音響振動エネルギー制御工学特論2026

授業

第1回(2026.4.14)†

シラバス：シラバス詳細.pdf
本科目の目的：以下の研究について、文献を調査・議論することで現在の動向を理解する。
- (i)音響境界条件の能動制御（電力消費を許す）の研究（特にロバスト制御を用いて系統的な制御系設計を行っているもの）
  - Bothien et al. 2008:Active control of the acoustic boundary conditions of combustion test rigs
- (ii)発振を維持・促進させる受動制御（電力消費を許さない）の研究
  - Desjouy et al. 2010:Active control of thermoacoustic amplification in an annular engine

第1回の目的：2センサ法（2箇所の圧力計測で流速が分かる）を理解する
- 具体的には、篠田他2018 の (3)式、または Kobayashi et al.2019 の (23)式を理解する
- 参考資料：B2.pdf の 3.1節、3.2節、付録A, B
  - 複素振幅による調和振動の表現 ... 3.1節、式(2)
  - 圧力と粒子（体積）速度に関する基本の式 ... 付録A、式(27)と(31)

第2回(2026.4.21)†

Objective of this course: To understand current trends in the following research topics by investigating and discussing the literature.
- (i)Research on active control of acoustic boundary conditions (allowing power consumption) (particularly those involving systematic control system design using robust control).
- (ii)Research on passive control (without allowing power consumption) to maintain and promote oscillation
Objective of [Bothien et al. 2008]
- thermoacoustic instability
- simulated tube section (to simulate acoustic boundary conditions)
- two microphone method ... Eq.(16)
two microphone method (cont.)
- frequency response of time delay
- steady-state response
- traveling-wave sound field when ~B_2 = 0
- relation between the wave equation and ~p(x)

板書1

板書2

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第3回(2026.4.28)†

controller design? of [Bothien et al. 2008]
- first calculate the ideal frequency response, then approximate it to obtain the resultant state-space representation
- no consideration of closed-loop stability (manual tuning is necessary e.g. control gain Kg in [Bothien et al 2010])
review of classical and modern control theory in lec.#1, #2 of 授業/制御工学特論2025
- transfer functions / state-space representation
- system stability / poles / eigenvalues
- Bode plot / Nyquist plot ...

第4回(2026.5.19)†

literature survey for research on active control of acoustic boundary conditions : find papers that meet the following conditions:
- (i) active control system design for simulated tube is considered
- (ii) robust stability of closed-loop system against plant variations is considered
example (insufficient)
- Li et al. 2004:Dual-driver standing wave tube: acoustic impedance matching with robust repetitive control
  - acoustic impedance matching = acoustic boundary control
  - robust (repetitive) control = robust closed-loop stability is considered
  - BUT tonal excitation ... oscillation frequency is previously known
review of classical and modern control theory
- 2nd order system, poles, impulse response, ... ex0519_1.m mod0519_1.mdl

板書1

板書2

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第5回(2026.5.26)†

literature survey for research on active control of acoustic boundary conditions (cont.)
- (i) active control system design for simulated tube is considered
  - simulated tube is active acoustical system that simulates the behavior of a passive acoustical tube
- (ii) robust stability of closed-loop system against plant variations is considered
  - diffinition of H infinity norm ?

板書1

板書2

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第6回(2026.6.2)†

literature survey for research on active control of acoustic boundary conditions (cont.)
- (i) active control system design for simulated tube is considered
  - simulated tube is active acoustical system that simulates the behavior of a passive acoustical tube
- (ii) robust stability of closed-loop system against plant variations is considered
  - diffinition of H infinity norm ? ... this was not requirement for selecting papers
discussion on selected papers
example (insufficient)
- Cheng et al. 2018:Acoustic impedance tuning with active disturbance rejection control
  - (i) yes: simulated tube is considered
  - (ii) no: parameter tuning is necessary in ADRC

板書1

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第7回(2026.6.9)†

literature survey for research on active control of acoustic boundary conditions (cont.)
- (i) active control system design for simulated tube is considered
  - simulated tube is active acoustical system that simulates the behavior of a passive acoustical tube
- (ii) robust stability of closed-loop system against plant variations is considered
abount `simulated tube' for the 1st paper Bothien et al. 2008:Active control of the acoustic boundary conditions of combustion test rigs
- `simulated tube' is only named by Kobayashi (not the author) to represent the objective of the paper as in the sentences e.g. `the test rig length can be virtually extended' in abstract, and `the aim of the control scheme to be presented is to mimic certain prescribed impedances' in the explanation of Fig.1 on p.680.
- final goal is to develop full-scale engine with new burner generations such as a swirl-stabilized burner (in 2008),
- but the goal of the paper is, in the design stage, to provide an active control mean to change acoustic boundary condition without hardware changes.
discussion on selected papers
- Annaswamy et al. 2000:Thermoacoustic instability: model-based optimal control designs and experimental validation
  - active noise control to suppress pressure fluctuation by using single microphone and a loudspeaker ... simulated tube is not considered
  - additive uncertainties ΔP, H infinity control, mixed sensitivity problem ... robust control is considered
  - extends the results of [1]
- Zhao et al. 2018:A review of active control approaches in stabilizing combustion systems in aerospace industry
  - [152] is the 1st paper Bothien et al. 2008: `This can be overcome by applying an array of sensors, ...'
  - no mention for the `simulated tube' is given ... further survey is difficult

板書1

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!以下は過去の情報です!!!!!!!!!!!!!!!!!!!!!!!!!!

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第3回(2021.9.16)†

目的（つづき）：電力フィードバック型熱音響発電機の安定性解析用mファイルを理解する
- 管路部の周波数応答の算出 ... [篠田他2018](12)式
```
tmp = frd(exp(-1i*k*Ltube), w); % (20)式
Gtube_g = [0, tmp; tmp, 0];
```
- 回路部の周波数応答の算出 ... [篠田他2018](14)式
```
Z1 = Rinf;
Z2 = Rinf;
Z3 = R;
Tcirc = [1 + Z3/Z2, -(Z1 + Z2 + Z3)/(Z1*Z2); -Z3, 1 + Z3/Z1]; % (19)式
Gcirc = chain_inv(Tcirc); % その下の式
```
- コア部から見た管路の周波数応答の算出 ... [篠田他2018](15)式 &ref(): File not found: "chain_inv.m" at page "音響振動エネルギー制御工学特論2026";
```
Gother_g = lft(lft(chain_inv(H2p_g), Gcirc,  1, 1), lft(chain_inv(inv(H1_g)), Gtube_g, 1, 1), 1, 1); % (22)式
```
- ナイキストの安定判別に基づく発振周波数などの解析 &ref(): File not found: "nyquist_analysis_spline_frange_fixed.m" at page "音響振動エネルギー制御工学特論2026";
```
result{num} = nyquist_analysis_spline_frange_fixed(G_g*[0, 1; 1, 0]*Gother_g*[0, 1; 1, 0], 20, fmin(num), fmax(num))
```
```
function [s] = nyquist_analysis_spline_frange_fixed(L_g, m, fmin, fmax);
phi0_g = (1 - L_g(1,1))*(1 - L_g(2,2)) - L_g(1,2)*L_g(2,1);
```

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第4回(2021.9.27)†

目的2：相関法、フーリエ級数におけるフーリエ係数の導出（2018年度第6回(2018.7.3)参照)
伝達マトリクスと因果的システム表現 ... 小林、山田2017
- 例：長さlで断面が一様な管
- 伝達マトリクスに対応する伝達関数行列は非因果的
- 因果的システム表現(scattering matrix)

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ナイキストの安定判別とシミュレーション
- Matlabソース &ref(): File not found: "simu.m" at page "音響振動エネルギー制御工学特論2026";
- Simulinkモデル &ref(): File not found: "simple.mdl" at page "音響振動エネルギー制御工学特論2026";
- その他、必要なもの ... nyquistplot.m, setoptions.m

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第4回(2019.7.18)†

行列表現によるナイキスト安定判別：因果的システム表現を用いる場合と、伝達マトリクスを用いる場合
例題（Matlab）
- 定在波管の場合（前回の例と同一）&ref(): File not found: "simu_add.m" at page "音響振動エネルギー制御工学特論2026";
  - 因果的システム表現による解析結果は、前回と同一になる
  - 伝達マトリクスは、分割されたシステムに対して定義できない（解析不可）
- ループ管の場合 &ref(): File not found: "simu_loop.m" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "chain.m" at page "音響振動エネルギー制御工学特論2026";
  - 伝達マトリクスを因果的システムと誤って使用すると、意味のないナイキスト軌跡が得られる
  - 因果的システム表現による解析結果 ... 発振周波数が単純計算した共振周波数に合わないかも、■■■要検討■■■

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第5回(2019.7.25)†

第4回の補足：ナイキストの安定判別が単純計算したループ管の共振周波数に合わない理由 &ref(): File not found: "simu_loop_fixed.m" at page "音響振動エネルギー制御工学特論2026";
第3回の補足：「反射係数」が共振周波数に与える効果（複素数の場合）...電力フィードバックの共振周波数のヒント &ref(): File not found: "simu_comp_r.m" at page "音響振動エネルギー制御工学特論2026";
段付の管を含む共振周波数の計算 &ref(): File not found: "check_freqresp_calibration.m" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "freqresp_calibration.zip" at page "音響振動エネルギー制御工学特論2026";

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前回のつづき
- 粒子（体積）速度に関する基本の式(31)
- 特性音響インピーダンス
周波数応答実験結果とモデルの比較
- 周波数応答実験の結果（3年学生実験の装置）: &ref(): File not found: "spk1.dat" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "spk2.dat" at page "音響振動エネルギー制御工学特論2026";
- mファイル: &ref(): File not found: "freqresp_distx_p.m" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "p_tilde_down.m" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "p_tilde_up.m" at page "音響振動エネルギー制御工学特論2026";

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第3回(2018.5.9)†

管内の圧力分布（前回の続き）:&ref(): File not found: "freqresp_distx_p_fixed.m" at page "音響振動エネルギー制御工学特論2026";
- 周波数が高くなると、（圧力の）腹と節の数が増える
- マイクの位置が節に重なる周波数で、ゲイン特性が下向きのピークを示す
- wからz,yまでの周波数応答における違い：リファレンスマイクは何度も節を横切るが、エラーセンサは周波数が十分高くなって初めて節を横切る
- ...
むだ時間要素（導波管、2センサ法、指向性センサ、etc. の基本）の伝達関数と周波数応答

2センサ法による進行波圧力成分の計算 &ref(): File not found: "load_data_raw_AB_fixed_rows_changed_PCB.m" at page "音響振動エネルギー制御工学特論2026";

pc2_jw = frdata(:,4).*exp(i*pi/180.0*frdata(:,5))/pcb_coeff_12638; % 
ps1_jw = frdata(:,8).*exp(i*pi/180.0*frdata(:,9))/pcb_coeff_12992; % dummy
ps2_jw = frdata(:,2).*exp(i*pi/180.0*frdata(:,3))/pcb_coeff_12637; % 
pc1_jw = frdata(:,6).*exp(i*pi/180.0*frdata(:,7))/pcb_coeff_12991; % dummy

A1_jw = ( exp(-i*k*dl).*ps1_jw - exp(-i*k*(ls+dl)).*pc1_jw)./( 2*i*sin(k*ls));
B1_jw = (-exp( i*k*dl).*ps1_jw + exp( i*k*(ls+dl)).*pc1_jw)./( 2*i*sin(k*ls));
A2_jw = (-exp( i*k*dl).*ps2_jw + exp( i*k*(ls+dl)).*pc2_jw)./( 2*i*sin(k*ls));
B2_jw = ( exp(-i*k*dl).*ps2_jw - exp(-i*k*(ls+dl)).*pc2_jw)./( 2*i*sin(k*ls));

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第4回(2018.5.14)†

前回のつづき：2センサ法による進行波圧力成分の計算 ... https://doi.org/10.5687/iscie.28.392 (22)式の下の式

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第5回(2018.5.316.11)†

2センサ法の限界（特定の周波数では算出できない）

指向性センサの周波数帯域
/home/baba/spkcont/&ref(): File not found: "spkcont_app.c" at page "音響振動エネルギー制御工学特論2026"; (参考：&ref(): File not found: "spkcont_module.c" at page "音響振動エネルギー制御工学特論2026"; &ref(): File not found: "spkcont.h" at page "音響振動エネルギー制御工学特論2026";):

#ifdef PCB
    As1 = sqrt(msg->as1*msg->as1 + msg->bs1*msg->bs1) / PCB_COEFF_12638;
    Ac1 = sqrt(msg->ac1*msg->ac1 + msg->bc1*msg->bc1) / PCB_COEFF_12637;
    As2 = sqrt(msg->as2*msg->as2 + msg->bs2*msg->bs2) / PCB_COEFF_12992;
    Ac2 = sqrt(msg->ac2*msg->ac2 + msg->bc2*msg->bc2) / PCB_COEFF_12991;
#else // NAGANO_KEIKI
    As1 = sqrt(msg->as1*msg->as1 + msg->bs1*msg->bs1) * NAGANO_KEIKI_COEFF;
    Ac1 = sqrt(msg->ac1*msg->ac1 + msg->bc1*msg->bc1) * NAGANO_KEIKI_COEFF;
    As2 = sqrt(msg->as2*msg->as2 + msg->bs2*msg->bs2) * NAGANO_KEIKI_COEFF;
    Ac2 = sqrt(msg->ac2*msg->ac2 + msg->bc2*msg->bc2) * NAGANO_KEIKI_COEFF;
#endif
               
// Phase
Ps1 = atan(msg->bs1/msg->as1) + M_PI * (msg->as1 < 0);
Pc1 = atan(msg->bc1/msg->ac1) + M_PI * (msg->ac1 < 0);
Ps2 = atan(msg->bs2/msg->as2) + M_PI * (msg->as2 < 0);
Pc2 = atan(msg->bc2/msg->ac2) + M_PI * (msg->ac2 < 0);

A1 = sqrt(As1*As1 - 2*As1*Ac1*cos(k*L + Ps1 - Pc1) + Ac1*Ac1) / (2*fabs(sin(k*L)));
B1 = sqrt(As1*As1 - 2*As1*Ac1*cos(k*L + Pc1 - Ps1) + Ac1*Ac1) / (2*fabs(sin(k*L)));
A2 = sqrt(Ac2*Ac2 - 2*Ac2*As2*cos(k*L + Pc2 - Ps2) + As2*As2) / (2*fabs(sin(k*L)));
B2 = sqrt(Ac2*Ac2 - 2*Ac2*As2*cos(k*L + Ps2 - Pc2) + As2*As2) / (2*fabs(sin(k*L)));

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第6回(2018.7.3)†

前回のつづき

/home/baba/spkcont/&ref(): File not found: "spkcont_module.c" at page "音響振動エネルギー制御工学特論2026"; の一部

if(theta > 2*PERIODS*M_PI){
        theta -= 2*PERIODS*M_PI;
        msg->as1 = 2.* as1 / count;
        msg->bs1 = 2.* bs1 / count;
        msg->ac1 = 2.* ac1 / count;
        msg->bc1 = 2.* bc1 / count;
        msg->as2 = 2.* as2 / count;
        msg->bs2 = 2.* bs2 / count;
        msg->ac2 = 2.* ac2 / count;
        msg->bc2 = 2.* bc2 / count;

        as1 = 0;
        bs1 = 0;
        ac1 = 0;
        bc1 = 0;
        as2 = 0;
        bs2 = 0;
        ac2 = 0;
        bc2 = 0;
        msg->count = count;
        count = 0;
}
（略）
ad_conv(&y);

ps1 = y[1]; // / PCB_COEFF_12638;
pc1 = y[2]; // / PCB_COEFF_12637;
//              pc1 = y[0]; // / PCB_COEFF_12637;
pc2 = y[2]; // / PCB_COEFF_12991;
ps2 = y[3]; // / PCB_COEFF_12992;

as1 += ps1 * cos(theta);
bs1 -= ps1 * sin(theta);
ac1 += pc1 * cos(theta);
bc1 -= pc1 * sin(theta);
as2 += ps2 * cos(theta);
bs2 -= ps2 * sin(theta);
ac2 += pc2 * cos(theta);
bc2 -= pc2 * sin(theta);