diff --git a/docs/active-damping.html b/docs/active-damping.html index 5607b64..e88d9a2 100644 --- a/docs/active-damping.html +++ b/docs/active-damping.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Stewart Platform - Decentralized Active Damping @@ -271,25 +271,25 @@ for the JavaScript code in this tag.
  • 1. Inertial Control
  • 2. Integral Force Feedback
  • 3. Direct Velocity Feedback
    • @@ -322,11 +322,12 @@ stewart = initializeFramesPositions(stewart, 'H' stewart = generateGeneralConfiguration(stewart); stewart = computeJointsPose(stewart); stewart = initializeStrutDynamics(stewart); -stewart = initializeJointDynamics(stewart, 'disable', true); +stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p'); stewart = initializeCylindricalPlatforms(stewart); stewart = initializeCylindricalStruts(stewart); stewart = computeJacobian(stewart); stewart = initializeStewartPose(stewart); +stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3); @@ -362,20 +363,31 @@ The transfer function from actuator forces to force sensors is shown in Figure < -
    -

    1.2 Effect of the Flexible Joint stiffness on the Dynamics

    +
    +

    1.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics

    We add some stiffness and damping in the flexible joints and we re-identify the dynamics.

    -
    stewart = initializeJointDynamics(stewart);
+
    stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
 Gf = linearize(mdl, io, options);
 Gf.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
 Gf.OutputName = {'Vm1', 'Vm2', 'Vm3', 'Vm4', 'Vm5', 'Vm6'};
    +

    +We now use the amplified actuators and re-identify the dynamics +

    +
    +
    stewart = initializeAmplifiedStrutDynamics(stewart);
+Ga = linearize(mdl, io, options);
+Ga.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+Ga.OutputName = {'Vm1', 'Vm2', 'Vm3', 'Vm4', 'Vm5', 'Vm6'};
+
    +
    +

    The new dynamics from force actuator to force sensor is shown in Figure 2.

    @@ -388,8 +400,8 @@ The new dynamics from force actuator to force sensor is shown in Figure
    -
    -

    1.3 Obtained Damping

    +
    +

    1.3 Obtained Damping

    The control is a performed in a decentralized manner. @@ -403,7 +415,7 @@ The \(6 \times 6\) control is a diagonal matrix with pure proportional action on

    -The root locus is shown in figure 3 and the obtained pole damping function of the control gain is shown in figure 4. +The root locus is shown in figure 3.

    @@ -411,22 +423,15 @@ The root locus is shown in figure 3 and the obtained p

    Figure 3: Root Locus plot with Decentralized Inertial Control when considering the stiffness of flexible joints (png, pdf)

    - - -
    -

    pole_damping_gain_inertial_rot_stiffness.png -

    -

    Figure 4: Damping of the poles with respect to the gain of the Decentralized Inertial Control when considering the stiffness of flexible joints (png, pdf)

    -
    -
    -

    1.4 Conclusion

    +
    +

    1.4 Conclusion

    -Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors. +We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.

    @@ -442,8 +447,8 @@ Joint stiffness does increase the resonance frequencies of the system but does n

    -
    -

    2.1 Identification of the Dynamics with perfect Joints

    +
    +

    2.1 Identification of the Dynamics with perfect Joints

    We first initialize the Stewart platform without joint stiffness. @@ -454,12 +459,12 @@ stewart = initializeFramesPositions(stewart, 'H' stewart = generateGeneralConfiguration(stewart); stewart = computeJointsPose(stewart); stewart = initializeStrutDynamics(stewart); -stewart = initializeAmplifiedStrutDynamics(stewart); -stewart = initializeJointDynamics(stewart, 'disable', true); +stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p'); stewart = initializeCylindricalPlatforms(stewart); stewart = initializeCylindricalStruts(stewart); stewart = computeJacobian(stewart); stewart = initializeStewartPose(stewart); +stewart = initializeInertialSensor(stewart, 'type', 'none');

    @@ -487,25 +492,25 @@ G.OutputName = {'Fm1',

    -The transfer function from actuator forces to force sensors is shown in Figure 5. +The transfer function from actuator forces to force sensors is shown in Figure 4.

    iff_plant_coupling.png

    -

    Figure 5: Transfer function from the Actuator force \(F_{i}\) to the Force sensor of the same leg \(F_{m,i}\) and to the force sensor of the other legs \(F_{m,j}\) with \(i \neq j\) in grey (png, pdf)

    +

    Figure 4: Transfer function from the Actuator force \(F_{i}\) to the Force sensor of the same leg \(F_{m,i}\) and to the force sensor of the other legs \(F_{m,j}\) with \(i \neq j\) in grey (png, pdf)

    -
    -

    2.2 Effect of the Flexible Joint stiffness on the Dynamics

    +
    +

    2.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics

    We add some stiffness and damping in the flexible joints and we re-identify the dynamics.

    -
    stewart = initializeJointDynamics(stewart);
+
    stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
 Gf = linearize(mdl, io, options);
 Gf.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
 Gf.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
@@ -513,19 +518,30 @@ Gf.OutputName = {'Fm1', 
 
 
    
-The new dynamics from force actuator to force sensor is shown in Figure 6.
+We now use the amplified actuators and re-identify the dynamics
+
    
+
    
+
    stewart = initializeAmplifiedStrutDynamics(stewart);
+Ga = linearize(mdl, io, options);
+Ga.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+Ga.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
+
    
+
    
+
+
    
+The new dynamics from force actuator to force sensor is shown in Figure 5.
 
    
 
 
    
 
    iff_plant_flexible_joint_decentralized.png
 
    
-
    Figure 6: Transfer function from the Actuator force \(F_{i}\) to the force sensor \(F_{m,i}\) (png, pdf)
    
+
    Figure 5: Transfer function from the Actuator force \(F_{i}\) to the force sensor \(F_{m,i}\) (png, pdf)
    -
    -

    2.3 Obtained Damping

    +
    +

    2.3 Obtained Damping

    The control is a performed in a decentralized manner. @@ -539,26 +555,26 @@ The \(6 \times 6\) control is a diagonal matrix with pure integration action on

    -The root locus is shown in figure 7 and the obtained pole damping function of the control gain is shown in figure 8. +The root locus is shown in figure 6 and the obtained pole damping function of the control gain is shown in figure 7.

    root_locus_iff_rot_stiffness.png

    -

    Figure 7: Root Locus plot with Decentralized Integral Force Feedback when considering the stiffness of flexible joints (png, pdf)

    +

    Figure 6: Root Locus plot with Decentralized Integral Force Feedback when considering the stiffness of flexible joints (png, pdf)

    pole_damping_gain_iff_rot_stiffness.png

    -

    Figure 8: Damping of the poles with respect to the gain of the Decentralized Integral Force Feedback when considering the stiffness of flexible joints (png, pdf)

    +

    Figure 7: Damping of the poles with respect to the gain of the Decentralized Integral Force Feedback when considering the stiffness of flexible joints (png, pdf)

    -
    -

    2.4 Conclusion

    +
    +

    2.4 Conclusion

    @@ -579,8 +595,8 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib

    -
    -

    3.1 Identification of the Dynamics with perfect Joints

    +
    +

    3.1 Identification of the Dynamics with perfect Joints

    We first initialize the Stewart platform without joint stiffness. @@ -591,11 +607,12 @@ stewart = initializeFramesPositions(stewart, 'H' stewart = generateGeneralConfiguration(stewart); stewart = computeJointsPose(stewart); stewart = initializeStrutDynamics(stewart); -stewart = initializeJointDynamics(stewart, 'disable', true); +stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p'); stewart = initializeCylindricalPlatforms(stewart); stewart = initializeCylindricalStruts(stewart); stewart = computeJacobian(stewart); stewart = initializeStewartPose(stewart); +stewart = initializeInertialSensor(stewart, 'type', 'none');

    @@ -623,26 +640,26 @@ G.OutputName = {'Dm1',

    -The transfer function from actuator forces to relative motion sensors is shown in Figure 9. +The transfer function from actuator forces to relative motion sensors is shown in Figure 8.

    dvf_plant_coupling.png

    -

    Figure 9: Transfer function from the Actuator force \(F_{i}\) to the Relative Motion Sensor \(D_{m,j}\) with \(i \neq j\) (png, pdf)

    +

    Figure 8: Transfer function from the Actuator force \(F_{i}\) to the Relative Motion Sensor \(D_{m,j}\) with \(i \neq j\) (png, pdf)

    -
    -

    3.2 Effect of the Flexible Joint stiffness on the Dynamics

    +
    +

    3.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics

    We add some stiffness and damping in the flexible joints and we re-identify the dynamics.

    -
    stewart = initializeJointDynamics(stewart);
+
    stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
 Gf = linearize(mdl, io, options);
 Gf.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
 Gf.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
@@ -650,19 +667,30 @@ Gf.OutputName = {'Dm1', 
 
 
    
-The new dynamics from force actuator to relative motion sensor is shown in Figure 10.
+We now use the amplified actuators and re-identify the dynamics
+
    
+
    
+
    stewart = initializeAmplifiedStrutDynamics(stewart);
+Ga = linearize(mdl, io, options);
+Ga.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+Ga.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
+
    
+
    
+
+
    
+The new dynamics from force actuator to relative motion sensor is shown in Figure 9.
 
    
 
 
    
 
    dvf_plant_flexible_joint_decentralized.png
 
    
-
    Figure 10: Transfer function from the Actuator force \(F_{i}\) to the relative displacement sensor \(D_{m,i}\) (png, pdf)
    
+
    Figure 9: Transfer function from the Actuator force \(F_{i}\) to the relative displacement sensor \(D_{m,i}\) (png, pdf)
    -
    -

    3.3 Obtained Damping

    +
    +

    3.3 Obtained Damping

    The control is a performed in a decentralized manner. @@ -676,26 +704,19 @@ The \(6 \times 6\) control is a diagonal matrix with pure derivative action on t

    -The root locus is shown in figure 11 and the obtained pole damping function of the control gain is shown in figure 12. +The root locus is shown in figure 10.

    root_locus_dvf_rot_stiffness.png

    -

    Figure 11: Root Locus plot with Direct Velocity Feedback when considering the Stiffness of flexible joints (png, pdf)

    -
    - - -
    -

    pole_damping_gain_dvf_rot_stiffness.png -

    -

    Figure 12: Damping of the poles with respect to the gain of the Direct Velocity Feedback when considering the Stiffness of flexible joints (png, pdf)

    +

    Figure 10: Root Locus plot with Direct Velocity Feedback when considering the Stiffness of flexible joints (png, pdf)

    -
    -

    3.4 Conclusion

    +
    +

    3.4 Conclusion

    @@ -709,7 +730,7 @@ Joint stiffness does increase the resonance frequencies of the system but does n

    Author: Dehaeze Thomas

    -

    Created: 2020-02-11 mar. 15:50

    +

    Created: 2020-02-11 mar. 18:04

    diff --git a/docs/control-study.html b/docs/control-study.html index 7feb15e..c285d38 100644 --- a/docs/control-study.html +++ b/docs/control-study.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Stewart Platform - Control Study @@ -382,7 +382,7 @@ Kl = Kl * eye(6);

    Author: Dehaeze Thomas

    -

    Created: 2020-02-11 mar. 15:50

    +

    Created: 2020-02-11 mar. 17:52

    diff --git a/docs/cubic-configuration.html b/docs/cubic-configuration.html index 973581e..b4da0d2 100644 --- a/docs/cubic-configuration.html +++ b/docs/cubic-configuration.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Cubic configuration for the Stewart Platform @@ -349,7 +349,7 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'
    -

    3d-cubic-stewart-aligned.png +

    3d-cubic-stewart-aligned.png

    Figure 1: Centered cubic configuration

    @@ -547,7 +547,7 @@ The Jacobian is estimated at the cube center.
    -

    3d-cubic-stewart-misaligned.png +

    3d-cubic-stewart-misaligned.png

    Figure 4: Not centered cubic configuration

    @@ -896,7 +896,7 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff

    -This Matlab function is accessible here. +This Matlab function is accessible here.

    @@ -1039,7 +1039,7 @@ stewart.platform_M.Mb = Mb;

    Author: Dehaeze Thomas

    -

    Created: 2020-02-11 mar. 15:50

    +

    Created: 2020-02-11 mar. 17:52

    diff --git a/docs/dynamics-study.html b/docs/dynamics-study.html index b454573..4d4564b 100644 --- a/docs/dynamics-study.html +++ b/docs/dynamics-study.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Stewart Platform - Dynamics Study @@ -742,7 +742,7 @@ G.OutputName = {'L1', '

    Author: Dehaeze Thomas

    -

    Created: 2020-02-11 mar. 15:50

    +

    Created: 2020-02-11 mar. 17:52

    diff --git a/docs/figs/dvf_plant_coupling.pdf b/docs/figs/dvf_plant_coupling.pdf index 559b032..4ef3ad3 100644 Binary files a/docs/figs/dvf_plant_coupling.pdf and b/docs/figs/dvf_plant_coupling.pdf differ diff --git a/docs/figs/dvf_plant_coupling.png b/docs/figs/dvf_plant_coupling.png index 54cf17f..c299080 100644 Binary files a/docs/figs/dvf_plant_coupling.png and b/docs/figs/dvf_plant_coupling.png differ diff --git a/docs/figs/dvf_plant_flexible_joint_decentralized.pdf b/docs/figs/dvf_plant_flexible_joint_decentralized.pdf index d72d4fe..27dff6f 100644 Binary files a/docs/figs/dvf_plant_flexible_joint_decentralized.pdf and b/docs/figs/dvf_plant_flexible_joint_decentralized.pdf differ diff --git a/docs/figs/dvf_plant_flexible_joint_decentralized.png b/docs/figs/dvf_plant_flexible_joint_decentralized.png index f791b73..4a5e31f 100644 Binary files a/docs/figs/dvf_plant_flexible_joint_decentralized.png and b/docs/figs/dvf_plant_flexible_joint_decentralized.png differ diff --git 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a/docs/identification.html +++ b/docs/identification.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Identification of the Stewart Platform using Simscape @@ -268,29 +268,29 @@ for the JavaScript code in this tag.

    Table of Contents