diff --git a/docs/active-damping.html b/docs/control-active-damping.html similarity index 88% rename from docs/active-damping.html rename to docs/control-active-damping.html index b5d9a85..c5774dd 100644 --- a/docs/active-damping.html +++ b/docs/control-active-damping.html @@ -1,10 +1,11 @@ +
- +stewart = initializeStewartPlatform(); @@ -355,10 +356,10 @@ G.OutputName = {'Vm1',
-The transfer function from actuator forces to force sensors is shown in Figure 1. +The transfer function from actuator forces to force sensors is shown in Figure 1.
-
Figure 1: Transfer function from the Actuator force \(F_{i}\) to the absolute velocity of the same leg \(v_{m,i}\) and to the absolute velocity of the other legs \(v_{m,j}\) with \(i \neq j\) in grey (png, pdf)
@@ -366,8 +367,8 @@ The transfer function from actuator forces to force sensors is shown in Figure <
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
@@ -392,10 +393,10 @@ Ga.OutputName = {'Vm1',
-The new dynamics from force actuator to force sensor is shown in Figure 2.
+The new dynamics from force actuator to force sensor is shown in Figure 2.
Figure 2: Transfer function from the Actuator force \(F_{i}\) to the absolute velocity sensor \(v_{m,i}\) (png, pdf)
The control is a performed in a decentralized manner.
@@ -418,10 +419,10 @@ The \(6 \times 6\) control is a diagonal matrix with pure proportional action on
-The root locus is shown in figure 3.
+The root locus is shown in figure 3.
@@ -442,11 +443,11 @@ We do not have guaranteed stability with Inertial control. This is because of th
We first initialize the Stewart platform without joint stiffness.
@@ -509,10 +510,10 @@ G.OutputName = {'Fm1',
-The transfer function from actuator forces to force sensors is shown in Figure 4.
+The transfer function from actuator forces to force sensors is shown in Figure 4.
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)
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
@@ -546,10 +547,10 @@ Ga.OutputName = {'Fm1',
-The new dynamics from force actuator to force sensor is shown in Figure 5.
+The new dynamics from force actuator to force sensor is shown in Figure 5.
Figure 5: Transfer function from the Actuator force \(F_{i}\) to the force sensor \(F_{m,i}\) (png, pdf)
The control is a performed in a decentralized manner.
@@ -572,17 +573,17 @@ The \(6 \times 6\) control is a diagonal matrix with pure integration action on
-The root locus is shown in figure 6 and the obtained pole damping function of the control gain is shown in figure 7.
+The root locus is shown in figure 6 and the obtained pole damping function of the control gain is shown in figure 7.
Figure 6: Root Locus plot with Decentralized Integral Force Feedback when considering the stiffness of flexible joints (png, pdf)
@@ -604,11 +605,11 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
We first initialize the Stewart platform without joint stiffness.
@@ -675,10 +676,10 @@ G.OutputName = {'Dm1',
-The transfer function from actuator forces to relative motion sensors is shown in Figure 8.
+The transfer function from actuator forces to relative motion sensors is shown in Figure 8.
Figure 8: Transfer function from the Actuator force \(F_{i}\) to the Relative Motion Sensor \(D_{m,j}\) with \(i \neq j\) (png, pdf)
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
@@ -713,10 +714,10 @@ Ga.OutputName = {'Dm1',
-The new dynamics from force actuator to relative motion sensor is shown in Figure 9.
+The new dynamics from force actuator to relative motion sensor is shown in Figure 9.
The control is a performed in a decentralized manner.
@@ -739,10 +740,10 @@ The \(6 \times 6\) control is a diagonal matrix with pure derivative action on t
-The root locus is shown in figure 10.
+The root locus is shown in figure 10.
@@ -763,12 +764,12 @@ Joint stiffness does increase the resonance frequencies of the system but does n
We first initialize the Stewart platform without joint stiffness.
@@ -800,8 +801,8 @@ controller = initializeController('type',
Let’s first identify the transmissibility and compliance in the open-loop case.
@@ -839,25 +840,25 @@ K_dvf = 1e4*s/(1
Figure 11: Obtained transmissibility for Open-Loop Control (Blue), Integral Force Feedback (Red) and Direct Velocity Feedback (Yellow) (png, pdf)
Figure 12: Obtained compliance for Open-Loop Control (Blue), Integral Force Feedback (Red) and Direct Velocity Feedback (Yellow) (png, pdf)
Figure 13: Frobenius norm of the Transmissibility and Compliance Matrices (png, pdf) Created: 2020-03-12 jeu. 18:06 Created: 2020-03-13 ven. 10:34
-Control architectures can be divided in different ways.
-
-It can depend on the sensor used:
-
-It can also depends on the control objective:
-
In this section, we wish to study the use of the High Authority Control - Low Authority Control (HAC-LAC) architecture on the Stewart platform.
-The control architectures are shown in Figures 1 and 2.
+The control architectures are shown in Figures 1 and 2.
@@ -369,7 +348,7 @@ First, the LAC loop is closed (the LAC control is described
+
Figure 1: HAC-LAC architecture with IFF
Figure 2: HAC-LAC architecture with DVF
We first initialize the Stewart platform.
@@ -417,8 +396,8 @@ payload = initializePayload('type',
We identify the transfer function from the actuator forces \(\bm{\tau}\) to the absolute displacement of the mobile platform \(\bm{\mathcal{X}}\) in three different cases:
@@ -430,8 +409,8 @@ We identify the transfer function from the actuator forces \(\bm{\tau}\) to the
We use the Jacobian to express the actuator forces in the cartesian frame, and thus we obtain the transfer functions from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\).
@@ -536,11 +515,11 @@ We then design a controller based on the transfer functions from \(\bm{\mathcal{
We design a diagonal controller with equal bandwidth for the 6 terms.
@@ -583,7 +562,7 @@ Kd_dvf = diag(1./abs(diag(freqresp(1
+
We identify the transmissibility and compliance of the system.
@@ -629,7 +608,7 @@ We identify the transmissibility and compliance of the system.
We design a diagonal controller with equal bandwidth for the 6 terms.
@@ -673,7 +652,7 @@ Kd_iff = diag(1./abs(diag(freqresp(1
+
We identify the transmissibility and compliance of the system.
@@ -719,7 +698,7 @@ We identify the transmissibility and compliance of the system.
Figure 10: Comparison of the norm of the Compliance matrices for the HAC-LAC architecture (png, pdf)
Figure 11: Comparison of the norm of the Transmissibility matrices for the HAC-LAC architecture (png, pdf)
-Let’s define the system as shown in figure 13.
+Let’s define the system as shown in figure 13.
Figure 13: General Control Architecture1.3 Obtained Damping
+1.3 Obtained Damping
1.4 Conclusion
+1.4 Conclusion
2 Integral Force Feedback
+2 Integral Force Feedback
-2.1 Identification of the Dynamics with perfect Joints
+2.1 Identification of the Dynamics with perfect Joints
2.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics
+2.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics
2.3 Obtained Damping
+2.3 Obtained Damping
2.4 Conclusion
+2.4 Conclusion
3 Direct Velocity Feedback
+3 Direct Velocity Feedback
-3.1 Identification of the Dynamics with perfect Joints
+3.1 Identification of the Dynamics with perfect Joints
3.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics
+3.2 Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics
3.3 Obtained Damping
+3.3 Obtained Damping
3.4 Conclusion
+3.4 Conclusion
4 Compliance and Transmissibility Comparison
+4 Compliance and Transmissibility Comparison
4.1 Initialization
+4.1 Initialization
4.2 Identification
+4.2 Identification
4.3 Results
+4.3 Results
Table of Contents
-
-
-
-
-
-
-
-1 HAC-LAC (Cascade) Control - Integral Control
+1 HAC-LAC (Cascade) Control - Integral Control
1.1 Introduction
+1.1 Introduction
1.2 Initialization
+1.2 Initialization
1.3 Identification
+1.3 Identification
1.3.1 HAC - Without LAC
+1.3.1 HAC - Without LAC
controller = initializeController('type', 'open-loop');
@@ -456,8 +435,8 @@ G_ol.OutputName = {'Dx',
-
1.3.2 HAC - IFF
+1.3.2 HAC - IFF
controller = initializeController('type', 'iff');
@@ -483,8 +462,8 @@ G_iff.OutputName = {'Dx',
-
1.3.3 HAC - DVF
+1.3.3 HAC - DVF
controller = initializeController('type', 'dvf');
@@ -511,8 +490,8 @@ G_dvf.OutputName = {'Dx',
-
1.4 Control Architecture
+1.4 Control Architecture
1.5 6x6 Plant Comparison
+1.5 6x6 Plant Comparison
1.6 HAC - DVF
+1.6 HAC - DVF
1.6.1 Plant
+1.6.1 Plant
1.6.2 Controller Design
+1.6.2 Controller Design
1.6.3 Obtained Performance
+1.6.3 Obtained Performance
1.7 HAC - IFF
+1.7 HAC - IFF
1.7.1 Plant
+1.7.1 Plant
1.7.2 Controller Design
+1.7.2 Controller Design
1.7.3 Obtained Performance
+1.7.3 Obtained Performance
1.8 Comparison
+1.8 Comparison
2 MIMO Analysis
+2 MIMO Analysis