第 4 章 実験による各コントロ ーラの性能検証
4.1 PID 制御
以下のグラフは PID 制御により，線形チャープ応答とその周波数解析結果，平行移動モード，円旋回移 動モードの実験をおこなった結果となる．
(a) Log-swept chirp signals of bottom joint (b) Log-swept chirp signals of middle joint
(c) Coherence of bottom joint (d) Coherence of middle joint
0 20 40 60 80 100 120
-40 -30 -20 -10 0 10 20 30
40 入力データ<根元関節> : PID
Time [s]
Angle [deg]
目標角度 計測角度
0 20 40 60 80 100 120
-40 -30 -20 -10 0 10 20 30
40 入力データ<中間関節> : PID
Time [s]
Angle [deg]
目標角度 計測角度
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : PID <根元関節>
Frequency [Hz]
Magnitude [-]
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : PID <中間関節>
Frequency [Hz]
Magnitude [-]
第 4 章 実験による各コントローラの性能検証 145
(a) Bottom joint (b) Middle jointFig.4-2 Frequency analysis of loop transfer function: PID
(a) Complementary sensitivity function of bottom joint (b) Complementary sensitivity function of middle joint
(c) Sensitivity function of bottom joint (d) Sensitivity function of middle joint Fig.4-3 Frequency analysis of complementary sensitivity function and sensitivity function: PID
10-2 10-1 100 101
-80 -60 -40 -20 0 20
40 一巡伝達関数 L : PID <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-100 -50 0 50
100 一巡伝達関数 L : PID <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-80 -70 -60 -50 -40 -30 -20 -10 0 10
20 相補感度関数 T : PID <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-60 -50 -40 -30 -20 -10 0 10
20 相補感度関数 T : PID <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-40 -30 -20 -10 0 10
20 感度関数 S : PID <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-70 -60 -50 -40 -30 -20 -10 0 10
20 感度関数 S : PID <中間関節>
Frequency [Hz]
Gain [dB]
(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-4 Translation mode experiment: PID
(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
-20 0 20 40 60
100 110 120 130 140 150 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm] ReferenceResponse
0 2 4 6 8 10 12 14 16
30 35 40 45 50 55
60 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 2 4 6 8 10 12 14 16
40 45 50 55 60 65 70
75 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
0 10 20 30 40 50 60 70 80
110 120 130 140 150 160 170
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
Reference Response
0 5 10 15 20
20 25 30 35 40 45 50 55 60
65 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 5 10 15 20
20 30 40 50 60 70 80
90 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
第 4 章 実験による各コントローラの性能検証 147
4.2 -Synthesis と外乱オブザーバの併用
以下のグラフは
-Synthesis と外乱オブザーバにより，線形チャープ応答とその周波数解析結果，平行移 動モード，円旋回移動モードの実験をおこなった結果となる．(a) Log-swept chirp signals of bottom joint (b) Log-swept chirp signals of middle joint
(c) Coherence of bottom joint (d) Coherence of middle joint Fig.4-6 Frequency experiment simulation:
-Synthesis and disturbance observer0 20 40 60 80 100 120
-40 -30 -20 -10 0 10 20 30
40 入力データ<根元関節> : mu-Synthesis & DOB
Time [s]
Angle [deg]
目標角度 計測角度
0 20 40 60 80 100 120
-40 -30 -20 -10 0 10 20 30
40 入力データ<中間関節> : mu-Synthesis & DOB
Time [s]
Angle [deg]
目標角度 計測角度
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : mu-Synthesis & DOB <根元関節>
Frequency [Hz]
Magnitude [-]
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : mu-Synthesis & DOB <中間関節>
Frequency [Hz]
Magnitude [-]
(a) Bottom joint (b) Middle joint
Fig.4-7 Frequency analysis of loop transfer function:
-Synthesis and disturbance observer(a) Complementary sensitivity function of bottom joint (b) Complementary sensitivity function of middle joint
(c) Sensitivity function of bottom joint (d) Sensitivity function of middle joint
10-2 10-1 100 101
-80 -60 -40 -20 0 20
40 一巡伝達関数 L : mu-Synthesis & DOB <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-40 -20 0 20 40
60 一巡伝達関数 L : mu-Synthesis & DOB <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-70 -60 -50 -40 -30 -20 -10 0 10
20 相補感度関数 T : mu-Synthesis & DOB <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-40 -30 -20 -10 0 10
20 相補感度関数 T : mu-Synthesis & DOB <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-40 -30 -20 -10 0 10
20 感度関数 S : mu-Synthesis & DOB <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-50 -40 -30 -20 -10 0 10
20 感度関数 S : mu-Synthesis & DOB <中間関節>
Frequency [Hz]
Gain [dB]
第 4 章 実験による各コントローラの性能検証 149
(a) Manipulator reference trajectory (b) End effector trajectory(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-9 Translation mode experiment:
-Synthesis and disturbance observer(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-10 Circular mode experiment:
-Synthesis and disturbance observer-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
-20 0 20 40 60
110 120 130 140 150 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm] ReferenceResponse
0 2 4 6 8 10 12 14 16
30 35 40 45 50 55
60 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 2 4 6 8 10 12 14 16
40 45 50 55 60 65 70
75 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
10 20 30 40 50
125 130 135 140 145 150 155
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
Reference Response
0 5 10 15 20
20 25 30 35 40 45 50 55 60
65 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 5 10 15 20
20 30 40 50 60 70 80
90 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
4.3 SAC
以下のグラフは SAC により，線形チャープ応答とその周波数解析結果，平行移動モード，円旋回移動モ ードの実験をおこなった結果となる．
(a) Log-swept chirp signals of bottom joint (b) Log-swept chirp signals of middle joint
(c) Coherence of bottom joint (d) Coherence of middle joint Fig.4-11 Frequency experiment simulation: SAC
0 20 40 60 80 100 120
-50 -40 -30 -20 -10 0 10 20 30 40
50 入力データ<根元関節> : SAC
Time [s]
Angle [deg]
目標角度 計測角度
0 20 40 60 80 100 120
-50 -40 -30 -20 -10 0 10 20 30 40
50 入力データ<中間関節> : SAC
Time [s]
Angle [deg]
目標角度 計測角度
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : SAC <根元関節>
Frequency [Hz]
Magnitude [-]
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : SAC <中間関節>
Frequency [Hz]
Magnitude [-]
第 4 章 実験による各コントローラの性能検証 151
(a) Bottom joint (b) Middle jointFig.4-12 Frequency analysis of loop transfer function: SAC
(a) Complementary sensitivity function of bottom joint (b) Complementary sensitivity function of middle joint
(c) Sensitivity function of bottom joint (d) Sensitivity function of middle joint Fig.4-13 Frequency analysis of complementary sensitivity function and sensitivity function: SAC
10-2 10-1 100 101
-60 -40 -20 0 20
40 一巡伝達関数 L : SAC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-40 -20 0 20 40
60 一巡伝達関数 L : SAC <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-50 -40 -30 -20 -10 0 10
20 相補感度関数 T : SAC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-30 -20 -10 0 10 20
30 相補感度関数 T : SAC <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-40 -30 -20 -10 0 10
20 感度関数 S : SAC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-50 -40 -30 -20 -10 0 10 20
30 感度関数 S : SAC <中間関節>
Frequency [Hz]
Gain [dB]
(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-14 Translation mode experiment: SAC
(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
-10 0 10 20 30 40 50 60 70
110 120 130 140 150 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm] ReferenceResponse
0 2 4 6 8 10 12 14 16
30 35 40 45 50 55
60 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 2 4 6 8 10 12 14 16
40 45 50 55 60 65 70
75 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
10 20 30 40 50
125 130 135 140 145 150 155
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
Reference Response
0 5 10 15 20
20 25 30 35 40 45 50 55
60 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 5 10 15 20
20 30 40 50 60 70 80
90 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
第 4 章 実験による各コントローラの性能検証 153
4.4 SMC
以下のグラフは 1 型サーボ系 SMC により，線形チャープ応答とその周波数解析結果，平行移動モード，
円旋回移動モードの実験をおこなった結果となる．
(a) Log-swept chirp signals of bottom joint (b) Log-swept chirp signals of middle joint
(c) Coherence of bottom joint (d) Coherence of middle joint Fig.4-16 Frequency experiment simulation: SMC
0 20 40 60 80 100 120
-50 -40 -30 -20 -10 0 10 20 30 40
50 入力データ<根元関節> : SMC
Time [s]
Angle [deg]
目標角度 計測角度
0 20 40 60 80 100 120
-40 -30 -20 -10 0 10 20 30 40
50 入力データ<中間関節> : SMC
Time [s]
Angle [deg]
目標角度 計測角度
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : SMC <根元関節>
Frequency [Hz]
Magnitude [-]
10-2 10-1 100 101
0 0.2 0.4 0.6 0.8 1
コヒーレンス : SMC <中間関節>
Frequency [Hz]
Magnitude [-]
(a) Bottom joint (b) Middle joint Fig.4-17 Frequency analysis of loop transfer function: SMC
(a) Complementary sensitivity function of bottom joint (b) Complementary sensitivity function of middle joint
(c) Sensitivity function of bottom joint (d) Sensitivity function of middle joint
10-2 10-1 100 101
-60 -40 -20 0 20
40 一巡伝達関数 L : SMC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-40 -20 0 20 40
60 一巡伝達関数 L : SMC <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-200 -100 0 100 200
Frequency [Hz]
Phase [deg]
10-2 10-1 100 101
-50 -40 -30 -20 -10 0 10
20 相補感度関数 T : SMC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-40 -30 -20 -10 0 10
20 相補感度関数 T : SMC <中間関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-35 -30 -25 -20 -15 -10 -5 0 5 10
15 感度関数 S : SMC <根元関節>
Frequency [Hz]
Gain [dB]
10-2 10-1 100 101
-60 -50 -40 -30 -20 -10 0 10
20 感度関数 S : SMC <中間関節>
Frequency [Hz]
Gain [dB]
第 4 章 実験による各コントローラの性能検証 155
(a) Manipulator reference trajectory (b) End effector trajectory(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-19 Translation mode experiment: SMC
(a) Manipulator reference trajectory (b) End effector trajectory
(c) Joint trajectory of bottom (d) Joint trajectory of middle Fig.4-20 Circular mode experiment: SMC
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
-20 0 20 40 60
110 120 130 140 150 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm] ReferenceResponse
0 2 4 6 8 10 12 14 16
30 35 40 45 50 55
60 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 2 4 6 8 10 12 14 16
40 45 50 55 60 65 70
75 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
-50 0 50 100
0 20 40 60 80 100 120 140 160
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
10 20 30 40 50
125 130 135 140 145 150 155
Start Position.
End Position.
Trajectory interpolation in workspace
Distance X [mm]
Distance Y [mm]
Reference Response
0 5 10 15 20
20 25 30 35 40 45 50 55 60
65 根元関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答
0 5 10 15 20
20 30 40 50 60 70 80
90 中間関節 角度応答
Time [s]
Angle [deg]
目標角度 角度応答