JP2016052082A - Controller design device, control design method and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To design a controller that suppresses error of signals observed at a control point or magnification of noise even when the transfer function of a control target system varies.SOLUTION: Non-negative approximation inverse matrix forming means 14 achieves amplitude spectra |g(ω)|,|x(ω)| of transfer function matrixes G, X with respect to a band for which a linear mixture process of an amplitude spectrum is assumed, and forms a non-negative approximation inverse matrix h(ω) so that the amplitude spectrum |x(ω)| of the transfer function matrix X is equal to or approximate to the multiplication result as the product of the amplitude spectrum |g(ω)| of the transfer function matrix G and the non-negative approximation inverse matrix h(ω). Inverse matrix forming means 15 forms an inverse matrix h(ω) for bands other than the above band by a conventional method. Controller matrix forming unit 12 forms a transfer function matrix Hc of a controller D by using the non-negative approximation inverse matrix h(ω) formed by the non-negative approximation inverse matrix forming means 14 and the inverse matrix h(ω) formed by the inverse matrix forming means 15.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a technique for constructing a control system such as an acoustic system, and in particular, a controller design apparatus, a controller design method, and a controller design method for designing a controller for presenting a desired signal to a control point of a system to be controlled. Regarding the program.

  Conventionally, it is known to use an inverse system to construct a control system such as an acoustic system. An inverse system is a system having the reverse characteristics of the system to be controlled. A desired control system can be constructed by appropriately designing a reverse system according to a predetermined purpose.

[Reverse system]
5 and 6 are conceptual diagrams for explaining the reverse system. 5 and 6, the system 100 outputs a signal X _out to input signal X _in the system 101, and outputs the signal Y _out to input signal Y _in, control target system 101 System B (control target system) to be

Referring to FIG. 5, a system 101 that is a system to be controlled B inputs a signal X _out output from the system 100 as a signal Y _in . In such systems 100 and 101, when the signal Y _out output from the system 101 matches or approximates the signal X _in input to the system 100, the system 100 is an inverse system of the system 101 that is the control target system B. A.

In addition, referring to FIG. 6, system 100 inputs signal Y _out output from system 101 as control target system B as signal X _in . In such systems 100 and 101, even when the signal X _out output from the system 100 matches or approximates the signal Y _in input to the system 101, the system 100 is the reverse of the system 101 that is the control target system B. System A.

FIG. 7 is a conceptual diagram illustrating a multi-input multi-output inverse system. FIG. 7 is an extension of the one-input one-output systems 100 and 101 shown in FIG. 5 to a multi-input / multi-output system. The system 102 inputs signals X _in1 , X _in2 ,..., X _inN and outputs signals X _out1 , X _out2 ,..., X _outM , and the system 103 outputs signals Y _in1 , Y _{in2 ,. ..} , Y _inM is input and signals Y _out1 , Y _out2 ,..., Y _outN are output, and the system 103 is a control target system B.

As shown in FIG. 7, the system 103 that is the control target system B uses signals X _out1 , X _out2 ,..., X _outM output from the system 102 as signals Y _in1 , Y _{in2 ,.} As each input. In such systems 102 and 103, the signals Y _out1 , Y _out2 ,..., Y _outN output from the system 103 _coincide with the signals X _in1 , X _{in2 ,.} Or when making it approximate, the system 102 becomes the reverse system A of the system 103 which is the system B to be controlled.

In FIG. 5, the purpose of designing the reverse system A is to make the signal Y _out output from the system 101 that is the control target system B coincide with the signal X _in input to the system 100 that is the reverse system A. . The point at which the output in this case is observed is called a control point. In FIG. 5, a point at which the signal _Yout output from the system 101 that is the control target system B is observed becomes a control point. Similarly, in FIG. 7, a point at which the signals Y _out1 , Y _out2 ,..., Y _outN output from the system 103 which is the control target system B are observed becomes a control point. Here, an input point of the system 101 which is the control target system B shown in FIG. 5, that is, a point where the signal Y _in is presented to the control point is set as a presentation point. Each input point of the system 103 which is the system B to be controlled shown in FIG. 7, that is, a point where the signals Y _in1 , Y _{in2 ,.}

[Acoustic system]
Next, the control target system and the reverse system will be described with an example of the acoustic system. In an acoustic system, an inverse system is used for processing such as sound field reproduction or room dereverberation removal. The system to be controlled is a sound field in which sound field reproduction is performed or a sound field in a room from which reverberation is removed.

  FIG. 8 is a conceptual diagram for explaining the control target system and the reverse system when the listening sound field is the control target system in the acoustic system, and corresponds to the multi-input / multi-output systems 102 and 103 shown in FIG. ing. As shown in FIG. 8, when a control system for performing sound field reproduction processing is constructed, the listening sound field becomes the control target system B. The system 103 which is the system B to be controlled is a listening sound field, and five speakers 104-1 to 104-5 and two microphones 105-1 and 105-2 are arranged. The listening position to be controlled (the positions of the microphones 105-1 and 105-2) is the control point.

  Assuming that control is performed using acoustic signals reproduced from the speakers 104-1 to 104-5 arranged in the listening sound field, the acoustic signals input to these speakers 104-1 to 104-5 are controlled by the system B to be controlled. The input signal to.

  In the sound field reproduction, the speakers 104-1 to 104-5 are referred to as secondary sound sources, and the system 103 that is the control target system B is approximated by a transfer function that is an index indicating acoustic propagation from each secondary sound source to the control point. Modeled. In this case, the controlled system B is expressed as a matrix of transfer functions (transfer function matrix) of control points × secondary sound sources. In the example of FIG. 8, the number of control points (the number of microphones 105-1 and 105-2) is 2, and the number of speakers 104-1 to 104-5 that are secondary sound sources is 5, The system B is expressed as a transfer function matrix having 2 rows and 5 columns composed of 2 × 5 = 10 elements.

[Controller]
When a desired acoustic signal is presented to these control points, the desired acoustic signal may be input to the inverse system A after the system 102 that is the inverse system A is appropriately designed. FIG. 9 is a conceptual diagram illustrating a controller D that imparts a desired acoustic characteristic to an input signal in an acoustic system. The controller D outputs an acoustic signal to the control target system B so that an acoustic signal having a desired acoustic characteristic is observed at the control point. In addition to the system 102 that is the reverse system A shown in FIG. 8, a desired acoustic characteristic is given to the input signal so that a desired acoustic signal is presented to the microphones 105-1 and 105-2 that are control points. Assume system 110, which is system C. That is, the system 111 that is the controller D includes the system C and the reverse system A.

  FIG. 10 is a conceptual diagram illustrating an example of calculating the transfer function matrix of the inverse system in the frequency domain when the listening sound field is the control target system in the acoustic system. In order to simplify the explanation, both the number of secondary sound sources and the number of control points are set to two. The system 109 which is the control target system B is a listening sound field, and two speakers 104-1 and 104-2 and two microphones 105-1 and 105-2 are arranged. The listening position to be controlled (the positions of the microphones 105-1 and 105-2) is the control point. The system 108 that is the controller D includes a system 106 that is a system C that imparts a desired acoustic characteristic to the input signal u, and a system 107 that is an inverse system A.

In FIG. 10, the signal input to the system 107 which is the controller D is u, the transfer function of the desired acoustic characteristic given to the input signal u is x _i , and the transfer function representing the system 107 which is the inverse system A is h. _ij , in the system 109 that is the system B to be controlled, the transfer function between the speaker 104-j, which is the jth secondary sound source, and the microphone 105-i, which is the ith control point, at _gij , the control point Let y _i be the observed acoustic signal. i = 1,2, j = 1,2. Here, the transfer function x _i of the system 106 that is the system C indicates a desired acoustic characteristic to be realized by an acoustic signal observed at the control point.

The inverse system design apparatus for obtaining the transfer function matrix of the inverse system A first transfers the transfer function g _ij (from the speaker 104-j as the j-th secondary sound source to the microphone 105-i as the i-th control point. ω). Specifically, the inverse system design apparatus obtains a frequency domain transfer function g _ij (ω) by measuring the impulse response and converting the impulse response into a frequency domain spectrum by discrete Fourier transform or the like.

ここで、ω_kは離散周波数ビンを示し、周波数領域の表現であることを明示するために記述される。 The relationship from the input signal u of the controller D to the acoustic signal y _i observed at the control point is expressed by the following equation for each discrete frequency bin.

Here, ω _k represents a discrete frequency bin and is described to clearly indicate that it is a frequency domain representation.

The inverse system design apparatus performs processing for the purpose of matching the observed acoustic signal y _i with the signal obtained by adding the transfer function x _i of the desired acoustic characteristic to the input signal u, as shown in the following equation. Do.

Each matrix element is a complex number. As shown in the following equation, the inverse system design apparatus uses the transfer function matrix of the control target system B having the transfer function g _ij (ω _k ) as an element, and calculates the transfer function h _ij (ω _k ) by inverse matrix calculation. A transfer function matrix of the inverse system A having as elements is obtained.

ここで、ｋは、時間領域の表現であることを明示するために記述される。 The inverse system design apparatus performs the calculation of Equation (3) for each discrete frequency bin ω _k . Then, the inverse system design apparatus returns the transfer function matrix of the inverse system A from the frequency domain to the time domain by discrete Fourier inverse transform or the like as shown in the following equation.

Here, k is described to clearly indicate that it is a time domain representation.

  Thus, the inverse system design apparatus obtains the transfer function matrix of the inverse system A, and the inverse system A is implemented as an FIR or IIR filter.

  As described above, the expression when the impulse response is converted into the spectrum in the frequency domain is a complex spectrum. Therefore, when designing the inverse system A in the frequency domain, it is assumed that the complex mixing process is a linear mixing process (a process in which a plurality of complex spectrum acoustic signals are mixed (synthesized) linearly at a control point). In many cases, the inverse of a complex matrix is calculated. This is because the inverse system A aims at a strict design that takes into account and compensates for both the phase and amplitude of the transfer function of the controlled system B. That is, the inverse system A is designed by assuming a linear mixing process of a complex spectrum expressed by phase and amplitude.

However, many of the control target systems B often do not hold the above-mentioned assumption (the linear mixing process of complex spectrum) due to various factors. For example, in the control target system B shown in FIG. 10, when the direction or position of the speakers 104-1 and 104-2 as the secondary sound source or the microphones 105-1 and 105-2 as the control points are slightly shifted. Even so, the transfer function g _ij of the control target system B changes.

FIG. 11 is a conceptual diagram for explaining an example in which the control points are the listener's ears 112-1 and 112-2 instead of the microphones 105-1 and 105-2 shown in FIG. 10 in the acoustic system. is there. In the system 109 that is the control target system B, the acoustic signal y _i is observed at the positions of the ears 112-1 and 112-2 that are control points, and the listener's head is used as the transfer function g _ij of the control target system B. A transfer function g _ij is used.

The sound field reproduction in the control target system B shown in FIG. 11 is referred to as binaural reproduction. Since the head-related transfer function g _ij between the speakers 104-1 and 104-2 and the ears 112-1 and 112-2, which are control points, changes depending on the shape of the listener's head or ear, etc. However, the transfer function g _ij of the control target system B also changes.

In the calculation example described with reference to FIG. 10, the inverse system A is strictly designed, and it is not considered that the transfer function g _ij of the control target system B changes. For this reason, the calculation example of FIG. 10 is vulnerable to changes in the transfer function g _ij of the control target system B.

From FIG. 10, it can be seen that, at the control point in the acoustic system, the synthesized acoustic signal y _i is obtained by superimposing the acoustic signals reproduced from the secondary sound source. When the transfer function g _ij of the control target system B changes and its phase is inverted, there arises a problem that the acoustic signal to be added is canceled or the acoustic signal to be canceled is added and amplified. . In particular, when an acoustic signal having a large amplitude is canceled in the opposite phase, if the phase is inverted, acoustic signals having a large amplitude are added to each other, and a large error and noise are generated.

  In order to solve such a problem, for example, a method of suppressing the amplitude of an acoustic signal and suppressing the expansion of an error and noise by inserting a regular term when calculating an inverse matrix is disclosed (for example, (Refer nonpatent literature 1).

  Further, a method of suppressing the amplitude of the acoustic signal and suppressing the expansion of the error and noise by singular value decomposition of the transfer function of the control target system B and ignoring the singular value having a large value among the singular values of the inverse matrix as 0 Is also disclosed (see, for example, Non-Patent Document 2).

H. Tokuno et al., “Inverse Filter of Sound Reproduction Systems of Virtual Acoustic Sources”, IEICE Trans., EA80-A, 5, 809-820, 1997. Nagata et al., “Sequential Relaxation Algorithm of Inverse Filter Adaptive to Environmental Changes in Sound Field Reproduction System”, IEICE (A), J86-A, 824-834, 2003.

  However, the methods of Non-Patent Documents 1 and 2 described above have a problem that an error and noise of an acoustic signal may be excessively suppressed depending on the frequency band. For this reason, the above-described methods of Non-Patent Documents 1 and 2 completely eliminate the problem that a large error and noise are generated in the acoustic signal observed at the control point in accordance with the change of the transfer function of the control target system B. It cannot be solved.

  Therefore, it has been desired to suppress the amplitude of the acoustic signal and suppress the expansion of the error and noise of the acoustic signal observed at the control point without depending on the frequency band. That is, even when the acoustic signal to be added is canceled or the acoustic signal to be canceled is added and amplified with the change in the transfer function of the control target system B, the controller that suppresses the cancellation and amplification. A design device was desired.

  Therefore, the present invention has been made to solve the above-described problems, and the purpose of the present invention is to reduce the error or noise of the signal observed at the control point even when the transfer function of the controlled system changes. It is an object of the present invention to provide a controller design device, a controller design method, and a program capable of designing a controller that suppresses expansion.

  In order to achieve the above object, the controller designing apparatus according to claim 1 is provided between a predetermined number of control points at which signals are observed and a predetermined number of presentation points that respectively present signals to the predetermined number of control points. A controller that outputs a predetermined signal to a control target system represented by a transfer function matrix, in order to match a characteristic of a signal observed at the control point of the control target system with a desired characteristic The controller comprising: a characteristic system represented by a transfer function matrix of: and an inverse system represented by the controlled object inverse matrix when an inverse matrix for the transfer function matrix of the controlled system is an inverse matrix to be controlled In the controller design apparatus for forming the transfer function matrix of the matrix, a matrix forming unit for forming the transfer function matrix of the controlled system and the transfer function matrix of the characteristic system for each frequency bin, and the matrix form An inverse matrix forming unit that forms an inverse matrix for the controller for each frequency bin based on the transfer function matrix for each frequency bin formed by the unit, and a controller for each frequency bin formed by the inverse matrix forming unit A controller matrix forming unit that forms a transfer function matrix of the controller based on an inverse matrix, and the inverse matrix forming unit determines whether or not the frequency of the frequency bin is a predetermined frequency When the frequency bin determining means and the frequency bin determining means determine that the frequency is a predetermined frequency, the amplitude spectrum of the transfer function matrix of the controlled system and the amplitude spectrum of the transfer function matrix of the characteristic system in the frequency bin are A first amplitude spectrum of the transfer function matrix of the characteristic system is obtained and an amplitude spectrum of the transfer function matrix of the controlled system is obtained. The first inverse matrix forming means for forming the first controller inverse matrix so as to approximate the product of the controller inverse matrix equal to or less than a predetermined threshold value, and the frequency bin determination means must be a predetermined frequency. A second inverse matrix forming unit that forms the controlled object inverse matrix when formed, and forms a product of the controlled object inverse matrix and the transfer function matrix of the characteristic system as a second controller inverse matrix; The controller matrix forming unit includes: a first controller inverse matrix formed by the first inverse matrix forming means; and a second controller inverse formed by the second inverse matrix forming means. Based on the matrix, a transfer function matrix of the controller is formed.

  The controller design device according to claim 2 is the controller design device according to claim 1, wherein the frequency bin determination means determines whether or not the frequency of the frequency bin is a predetermined frequency. The frequency bin is compared with a predetermined threshold value, and if the frequency is higher than the predetermined threshold value, it is determined that the frequency bin frequency is the predetermined frequency, and the frequency is the predetermined threshold value. When it is below, it is determined that the frequency of the frequency bin is not a predetermined frequency.

  The controller design device according to claim 3 is the controller design device according to claim 1 or 2, wherein the first inverse matrix forming means includes an amplitude spectrum of a transfer function matrix of the characteristic system, and the control The inverse matrix is formed so that the degree of divergence between the amplitude spectrum of the transfer function matrix of the target system and the product of the inverse matrix to be formed is minimized.

  Furthermore, the controller design method according to claim 4 is represented by a transfer function matrix between a predetermined number of control points at which signals are observed and a predetermined number of presentation points that respectively present signals to the predetermined number of control points. A controller that outputs a predetermined signal to the control target system, wherein the characteristics of the signal observed at the control point of the control target system are represented by a transfer function matrix for matching the desired characteristics. A transfer function matrix of the controller comprising: a characteristic system to be controlled; and an inverse system represented by the control target inverse matrix when the inverse matrix for the transfer function matrix of the control target system is the control target inverse matrix In the controller design method by the controller design apparatus, the transfer function matrix of the control target system and the transfer function matrix of the characteristic system are formed for each frequency bin, and each transfer for each frequency bin is performed. A first step of storing a function matrix in a storage unit; and reading out the transfer function matrix of the controlled system and the transfer function matrix of the characteristic system for each frequency bin from the storage unit, and the frequency of the frequency bin is a predetermined frequency A second step of determining whether the frequency bin is equal to the amplitude spectrum of the transfer function matrix of the system to be controlled in the frequency bin and the characteristic system when it is determined that the frequency of the frequency bin is the predetermined frequency The amplitude spectrum of the transfer function matrix of the characteristic system is equal to or equal to the product of the amplitude spectrum of the transfer function matrix of the controlled system and the first controller inverse matrix to be formed. A third step of forming an inverse matrix for the first controller to approximate below a threshold; If the frequency is determined not to be the predetermined frequency, the control object inverse matrix is formed, and the product of the control object inverse matrix and the transfer function matrix of the characteristic system is formed as a second controller inverse matrix. 4 and the first controller inverse matrix formed in the third step and the second controller inverse matrix formed in the fourth step, the transfer function matrix of the controller And a fifth step of forming.

  Furthermore, a program according to claim 5 causes a computer to function as the controller design device according to any one of claims 1 to 3.

  As described above, according to the present invention, it is possible to design a controller that suppresses signal error or noise expansion observed at a control point even when the transfer function of the control target system changes. It becomes possible.

It is the schematic which shows the hardware constitutions of the controller design apparatus by embodiment of this invention. It is a block diagram which shows the function structure of the control part in the controller design apparatus by embodiment of this invention. It is a flowchart which shows the process which forms the transfer function matrix of the controller by a control part. It is a flowchart which shows the process (process of step S305) which forms a nonnegative approximated inverse matrix. It is a conceptual diagram explaining a reverse system. It is a conceptual diagram explaining a reverse system. It is a conceptual diagram explaining the multi-input multi-output reverse system. In an acoustic system, it is a conceptual diagram explaining a controlled object system and a reverse system at the time of making a listening sound field into a controlled object system. It is a conceptual diagram explaining the controller which provides a desired acoustic characteristic to an input signal in an acoustic system. In an acoustic system, it is a figure explaining the example which calculates the transfer function matrix of an inverse system at the time of making a listening sound field into a control object system in a frequency domain. In an acoustic system, it is a key map explaining an example when a listener's ear is a control point of a controlled system.

  Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings. The present invention provides an insignificant frequency of phase information when a controller configured with a system (characteristic system) that imparts a desired characteristic to an input signal and an inverse system with respect to a control target system is designed in the frequency domain. Focusing on only the amplitude spectrum of the transfer function of the controlled system for the band, assuming its linear mixing process, and focusing on only the amplitude spectrum for the desired characteristics at each control point of the controlled system And The present invention also designs the controller so that the characteristics of the signal observed at each control point through the inverse system and the controlled system match or approximate the desired characteristics.

  As a result, the controller is designed by paying attention only to the amplitude spectrum for the insignificant frequency band of the phase information, so that the transfer functions of all elements constituting the transfer function matrix of the controller have non-negative coefficients. It will be. Therefore, the amplitude of the signal input from the controller to the controlled system during playback in the controlled system is suppressed, and as a result, the error of the signal observed at the control point or the expansion of noise is suppressed. Can do. Hereinafter, an acoustic system will be described as an example.

[Hardware configuration]
First, the hardware configuration of the controller design device according to the embodiment of the present invention will be described. FIG. 1 is a schematic diagram illustrating a hardware configuration of a controller design device according to an embodiment of the present invention. The controller design device 1 includes a CPU 51, a storage unit 52 including a ROM and a RAM for storing programs and tables, a storage device (hard disk device) 53 for storing application programs, tables and data, and the control. In accordance with the operation of the keyboard and mouse by the operator of the device design apparatus 1, an operation / input unit 54 for controlling input of predetermined data, and a display for outputting screen information for prompting the operator to perform data input operation, etc. An output interface unit 55 and a communication unit 56 that transmits and receives a program and data via a network such as the Internet are configured, and these components are connected to each other via a system bus 57.

  The storage device 53 includes an OS (operating system) program that provides basic functions of the controller design device 1 and a high-frequency band in which the amplitude information of the acoustic signal is important from the viewpoint of human direction perception based on the amplitude. By forming a transfer function matrix of the approximate solution, a controller design program for designing the controller D and various tables and data used in the controller design program are stored.

  The controller design program is read from the storage device 53 to the RAM of the storage unit 52 and executed by the CPU 51 when the controller design apparatus 1 performs processing. Various tables and data are generated with the execution of the controller design program, written by the CPU 51 from the RAM of the storage unit 52 to the storage device 53, and with the execution of the controller design program, the CPU 51 stores the storage device 53. To the RAM of the storage unit 52.

  Here, the OS program is executed by the CPU 51 and manages the storage unit 52, the storage device 53, the operation / input unit 54, the display output interface unit 55, and the communication unit 56 as basic functions of the controller design device 1. . The controller design program described above is executed in a state where the OS program is executed by the CPU 51.

  The control unit 50 includes a CPU 51 and a storage unit 52, and the CPU 51 reads and executes a controller design program stored in the storage device 53 to the storage unit 52, thereby performing overall control of the controller design device 1 as a whole. FIG. 1 shows a state where the controller design program is read from the storage device 53 to the storage unit 52. As described above, in the controller design device 1, the control unit 50 performs various processes according to the controller design program with the hardware configuration shown in FIG.

[Function configuration]
FIG. 2 is a block diagram showing a functional configuration of the control unit 50 in the controller design device 1 shown in FIG. 1, and a functional configuration when the control unit 50 shown in FIG. 1 executes processing of the controller design program. Is shown. The control unit 50 includes an initial matrix forming unit 10, an inverse matrix forming unit 11, a controller matrix forming unit 12, and a storage unit 52. The inverse matrix forming unit 11 includes frequency bin determining means 13, non-negative approximate inverse matrix forming means 14, and inverse matrix forming means 15.

[Process for forming transfer function matrix of controller D]
FIG. 3 is a flowchart showing a process for forming a transfer function matrix of the controller D by the control unit 50. Hereinafter, the components shown in FIG. 2 and the flowchart shown in FIG. 3 will be described using the acoustic system shown in FIGS. 10 and 11 as an example.

The initial matrix forming unit 10 transfers the transfer function of the control target system B from the speakers 104-1 and 104-2 as secondary sound sources to the microphones 105-1 and 105-2 as control points and the ears 112-1 and 112-2. Transfer function g ₁₁ (ω _k ) to g ₂₂ (ω _k )) and the transfer function of the system C (in the microphones 105-1 and 105-2 and the ears 112-1 and 112-2 as control points) Using the transfer function x ₁ (ω _k ), x ₂ (ω _k )) indicating the desired acoustic characteristics to be realized, the transfer function matrix of the control target system B and the system among the matrices shown in the equation (1) A C transfer function matrix is formed for each discrete frequency bin as an initial transfer function matrix (step S301).

Each matrix shown in the equation (1) means each matrix representing the relationship between the input signal u and the acoustic signal y _i observed at the control point. In the above equation (1), Y is a matrix whose elements are acoustic signals y ₁ (ω _k ) and y ₂ (ω _k ) observed at control points, and transfer functions g ₁₁ (ω _k ) to g ₂₂ (ω _k ) is the transfer function matrix of the system B to be controlled, G is the transfer function matrix of the inverse system A having the transfer functions h ₁₁ (ω _k ) to h ₂₂ (ω _k ) as elements, and the input signal u ( omega _k) the transfer function of the desired acoustic properties imparted to x ₁ (omega _k), when a matrix with x ₂ (omega _k) element is X, the equation (1) is a Y = GHXu = GHcu expressed. The transfer function matrix Hc is a matrix product obtained by multiplying the transfer function matrix H by the transfer function matrix X (Hc = HX), and is a transfer function matrix of the controller D as will be described later.

  That is, the controlled system B is represented by a transfer function matrix G, the inverse system A is represented by a transfer function matrix H, the system C is represented by a transfer function matrix X, and the controller D is represented by a transfer function matrix Hc. .

  In step S301, the initial matrix forming unit 10 forms the transfer function matrix G of the control target system B and the transfer function matrix of the system C for each discrete frequency bin. Then, the initial matrix forming unit 10 stores the transfer function matrices G and X formed in step S301 in the storage unit 52 for each discrete frequency bin.

  The frequency bin determining unit 13 of the inverse matrix forming unit 11 reads the transfer function matrices G and X from the storage unit 52 for each discrete frequency bin, and performs the process of step S303 described later in ascending order from the discrete frequency bin having the lowest center frequency. At the same time, the non-negative approximate inverse matrix forming unit 14 is caused to perform the processing of steps S304 and S305 described later, and the inverse matrix forming unit 15 is performed to perform the processing of step S306 described later (step S302).

  The number of discrete frequency bins is assumed to be N, and numbers 1 to N are assigned to the discrete frequency bins in ascending order from the discrete frequency bin having the lowest center frequency. The frequency bin determining unit 13 performs processing up to i = 1,..., N in this order, and causes the non-negative approximate inverse matrix forming unit 14 and the inverse matrix forming unit 15 to perform processing.

  The frequency bin determining means 13 determines whether or not the i-th discrete frequency bin is the target discrete frequency bin, that is, whether or not the band assumes a linear mixing process of the amplitude spectrum considering only the amplitude (step). S303).

  For example, the frequency bin determination unit 13 compares the frequency of the i-th discrete frequency bin with a preset threshold value, and when the frequency is higher than the threshold value, the frequency bin determination unit 13 assumes a band assuming a linear mixing process of the amplitude spectrum. If the frequency is equal to or lower than the threshold, it is determined that the frequency band is not a band assuming a linear mixing process of the amplitude spectrum.

  In general, human direction perception emphasizes phase information such as interaural phase difference at low frequencies, and emphasizes amplitude information such as interaural level differences at high frequencies. That is, as the frequency increases, the importance shifts from phase information to amplitude information. Therefore, the control unit 50 uses a frequency at which the phase information is not important as a threshold, and when the center frequency of the discrete frequency bin is higher than the threshold, the frequency is a band assuming a linear mixing process of the amplitude spectrum. Therefore, even if the phase is ignored, it is assumed that the band is not significantly affected from the viewpoint of human direction perception, and in step S304, step S305, and step S307, which will be described later, based on only the amplitude information, the transmission of the controller D A function matrix Hc is formed.

  Further, the frequency bin determining means 13 compares the frequency of the i-th discrete frequency bin with a preset threshold value, and if the frequency is within a threshold range that defines a predetermined bandwidth, linear mixing of the amplitude spectrum It may be determined that the band is assumed to be a process, and if the frequency is not within the range of a threshold that defines a predetermined bandwidth, it may be determined that the band is not assumed to be a linear mixing process of the amplitude spectrum.

  Further, the frequency bin determining means 13 compares the frequency of the i-th discrete frequency bin with a preset threshold value, and if the frequency is outside the threshold value range that defines a predetermined bandwidth, linear mixing of the amplitude spectrum It may be determined that the band is assumed to be a process, and if the frequency is not outside the range of a threshold that defines a predetermined bandwidth, it may be determined that the band is not assumed to be a linear mixing process of the amplitude spectrum.

  When the frequency bin determination unit 13 determines in step S303 that the i-th discrete frequency bin is the target discrete frequency bin (step S303: Y), the transmission of the i-th discrete frequency bin read from the storage unit 52 is performed. The function matrices G and X are output to the non-negative approximate inverse matrix forming unit 14 to cause the non-negative approximate inverse matrix forming unit 14 to perform the processes of Step S304 and Step S305 described later.

  On the other hand, when the frequency bin determination unit 13 determines in step S303 that the i-th discrete frequency bin is not the target discrete frequency bin (step S303: N), the frequency bin determination unit 13 determines the i-th discrete frequency bin read from the storage unit 52. The transfer function matrices G and X are output to the inverse matrix forming means 15, and the inverse matrix forming means 15 is caused to perform the process of step S306 described later.

When the frequency bin determining unit 13 determines that the non-negative approximate inverse matrix forming unit 14 is the target discrete frequency bin in step S303, the non-negative approximate inverse matrix forming unit 14 transfers the i-th discrete frequency bin transfer function matrix G from the frequency bin determining unit 13. , X. Then, the non-negative approximate inverse matrix forming unit 14 calculates the amplitude spectra | g (ω) | and | x (ω) | of the input transfer function matrices G and X of the i-th discrete frequency bin as shown in the following equation. Obtain (step S304). That is, the non-negative approximate inverse matrix forming unit 14 calculates the absolute value of each element constituting the transfer function matrices G and X of the i-th discrete frequency bin.

As shown in the following equation, the nonnegative approximate inverse matrix forming unit 14 determines that the amplitude spectrum | x (ω) | of the transfer function matrix X is equal to the amplitude spectrum | g (ω) | of the transfer function matrix G and the (negative) A non-negative approximate inverse matrix h _c (ω) is formed so as to be the same as or approximate to the multiplication result that is the product of the matrix (non-negative approximate inverse matrix, controller inverse matrix) h _c (ω) (step consisting of non-elements) (step S305). Details of the processing in step S305 will be described later.

  Note that the amplitude spectrum | x (ω) | approximates the multiplication result means that the difference between the two data is equal to or less than a predetermined threshold value. The equation (7) is derived from the equations (1) and (2).

Here, the non-negative approximated inverse matrix h _c (ω) is expressed by the following expression, and indicates a multiplication result (Hc = HX) that is a product of the transfer function matrix H of the inverse system A and the transfer function matrix X of the system C. .

The nonnegative approximate inverse matrix forming unit 14 stores the nonnegative approximate inverse matrix h _c (ω) formed in step S 305 in the storage unit 52.

When the frequency bin determining unit 13 determines that the inverse matrix forming unit 15 is not the target discrete frequency bin in step S303, the inverse matrix forming unit 15 obtains the transfer function matrices G and X of the i-th discrete frequency bin from the frequency bin determining unit 13. input. Then, the inverse matrix forming means 15 forms the inverse matrix h _c (ω) by other means different from the processes in steps S304 and S305 (step S306).

For example, the inverse matrix forming means 15 performs the transfer function matrix H of the inverse system A (inverse matrix (control to the transfer function matrix G of the control target system B) by the conventional method described in the equations (1) to (4). The inverse matrix h _c (ω) is formed by multiplying the transfer function matrix H of the inverse system A by the transfer function matrix X of the system C according to the equation (8). Then, the inverse matrix forming means 15 stores the inverse matrix (inverse matrix for controller) h _c (ω) formed in step S306 in the storage unit 52.

The controller matrix forming unit 12 reads the non-negative approximate inverse matrix h _c (ω) and the inverse matrix h _c (ω) from the storage unit 52 after the processing of Step S303 to Step S306 for the number of discrete frequency bins is completed, These are arranged in order of frequency to form the transfer function matrix Hc of the controller D (step S307). The controller matrix forming unit 12 stores the formed transfer function matrix Hc of the controller D in the storage unit 52.

[Process for forming non-negative approximated inverse matrix h _c (ω)]
Next, details of the process of forming the nonnegative approximate inverse matrix h _c (ω) shown in step S305 of FIG. 3 will be described. As described above, in step S305, the non-negative approximated inverse matrix forming unit 14 converts the amplitude spectrum | x (ω) | of the transfer function matrix X into the amplitude spectrum | g of the transfer function matrix G as shown in the equation (7). The nonnegative approximate inverse matrix h _c (ω) is formed so as to be the same as or approximate to the multiplication result that is the product of (ω) | and the nonnegative approximate inverse matrix h _c (ω).

FIG. 4 is a flowchart showing the process of forming the nonnegative approximate inverse matrix h _c (ω) (the process of step S305). The process of FIG. 4 is an example of a process for forming the nonnegative approximate inverse matrix h _c (ω), and is an example using supervised nonnegative matrix factorization. In the present invention, the process of forming the nonnegative approximate inverse matrix h _c (ω) is not limited to the process of FIG. 4, and other methods may be used.

ｍ，ｎは、各行列を構成する要素の番号を示す。 First, as shown in the following equation, the non-negative approximate inverse matrix forming unit 14 determines the amplitude spectrum | x (ω) | of the transfer function matrix X of the system C and the amplitude spectrum | g of the transfer function matrix G of the controlled system B. A reference expression D (deviation degree D) indicating a deviation degree between the multiplication result which is a product of (ω) | and a non-negative approximate inverse matrix h _c (ω) is set (step S401).

m and n indicate the numbers of elements constituting each matrix.

  The equation (9) is an equation representing the square of the Frobenius norm, and | · | representing the amplitude response and ω representing the discrete frequency bin are omitted. The minimization of Equation (9) becomes a nonlinear optimization problem with non-negative value restriction. This solution is not particularly defined, but for example, a solution is obtained using an auxiliary function A described later. The present invention is not limited to solving Equation (9) using an auxiliary function A described later, and other solution methods may be used.

λ_mnは変数である。 The non-negative approximate inverse matrix forming unit 14 sets Expression (10) as an example of the auxiliary function A with respect to the divergence degree D shown in Expression (9) (Step S402). The auxiliary function A is used instead of the divergence degree D in the minimization process described later.

λ _mn is a variable.

The auxiliary function A shown in the equation (10) is already known, and for example, refer to the following document.
“Hirokazu Kameoka,“ Nonnegative matrix factorization ”, Measurement and Control, Vol. 51, No. 9, p. 835-844, September 2012”
The auxiliary function A shown in the equation (10) is just an example, and the non-negative approximate inverse matrix forming unit 14 may set another auxiliary function.

  The non-negative approximate inverse matrix forming unit 14 performs the minimizing process of the auxiliary function A (the process of Steps S403 to S406 described later) instead of the process of minimizing the divergence degree D unless the condition of Step S406 described later is satisfied. Is repeated (step S403).

The non-negative approximate inverse matrix forming unit 14 _obtains a variable λ _mn that minimizes the auxiliary function A, and sets the obtained variable λ _mn as the variable λ (step S404). Then, the non-negative approximate inverse matrix forming means 14 substitutes the variable λ for the variable λ _mn in the equation (10) to obtain the variable h _n that minimizes the auxiliary function A, and the obtained variable h _n is set as the variable h _c . (Step S405).

The non-negative approximate inverse matrix forming unit 14 substitutes the variable h _c obtained in step S405 for the variable h _n in the equation (9) to calculate the divergence degree D. Then, the non-negative approximate inverse matrix forming means 14 compares the calculated divergence degree D with a preset threshold value a, and the number of iterations in step S403 (the process of minimizing the auxiliary function A (the process of steps S403 to S406). ) Is compared with a preset threshold value b (step S406).

  If the nonnegative approximate inverse matrix forming unit 14 determines in step S406 that the degree of divergence D is less than the threshold value a, or if it is determined that the number of iterations exceeds the threshold value b (step S406: Y), the process proceeds to step S407. Transition. On the other hand, if the non-negative approximate inverse matrix forming unit 14 determines in step S406 that the divergence degree D is not less than the threshold value a and the number of iterations does not exceed the threshold value b (step S406: N), step The process proceeds to S403, and the auxiliary function A minimization process is repeated.

  That is, the non-negative approximate inverse matrix forming unit 14 repeats the minimization process of the auxiliary function A until the divergence degree D is less than the threshold value a or the number of iterations exceeds the threshold value b.

Nonnegative approximate inverse matrix forming means 14 shifts from step S406, the current obtained in step S405 the variable h _c nonnegative approximate inverse matrix (variable h _c determined last before the program proceeds from step S406) h _c (Ω) is formed (step S407).

As described above, according to the controller designing apparatus 1 according to the embodiment of the present invention, the initial matrix forming unit 10 performs the transfer function of the control target system B (transfer function g ₁₁ (secondary sound source to control point) ω _k ) to g ₂₂ (ω _k )) and the transfer function of system C (transfer functions x ₁ (ω _k ), x ₂ (ω _k ) indicating desired acoustic characteristics to be realized at the control point), As the initial transfer function matrix, the transfer function matrix G of the control target system B and the transfer function matrix X of the system C are formed for each discrete frequency bin.

Then, the frequency bin determining means 13 of the inverse matrix forming unit 11 determines whether or not the frequency of the discrete frequency bin is a band assuming a linear mixing process of the amplitude spectrum, and the non-negative approximated inverse matrix of the inverse matrix forming unit 11 When it is determined that the frequency of the discrete frequency bin is a band assuming a linear mixing process of the amplitude spectrum, the forming unit 14 determines the amplitude spectrum | g (ω) |, | x (ω) of the transfer function matrices G and X. | Is obtained and the absolute value of each element is calculated. As shown in the equation (7), the amplitude spectrum | x (ω) | of the transfer function X is equal to the amplitude spectrum | g (ω) | same or to approximate a multiplication result is a product of the approximate inverse matrix h _c (ω), and so as to form a non-negative approximate inverse matrix h _c (ω).

Further, the inverse matrix forming means 15 of the inverse matrix forming unit 11 determines that the frequency of the discrete frequency bin is not a band assuming a linear mixing process of the amplitude spectrum, and the inverse matrix h _c (ω) by a conventional method. To form. Then, after the processing for the number of discrete frequency bins is completed, the controller matrix forming unit 12 is formed by the nonnegative approximate inverse matrix h _c (ω) and the inverse matrix forming unit 15 formed by the nonnegative approximate inverse matrix forming unit 14. The inverse matrix h _c (ω) thus arranged is arranged in the order of frequency so as to form the transfer function matrix Hc of the controller D.

  Thus, the transfer function matrix Hc of the controller D is set to a high frequency band by setting a high frequency band where the amplitude information of the acoustic signal is important from the viewpoint of human direction perception as a band assuming a linear mixing process of the amplitude spectrum. Is formed on the basis of the absolute value of each element which is the amplitude spectrum | g (ω) |, | x (ω) | of the transfer function matrices G and X, the elements in the high frequency band are non-negative values. Become.

  That is, the controller design apparatus 1 is based on the amplitude instead of obtaining a strict transfer function matrix of the controller D using a conventional method for a high frequency band where amplitude information is important from the viewpoint of human direction perception. Since the transfer function matrix of the approximate solution is obtained, the amplitude of the transfer function of the controller D can be kept low.

In the conventional method, the transfer function matrix Hc of the controller D is formed using x (ω) = g (ω) h _c (ω) derived from the equations (1) and (2). When comparing the formula (7) used in the embodiment of the present invention, that is, the calculation formula based on the absolute value, with the formula x (ω) = g (ω) h _c (ω) used in the conventional method. In any case, the elements of the transfer function matrix X are calculated by adding the result of multiplying the elements of the transfer function matrix G by the elements of the transfer function matrix Hc. In the conventional method, the elements of the transfer function matrices G and X are positive and negative values including 0 as coefficients, whereas in the embodiment of the present invention, the elements of the transfer function matrices G and X are 0. Only positive values are included as coefficients. For this reason, since the elements of the transfer function matrix Hc in the embodiment of the present invention are limited in the process of multiplication and addition as compared with the conventional method, the amplitude thereof is small. That is, the amplitude of the transfer function of the controller D can be kept low.

  Therefore, since the amplitude of the transfer function of the controller D can be kept low, the amplitude of the signal input from the controller D to the controlled system B can also be kept low. As a result, even when the transfer function of the control target system B changes, acoustic signals with large amplitudes are not added to each other at the control point. The problem that noise is generated can be solved.

  The present invention has been described with reference to the embodiment. However, the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the technical idea thereof. In the embodiment, for the sake of simplicity, the number of speakers 104-1 and 104-2 that are secondary sound sources is two, and the number of microphones 105-1 and 105-2 that are control points is two. The present invention does not limit the number of secondary sound sources and control points.

  In the above-described embodiment, the acoustic system has been described as an example. However, the acoustic system is an example, and the present invention is applicable to a control system other than the acoustic system. For example, the present invention can be applied to a control system that controls the temperature of a plurality of control points or controls the humidity.

DESCRIPTION OF SYMBOLS 1 Controller design apparatus 10 Initial matrix formation part 11 Inverse matrix formation part 12 Controller matrix formation part 13 Frequency bin determination means 14 Non-negative approximate inverse matrix formation means 15 Inverse matrix formation means 50 Control part 51 CPU
52 Storage Unit 53 Storage Device 54 Operation / Input Unit 55 Display Output Interface Unit 56 Communication Unit 57 System Bus 100-103, 106, 107, 109, 110 System 104 Speaker 105 Microphone 108, 111 Controller 112 Ear

Claims (5)

A predetermined signal is output to the controlled system represented by a transfer function matrix between a predetermined number of control points at which signals are observed and a predetermined number of presentation points that respectively present signals to the predetermined number of control points. A characteristic system represented by a transfer function matrix for matching a characteristic of a signal observed at the control point of the control target system with a desired characteristic, and transmission of the control target system In a controller design device for forming a transfer function matrix of the controller, comprising an inverse system represented by the inverse matrix to be controlled when the inverse matrix for the function matrix is an inverse matrix to be controlled,
A matrix forming unit for forming a transfer function matrix of the controlled system and a transfer function matrix of the characteristic system for each frequency bin;
An inverse matrix forming unit that forms a controller inverse matrix for each frequency bin based on the respective transfer function matrix for each frequency bin formed by the matrix forming unit;
A controller matrix forming unit that forms a transfer function matrix of the controller based on the inverse matrix for the controller for each frequency bin formed by the inverse matrix forming unit, and
The inverse matrix forming unit includes:
A frequency bin determining means for determining whether or not the frequency of the frequency bin is a predetermined frequency;
When the frequency bin determining means determines that the frequency is a predetermined frequency, an amplitude spectrum of the transfer function matrix of the control target system and an amplitude spectrum of the transfer function matrix of the characteristic system in the frequency bin are acquired, and the characteristic system For the first controller so that the amplitude spectrum of the transfer function matrix of the first controller is approximated to be equal to or less than a predetermined threshold value with the product of the amplitude spectrum of the transfer function matrix of the controlled system and the inverse matrix for the first controller to be formed First inverse matrix forming means for forming an inverse matrix;
When the frequency bin determining means determines that the frequency is not a predetermined frequency, the control target inverse matrix is formed, and the product of the control target inverse matrix and the transfer function matrix of the characteristic system is used as a second controller inverse matrix. Second inverse matrix forming means for forming,
The controller matrix forming unit includes:
Based on the first controller inverse matrix formed by the first inverse matrix forming means and the second controller inverse matrix formed by the second inverse matrix forming means, the transfer function of the controller A controller design device characterized by forming a matrix. The controller design device according to claim 1,
The frequency bin determining means includes
When determining whether the frequency bin frequency is a predetermined frequency, the frequency bin frequency is compared with a predetermined threshold, and if the frequency is higher than the predetermined threshold, A controller design device that determines that the frequency is the predetermined frequency, and determines that the frequency of the frequency bin is not the predetermined frequency when the frequency is equal to or less than the predetermined threshold. The controller design device according to claim 1 or 2,
The first inverse matrix forming means includes:
Forming the inverse matrix so that the degree of divergence between the amplitude spectrum of the transfer function matrix of the characteristic system and the product of the amplitude spectrum of the transfer function matrix of the controlled system and the inverse matrix to be formed is minimized, A controller design device characterized by that. A predetermined signal is output to the controlled system represented by a transfer function matrix between a predetermined number of control points at which signals are observed and a predetermined number of presentation points that respectively present signals to the predetermined number of control points. A characteristic system represented by a transfer function matrix for matching a characteristic of a signal observed at the control point of the control target system with a desired characteristic, and transmission of the control target system In a controller design method by a controller design device for forming a transfer function matrix of the controller, comprising an inverse system represented by the inverse matrix to be controlled when an inverse matrix for the function matrix is an inverse matrix to be controlled,
Forming a transfer function matrix of the controlled system and a transfer function matrix of the characteristic system for each frequency bin, and storing each transfer function matrix for each frequency bin in a storage unit;
A second step of reading out the transfer function matrix of the control target system and the transfer function matrix of the characteristic system for each frequency bin from the storage unit, and determining whether the frequency of the frequency bin is a predetermined frequency;
When it is determined that the frequency of the frequency bin is the predetermined frequency, an amplitude spectrum of the transfer function matrix of the control target system and an amplitude spectrum of the transfer function matrix of the characteristic system in the frequency bin are acquired, and the characteristic system For the first controller so that the amplitude spectrum of the transfer function matrix of the first controller is approximated to be equal to or less than a predetermined threshold value with the product of the amplitude spectrum of the transfer function matrix of the controlled system and the inverse matrix for the first controller to be formed A third step of forming an inverse matrix;
When it is determined that the frequency of the frequency bin is not the predetermined frequency, the control target inverse matrix is formed, and the product of the control target inverse matrix and the transfer function matrix of the characteristic system is defined as a second controller inverse matrix. A fourth step of forming;
A fifth transfer function matrix for the controller is formed based on the first controller inverse matrix formed in the third step and the second controller inverse matrix formed in the fourth step. And the steps
A controller design method characterized by comprising:   A program for causing a computer to function as the controller design device according to any one of claims 1 to 3.

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