximately equal to the square of the order of the controller, whereas when the control band is divided, it is equal to the sum of the number of multiplications of each controller. . As a result, the sampling frequency on the hardware of the digital control system can be improved, and wide-band real-time control including a high frequency region can be realized.

  FIG. 12 is a block diagram showing an embodiment of a vibration reducing apparatus having a single controller corresponding to FIG. The basic configuration of the vibration reducing device 10 is the same as that in FIG. 1 described above, but the difference from FIG. 1 is that the control object 11 is given as a specific engine / ejector system and the disturbance related to external force is reduced. It is that it works with an impulse hammer.

  First, the frequency response measurement method and results will be described. A disturbance input is given by an impulse hammer, the acceleration of the controlled object 11 is measured by the acceleration sensor 12, and an input signal of an excitation force by the impulse hammer and an output signal from the acceleration sensor 12 are input to the FFT analyzer 16 to input force. Measure the frequency response of acceleration output to.

  FIG. 13 is a diagram showing the frequency response (acceleration) from the measured disturbance excitation input to the output signal of the acceleration sensor 12. From FIG. 13, it can be seen that there are large peaks at 400 Hz, 1600 Hz, and 2300 Hz. Similarly, an excitation input signal is given as a control input disturbance, an excitation force is applied to the controlled object 11 from the control actuator 15, the vibration response of the controlled object 11 is measured by the acceleration sensor 12, and the controlled input disturbance signal and the acceleration sensor are measured. The frequency response is measured by processing the 12 output signals with the FFT analyzer 16.

  FIG. 14 is a diagram illustrating a frequency response (acceleration) from the measured control input disturbance signal to the output signal of the acceleration sensor 12. From the result of FIG. 14, it can be seen that a resonance peak exists at the same frequency as the result of FIG.

Next, a method and result of frequency response curve fitting will be described. The mode characteristics are identified by curve fitting from the measured frequency response. The target frequency response includes acceleration and compliance. Here, identification is performed based on the latter. Since the acceleration (| acceleration / force |) is measured in the experiment, it is converted into compliance (| displacement / force |) by multiplying this by -1 / ω ² (ω is the angular frequency). As a method for identifying the mode characteristics, a partial iteration method is used. The frequency response (compliance) G (s) of the system in the proportional viscous damping system is described as the following expression (17) in the s region obtained by Laplace transforming the system equation of motion.

ここで、Ω_ｒおよびζ_ｒはそれぞれｒ次の固有振動数および減衰比であり、φ_ｒｉおよびφ_ｒｊはそれぞれｒ次モードにおける入力点ｉおよび出力点ｊの固有モード成分である。これらをモード特性と呼び、実験モード解析におけるカーブフィッティングにより同定される。ｒ次モードに関する入出力関係を状態方程式で表すと次式（１８）、（１９）のようになる。

Here, Ω _r and ζ _r are the r-order natural frequency and damping ratio, respectively, and φ _ri and φ _rj are the eigen-mode components of the input point i and the output point j in the r-order mode, respectively. These are called mode characteristics and are identified by curve fitting in experimental mode analysis. The input / output relationship regarding the r-order mode is expressed by the following equations (18) and (19).

ここで、ｑ_ｅ，ｒ、ｙ_ｒはそれぞれｒ次モードに関する状態量および出力であり、Ａ_ｅ，ｒ、Ｂ_ｌｅ，ｒ、Ｂ_２ｅ，ｒおよびＣ_２ｅ，ｒはｒ次モードに関する状態方程式のシステム行列を表す。ｗおよびｕは、それぞれ外乱入力および制御入力である。φ_ｒａ、φ_ｒｂおよびφ_ｒｃは、それぞれｒ次モードにおける応答出力点ａ、外乱入力点ｂおよび制御入力点ｃの固有モード成分である。上式を全モードについて重ね合わせると、次式（２０）、（２１）のシステム方程式が得られる。

Here, q _{e, r} and y _r are state quantities and outputs relating to the r-order mode, respectively, and A _{e, r} , B _{le, r} , B _{2e, r} and C _{2e, r} are state equations relating to the r-order mode. Represents a system matrix. w and u are a disturbance input and a control input, respectively. φ _ra , φ _rb, and φ _rc are eigenmode components of the response output point a, the disturbance input point b, and the control input point c in the r-order mode, respectively. When the above equation is overlaid for all modes, the following system equations (20) and (21) are obtained.

ここで、ｑ_ｅ，ｒ、ｙはそれぞれ全モード成分を含む状態量および出力であり、Ａ_ｅ、Ｂ_ｌｅ、Ｂ_２ｅおよびＣ_２ｅは全モード成分を含む状態方程式のシステム行列を表す。また、Ｄ_ｂおよびＤ_ｃはそれぞれ外乱入力および制御入力に対する応答をカーブフィッティングした際に、高次モードを省略したことによる補正項として同定される剰余剛性である。一方、低次モードを省略することによる補正項は剰余質量として同定されるが、一般に剰余質量を用いなくても対象とする周波数帯域の低域側における冗長なモードを採用することにより、その影響を補正することが可能である。

Here, q _{e, r} and y are state quantities and outputs including all mode components, respectively, and A _e , B _le , B _2e and C _2e represent system matrices of state equations including all mode components. D _b and D _c are residual stiffnesses identified as correction terms due to omission of the higher-order mode when the response to the disturbance input and the control input is curve-fitted, respectively. On the other hand, the correction term due to the omission of the low-order mode is identified as the residual mass, but in general, it is not affected by adopting the redundant mode on the low frequency side of the target frequency band without using the residual mass. Can be corrected.

  15 to 18 are diagrams showing results (acceleration) of curve fitting by experimental mode analysis using data measured by vibration experiments. FIGS. 15 and 16 show the identification results of responses to the disturbance input and the control input, respectively, when the number of adopted modes is 4 in the low frequency band. 17 and 18 show the identification results of responses to the disturbance input and the control input, respectively, when the number of adopted modes is 6 in the high frequency band. It can be seen that good system identification that fits the experimental results accurately is performed in both frequency bands. Furthermore, since the target frequency band is divided and modeled, the model can be realized at a lower dimension than when all frequency bands are modeled together.

  Next, a model error and frequency weighting function creation method and results will be described.

FIG. 19 is a block diagram illustrating setting of frequency weights in consideration of robust stability. The multiplicative error of the following equation (22) is calculated from the identification result of the response to the control input shown in FIGS. Here, P (s) is the modeled control object, P˜ (s) is the actual control object (real system), and Δ _∞ (s) is the multiplicative error of the model.

図２０および図２１は、低周波数帯域および高周波数帯域において、両帯域の乗法的誤差Δ_∞Ｌ（s）およびΔ_∞Ｈ（s）を計算した結果をそれぞれ破線で示し、両帯域において与えた周波数重み関数Ｗ_∞Ｌ（s）およびＷ_∞Ｈ（s）の周波数特性をそれぞれ実線で示す図である。前述のとおり、次式（２３）となるように、両帯域の周波数重み関数Ｗ_∞Ｌ（s）およびＷ_∞Ｈ（s）を与えた上で、ロバスト安定条件（次式（２４））を満たすように制御系を設計することになる。ここで、Ｔ_ｕｗ（s）は図２０においてｗ_ｕからｕまでの伝達関数行列である。そして、周波数重み関数Ｗ_∞Ｌ（s）およびＷ_∞Ｈ（s）をプロパーな伝達関数として与え、それらが次式（２５）を満たすように、すなわち１入出力系ではＷ_∞Ｌ（s）およびＷ_∞Ｈ（s）の周波数応答がそれぞれΔ_∞Ｌ（s）およびΔ_∞Ｈ（s）の周波数応答よりも全周波数帯域にわたって大きくなるように設定する。

20 and 21 show the results of calculating the multiplicative errors Δ _∞L (s) and Δ _∞H (s) of both bands in the low frequency band and the high frequency band, respectively, and are given in both bands. It is a figure which shows the frequency characteristic of the frequency weight function _W∞L (s) and _W∞H (s) by a solid line, respectively. As described above, after _giving the frequency weighting functions W _∞L (s) and W _∞H (s) of both bands so that the following equation (23) is obtained, the robust stability condition (the following equation (24)) is The control system is designed to satisfy this. Here, T _uw (s) is a transfer function matrix from w _u to u in FIG. Then, the frequency weighting functions W _∞L (s) and W _∞H (s) are given as proper transfer functions so that they satisfy the following equation (25), that is, W _∞L (s) in one input / output system. _And the frequency response of W _∞H (s) is set to be larger over the entire frequency band than the frequency response of Δ _∞L (s) and Δ _∞H (s), respectively.

次に、コントローラの設計方法について説明する。上述のように両帯域の周波数重み関数Ｗ_∞Ｌ（s）およびＷ_∞Ｈ（s）を与えた上で、以下の混合Ｈ_２／Ｈ_∞制御問題（次式（２６）、（２７））を解くことによりコントローラを設計する。

Next, a controller design method will be described. _Given the frequency weighting functions W _∞L (s) and W _∞H (s) of both bands as described above, the following mixed H ₂ / H _∞ control problem (the following equations (26) and (27)) The controller is designed by solving

ここで、Ｔ_Ｚ２ｗ（s）は外乱ｗから周波数重み付き制御応答ｚ_２までの伝達関数行列、Ｔ_Ｚ１ｗ（s）は外乱ｗから周波数重み付き制御入力ｚ_１までの伝達関数行列であり、式（２６）はＴ_Ｚ２ｗ（s）のＨ_２ノルム、式（２７）の左辺はＴ_Ｚ１ｗ（s）のＨ_∞ノルムを表す。制御応答にかかる周波数重み関数Ｗ_２（s）は、モード座標から成る状態ベクトルｑ_ｅの成分に直接かかる重み係数として与える。こうすることにより、コントローラの次数を増加させることなく着目するモード（共振ピーク）を効果的に低減することができる。コントローラは、前述のとおり上記制御問題を線形行列不等式（ＬＭＩ）の形で記述した上で、数値探索法により設計される。設計されたコントローラは、次式（２８）の状態方程式として記述される。

Here, T _Z2w (s) is a transfer function matrix from the disturbance w to the frequency weighted control response z ₂ , and T _Z1w (s) is a transfer function matrix from the disturbance w to the frequency weighted control input z _1. (26) _{H 2} norm of _{T Z2w} (s), the left side of the equation (27) represents the H _∞ norm of _{T Z1w} (s). The frequency weighting function W ₂ (s) related to the control response is given as a weighting coefficient directly applied to the component of the state vector q _e composed of the mode coordinates. By doing so, the mode (resonance peak) of interest can be effectively reduced without increasing the order of the controller. The controller is designed by a numerical search method after describing the control problem in the form of a linear matrix inequality (LMI) as described above. The designed controller is described as a state equation of the following equation (28).

ここで、ｑ_ｃｐはコントローラの状態ベクトル、Ａ_ｃｐ、Ｂ_ｃｐ、Ｃ_ｃｐおよびＤ_ｃｐはコントローラのシステム行列であり、式（１２）は観測出力ｙから制御入力ｕの特性を表現したものである。行列Ａ_ｃｐ、Ｂ_ｃｐ、Ｃ_ｃｐおよびＤ_ｃｐが制御系設計により決定されることになる。

Here, q _cp is a controller state vector, A _cp , B _cp , C _cp, and D _cp are controller system matrices, and Equation (12) expresses the characteristics of the control input u from the observed output y. . The matrices A _cp , B _cp , C _cp and D _cp are determined by the control system design.

  22-25 is a figure which shows a simulation and an experimental result. 22 and 23 show simulation and experimental results in the low frequency band, and FIGS. 24 and 25 show simulation and experimental results in the high frequency band. For simulation, we describe a closed-loop extended state equation with the output of the designed controller as the control input for the model identified by the experimental mode analysis, and calculate the frequency response for it. Here, as a real system in the simulation, a large-scale control target model that adopts modes included in both the low-frequency band and the high-frequency band is created, and a closed-loop system is configured for it. The frequency response analysis of the closed loop system in the entire frequency band is performed. From FIG. 22 to FIG. 25, it can be seen that the simulation results and the experimental results correspond well.

  According to the controller designed as described above, the target peak around 400 Hz is reduced by about 10 dB in the experimental results in the low frequency band. Further, since robust stability is taken into consideration as shown in FIG. 20, it does not diverge even in a high frequency band that has not been modeled, and almost overlaps the response at the time of non-control. Regarding the experimental results in the high frequency band, the peak near 1600 Hz is reduced by about 10 dB and the peak near 2300 Hz is reduced by about 5 dB. As in the previous case, since robust stability is taken into consideration as shown in FIG. 21, a response similar to that at the time of non-control is shown without divergence even in a low frequency band that is not modeled. In both bands, the simulation results and the experimental results are in good agreement, indicating that modeling and control system design in each frequency band has been performed appropriately.

  Next, a description will be given of a vibration reducing apparatus configured by robustly coordinating a plurality of controllers for each band.

  FIG. 26 is a block diagram showing an embodiment of a vibration reducing apparatus having a plurality of controllers corresponding to FIG. The basic configuration of the vibration reducing device 20 is the same as that of FIG. 5 described above. However, the difference from FIG. 5 is that the controlled object 11 is given as a specific engine / ejector system, and disturbance related to external force is reduced. It is that it works with an impulse hammer.

First, the robust co-design method and results of the controller will be described. According to the steps shown in FIG. 11, robust co-design of the controller is performed. First, from Step 1 to obtain the low frequency band model error Δ _{∞L (s),} to create a low-frequency band the frequency weighting function W _{∞L (s),} to design a low-frequency band controller K _{L (s).}

FIG. 27 is a diagram illustrating frequency characteristics of Δ _∞L (s) and W _∞L (s). Then, calculated from the frequency response obtained in the measurement and controller designed frequency response of the state of feedback in the low frequency band controller K _{L (s)} in step 2, the high-frequency on which it was regarded as the response of the real system A model error Δ _∞H (s) with the band control object P _H (s) is obtained, and a high frequency band frequency weighting function W _∞H (s) is designed. From FIG. 9, the actual control object P to _H (s) in the high frequency band fed back by the low frequency band controller K _L (s) and the high frequency band model error _Δ∞H (s) are expressed by the following equation (29): (30)

ここで、Ｐ~（s）はノミナルモデルであり、その周波数特性は実験で計測された周波数応答に対応する。

Here, P˜ (s) is a nominal model, and its frequency characteristic corresponds to the frequency response measured in the experiment.

Figure 28 is compared with the time control during and uncontrolled frequency characteristic of the high frequency band model error delta _∞H created _(s) according to the low frequency band controller with P H _(s) and P ~ _{H (s)} It is a figure which shows a thing. As can be seen from FIG. 28, the error does not increase in the high frequency band by the low frequency band control, and the error decreases in the low frequency band. The fact that the error does not increase in the high frequency band can be understood from the fact that the control system is designed by giving the low frequency band frequency weighting function W _∞L (s) so as to satisfy the robust stability.

FIG. 29 shows the high frequency band frequency weights created to satisfy the robust stability with respect to the high frequency band model error Δ _∞H (s) created using the actual control object P _H (s) in the fed back state. It is a figure which shows function W _∞H (s). Then, the high frequency band controller K _H (s) is designed. Next, in step 3, a low frequency band model error Δ _∞L (s) in a state fed back by the high frequency band controller K _H (s) is _obtained . From FIG. 7, the actual control object P to _H (s) in the low frequency band in the state fed back by the high frequency band controller K _H (s) and the low frequency band model error Δ _∞L (s) are expressed by the following equation (31): (32)

ステップ３で求めた低周波数帯域モデル誤差Δ_∞Ｌ（s）に対し、ステップ１で作成した低周波数帯域周波数重み関数Ｗ_∞Ｌ（s）がロバスト安定を満たしていれば終了である。

If the low frequency band frequency weighting function W _∞L (s) created in Step 1 satisfies the robust stability with _respect to the low frequency band model error Δ _∞L (s) obtained in Step 3, the process ends.

Figure 30 is a low-frequency band model error delta _∞L obtained in Step 1 _(s), the low-frequency band model error delta _∞L determined again at step 3 _(s), and the low frequency band frequency weight created in step 1 It is the figure which compared the function _W∞L (s). The model error worsens around 2300 Hz, but almost overlaps around the control band of 0 to 800 Hz. This is because the high frequency band frequency weighting function W _∞H (s) in FIG. 29 is sufficiently robust outside the control band. The low frequency band frequency weighting function W _∞L (s) created in step 1 satisfies the robust stability with _respect to the low frequency band model error Δ _∞L (s) obtained again in step 3. Therefore, the low frequency band controller K _L (s) created in Step 1 has robustness even in the closed loop, and is thus designed.

  FIG. 31 and FIG. 32 are diagrams showing the results of simulation and experiment of a closed loop system using the controller designed as described above. As in the case of the single controller described above, in the simulation, a closed loop system is configured for a large-scale controlled object model that employs modes included in both the low frequency band and the high frequency band. From FIG. 31 and FIG. 32, it can be seen that the simulation result and the experimental result show a good correspondence.

  As described above, according to the method of co-designing a plurality of controllers for each band, from the results of FIG. 31 and FIG. 32, at the peaks near 400 Hz and 1600 Hz by the co-designed controller, The reduction was about 2 dB. As in the case of a single controller, it can be seen that the response is not deteriorated outside the control band while effectively controlling in the control band. In particular, the greatest feature is that vibrations in the low frequency band and the high frequency band are simultaneously reduced by this control method. The controller used here is a combination of low-dimensional controllers for each band in parallel, which significantly improves computational efficiency over a single controller designed directly from a large-scale model for wideband. The result is achieved. The reason for this can be understood from the comparison of the number of operations of the single controller and the parallel controller as described above. When control of vibration up to about 3 kHz is required as in this embodiment, a sampling frequency of about 30 kHz is generally required in a digital control system, but a single control designed directly from a large-scale model for a wide band. The sampling frequency that can be realized by the instrument was about 10 kHz, whereas 30 kHz was achieved when this method was used. The above is nothing but the excellent effectiveness of this robust collaborative design method.

  Next, for comparison, a vibration reduction apparatus configured by non-robust cooperative design of a plurality of controllers for each band will be described.

  FIG. 33 is a block diagram showing an embodiment of a vibration reducing apparatus having a plurality of controllers corresponding to FIG. The basic configuration of the vibration reducing device 20 is the same as that of FIG. 5 described above. However, the difference from FIG. 5 is that the controlled object 11 is given as a specific engine / ejector system, and disturbance related to external force is reduced. It is that it works with an impulse hammer.

First, the robust co-design method and results of the controller will be described. A single controller K _L (s) and K _H (s) for each of the low frequency band and the high frequency band designed in FIG. 19 is coupled in parallel to form a closed loop system. Therefore, the cooperative design considering the interference of both controllers is not performed, and the robust stability condition is not guaranteed.

  FIG. 34 is a diagram illustrating experimental results when a plurality of controllers using non-robust collaborative design is used. From the results shown in FIG. 34, the peak near 1600 Hz is reduced by about 3 dB, and the peak near 2300 Hz is reduced by about 4 dB, but the peak near 400 Hz is increased by about 2 dB. It can also be seen that there is a new large peak around 1800 Hz.

  Next, a comparison with the experimental results of a plurality of controllers by robust collaborative design will be described. From FIGS. 32 and 34, when multiple controllers based on robust co-design are used, the vibration control effect is obtained while maintaining robust stability in both the low frequency band and the high frequency band, whereas multiple controllers based on non-robust co-design are used. When it is used, it can be seen that there is a variation in the damping effect, and robust stability is not maintained. It can be considered that this is because the robust stability is not satisfied because the interference due to the outputs of the controllers is not considered when the controllers are connected in parallel. From this comparison, it can be said that when a plurality of controllers are used, it is effective to use the above robust collaborative design.

In the above-described embodiment, the number of controllers is described as two. However, the number of controllers can be expected to be basically any number of two or more. The grounds are as follows. Assume that the order of a single controller is n and that it can be equally divided into m subsystems. The number of multiplications in the controller calculation is about n ^{2 in} the former and about n ² / m in the latter. When m ≧ 2, the latter is necessarily smaller than the former. However, the effort of collaborative design of the control system increases as the number of controllers increases. That is, the number of times the frequency weighting function is corrected inevitably increases. However, the property that the design efficiency of each controller is higher as the number of divisions of the controller is larger is unchanged. From the above, it is considered that about 2 to 5 controllers are appropriate.

  Further, in the present embodiment, only control in one axis direction is shown, but it can be extended to control in three-dimensional direction. In this case, with respect to the installation positions and directions of the sensors and actuators, it is a condition that responses can be detected and driven in all three axis directions, or a plurality of sensors and actuators are used so as to satisfy them. This is nothing other than satisfying the basic conditions required for a control system of controllability and observability. It is only necessary to model the system and design the control system after satisfying these conditions. Here, even when there are a plurality of sensors and actuators, the system is modeled by the experimental mode analysis from the frequency response from each actuator to the sensor output, and the control system is designed by the same process as described above.

  In this embodiment, the number of disturbances (external excitation force) applied by the impulse hammer is 1, but the control system can be designed even when two or more disturbances are applied. In this case, if the frequency response from each disturbance to the sensor output is measured, or if the frequency response to the sensor output when an uncorrelated disturbance is applied simultaneously, the mode characteristics are identified by the experimental mode analysis. It will be. Then, according to the same process as described above, the control system may be designed by describing the state equation from the identified mode characteristics.

  Further, the vibration reduction device of this embodiment is applicable to vibrations of automobiles such as diesel and gasoline engines, automobile bodies, railway vehicle vibrations, aircraft vibrations, magnetic disk devices and optical disk devices, and printers. There are vibrations of information equipment such as equipment.

Further, this embodiment, in addition to be applied to the mixed H _{2 /} H _∞ control method can also be applied to H _∞ control method. That is, in the case of the _H∞ control, the control amount of the control response and the control amount of the robust stability are evaluated together by the _H∞ norm. However, since the evaluation index of the robust stability is common to the present invention, this _H∞ norm Is given as an evaluation function, the controller can perform robust co-design for _H∞ control by the same design method as the present invention.

In addition, the present embodiment can be applied to noise reduction control by modeling sound characteristics. In this case, if a microphone is used as a sensor and curve fitting is performed using a frequency response of sound pressure measured in a vibration experiment, a model from input to sound pressure is identified. If a control problem is defined by using this sound pressure as a control response, the controller is co-designed by the same method as the present invention. In the case of using a single controller, it has been demonstrated in the following paper that sound modeling and noise reduction control by system identification are possible.
(A) Ibara Sugawara, Masanao Fukuda, Hiroshi Shimojima, feedback acoustic control based on mode analysis and linear matrix inequalities, Transactions of the Japan Society of Mechanical Engineers (C), 64, 621, 1998, pp. 1668-1675
(B) Hiroshi Shimojima, Yoshihiro Matsunaga, Sekiya Koike, Irou Sugawara, Feedback acoustic control using multiple control sound sources based on mode analysis, Transactions of the Japan Society of Mechanical Engineers (C), 65, 633, 1999, pp . 1849-1856
In paper (a), performs modeling by curve fitting the system as a linear viscous damping system, design a controller with H _∞ control method and mixtures H _{2 /} H _∞ control method, noise by feedback control using the microphone and speaker Reduction is realized. In the paper (b), a system with multiple speakers (control sound source) is modeled by curve fitting as a general viscous damping system, and excellent noise reduction effect is achieved by the same control system design and feedback control experiment as in the paper (a). Has achieved. Although these papers show a single modeling and controller design method in a single frequency band, the method of the present invention can be applied as it is by dividing it into a plurality of frequency bands.

  In the modeling in the present embodiment, the proportional viscous damping system is treated as shown in the equations (17) to (21). However, modeling when the system is a general viscous damping system is also possible. The present invention can be applied as it is. A method of describing the system by a state equation from the mode characteristics in the general viscous damping system is shown in the paper (b) of the above (6).

  In addition, as a model error in this embodiment, an additive error can be handled in the same manner as a multiplicative error. When model error is treated as an additive error, this embodiment is obtained by giving a frequency weighting function with the additive error characteristic as an index to the transfer function from disturbance to control input acting on the observed output of the system. It can be applied as it is.

It is a block diagram which shows the vibration reduction apparatus provided with the single controller. FIG. 2 is a schematic first block diagram of a control system of the vibration reducing apparatus of FIG. 1. FIG. 3 is a schematic second block diagram of a control system of the vibration reducing apparatus of FIG. 1. FIG. 2 is a block diagram in which a model error of the vibration reducing apparatus of FIG. 1 is given as a multiplicative error and is described together with a position where a disturbance acts. It is a lineblock diagram showing a vibration reduction device provided with a plurality of controllers concerning one embodiment of the present invention. FIG. 6 is a block diagram of a control system in which two controllers for a low frequency band and a high frequency band of the vibration reduction device of FIG. 5 are coupled in parallel. FIG. 6 is a block diagram in which a model error of the low frequency band controller of the vibration reduction apparatus of FIG. 5 is given as a multiplicative error and is described together with a position where a disturbance acts. FIG. 6 is a block diagram fed back by a low frequency band controller of the vibration reducing apparatus of FIG. 5. FIG. 6 is a block diagram in which a model error of the high frequency band controller of the vibration reduction apparatus of FIG. 5 is given as a multiplicative error and is described together with a position where a disturbance acts. FIG. 6 is a block diagram fed back by a high frequency band controller of the vibration reducing apparatus of FIG. 5. FIG. 5 is a flowchart of steps 1 to 4 of the design method according to the embodiment of the present invention. It is a block diagram which shows the Example of the vibration reduction apparatus provided with the single controller corresponding to FIG. It is a figure which shows the frequency response (acceleration) from the measured disturbance excitation input of the vibration reduction apparatus of FIG. 12 to the output signal of an acceleration sensor. It is a figure which shows the frequency response (acceleration) from the measured control input disturbance signal of the vibration reduction apparatus of FIG. 12 to the output signal of an acceleration sensor. It is the 1st figure which shows the result (acceleration) which carried out curve fitting by experiment mode analysis using the data measured by the vibration experiment of the vibration reduction apparatus of FIG. It is the 2nd figure which shows the result (acceleration) which carried out curve fitting by experiment mode analysis using the data measured by the vibration experiment of the vibration reduction apparatus of FIG. It is the 3rd figure which shows the result (acceleration) which carried out curve fitting by experiment mode analysis using the data measured by the vibration experiment of the vibration reduction apparatus of FIG. It is the 4th figure which shows the result (acceleration) which carried out curve fitting by experiment mode analysis using the data measured by the vibration experiment of the vibration reduction apparatus of FIG. It is a block diagram shown about the setting of the frequency weight which considered the robust stability of the vibration reduction apparatus of FIG. The results of calculating the multiplicative errors Δ _∞L (s) and Δ _∞H (s) of both bands in the low frequency band and the high frequency band of the vibration reducing device of FIG. It is the 1st figure which shows the frequency characteristic of frequency weight function _W∞L (s) and _W∞H (s) by a solid line, respectively. The results of calculating the multiplicative errors Δ _∞L (s) and Δ _∞H (s) of both bands in the low frequency band and the high frequency band of the vibration reducing device of FIG. It is the 1st figure which shows the frequency characteristic of frequency weight function _W∞L (s) and _W∞H (s) by a solid line, respectively. It is a 1st figure which shows the simulation and experimental result of the vibration reduction apparatus of FIG. It is a 2nd figure which shows the simulation and experimental result of the vibration reduction apparatus of FIG. It is a 3rd figure which shows the simulation and experimental result of the vibration reduction apparatus of FIG. FIG. 13 is a fourth diagram showing simulation and experimental results of the vibration reducing device of FIG. 12. It is a block diagram which shows the Example of the vibration reduction apparatus provided with the several controller corresponding to FIG. FIG. 27 is a diagram illustrating frequency characteristics of Δ _∞L (s) and W _∞L (s) of the vibration reducing device in FIG. 26. Time control by the low frequency band controller frequency characteristic of the high frequency band model error delta _∞H created _(s) with a vibration damping system for P _{H (s)} and P ~ _{H (s)} of FIGS. 26 and non-control-period It is a figure which shows what was compared by. The high frequency created so as to satisfy the robust stability against the high frequency band model error Δ _∞H (s) created using the actual control object P _H (s) in the feedback state of the vibration reducing device of FIG. It is a figure which shows band frequency weight function _W∞H (s). Low frequency band model error delta _∞L obtained in Step 1 of the flow diagram of FIG. 11 _(s), the low-frequency band model error delta _∞L determined again at step 3 _(s), and low frequency bands created in step 1 It is the figure which compared frequency weight function _W∞L (s). It is the 1st figure which shows the result of having performed the simulation and experiment of the closed loop type | system | group using the controller designed by the flowchart of FIG. It is the 2nd figure which shows the result of having performed the simulation and experiment of the closed loop type | system | group using the controller designed by the flowchart of FIG. It is a block diagram which shows the Example of the vibration reduction apparatus provided with the several controller corresponding to FIG. It is a figure which shows the experimental result at the time of using the multiple controller by the non-robust cooperative design of the vibration reduction apparatus of FIG. It is a block diagram showing a control problem.

Explanation of symbols

  10, 20 Vibration reduction device, 11 Control target, 12 Acceleration sensor, 13 Low pass filter, 14 Digital control system, 14a AD converter, 14b Controller, 14c DA converter, 15 Actuator, 16 FFT analyzer, 17 Sensor amplifier, 18 Amplifier , 21 Low frequency band controller, 22 High frequency band controller

Claims (5)

A method for designing a plurality of controllers, which is provided in an apparatus for reducing vibrations generated by a vibration source and controls the reduction of vibrations in a plurality of frequency bands, respectively.
For one controller of the plurality of controllers, a model error is obtained from a control target of the one controller in a state fed back by one or more other controllers excluding the one controller, and robust stability is determined using the model error. A design method for a controller of a vibration reduction apparatus, wherein the one controller is designed by obtaining a weight function satisfying A method for designing a plurality of controllers, which is provided in an apparatus for reducing vibrations generated by a vibration source and controls the reduction of vibrations in a plurality of frequency bands, respectively.
With respect to one controller among the plurality of controllers, a model error is obtained from a control target of the one controller in a state fed back by all other controllers except the one controller, and robust stability is obtained using the model error. A controller design method for a vibration reduction apparatus, wherein the one controller is designed by obtaining a weighting function that satisfies the function. A first frequency band controller for controlling the reduction of vibrations in the first frequency band and a second frequency band for controlling reduction of vibrations in the second frequency band, provided in an apparatus for reducing vibrations generated by the vibration source A controller design method,
In a state where the second frequency band controller is not present, a first frequency band model error is obtained from the control target of the first frequency band controller, and robust stability is obtained using the first frequency band model error. Designing the first frequency band controller to determine a first frequency weighting function to satisfy;
The frequency response in the state fed back by the first frequency band controller is regarded as a response of the actual control target, a second frequency band model error is obtained from the control target of the second frequency band controller, and the second frequency Designing a second frequency band controller using a band model error to determine a second frequency weighting function that satisfies robust stability; and
The frequency response in the state fed back by the second frequency band controller is regarded as the response of the actual control target, a new first frequency band model error is obtained from the control target of the first frequency band controller, and the first If the frequency weighting function satisfies the robust stability with respect to the first frequency band model error, the design of each controller is terminated.
On the other hand, when the first frequency weight function does not satisfy the robust stability with respect to the first frequency band model error, the first frequency weight function uses the first frequency band model error to satisfy the robust stability. Modifying the frequency weighting function of 1 and redesigning the first frequency band controller to go to the next fourth step;
Further, the frequency response in the state fed back by the first frequency band controller is regarded as the response of the actual control target, and a new second frequency band model error is obtained from the control target of the second frequency band controller, If the second frequency weighting function satisfies the robust stability against the second frequency band model error, the design of each controller is terminated,
On the other hand, when the second frequency weight function does not satisfy the robust stability with respect to the second frequency band model error, the second frequency weight function uses the second frequency band model error to satisfy the robust stability. Modifying the frequency weighting function of 2 and redesigning the second frequency band controller and returning to the third step, and a fourth step,
A controller design method for a vibration reducing apparatus, wherein the controllers are designed until the controllers satisfy robust stability with each other. A controller for a vibration reduction apparatus, which is designed by the method for designing a controller for a vibration reduction apparatus according to any one of claims 1 to 3. A vibration reducing apparatus comprising the controller according to claim 4.

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