diff --git a/docs/control-tracking.html b/docs/control-tracking.html index af26d3f..1b1b89c 100644 --- a/docs/control-tracking.html +++ b/docs/control-tracking.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
- +The control architecture is shown in Figure 1. @@ -349,8 +349,8 @@ Then, a diagonal (decentralized) controller \(\bm{K}_\mathcal{L}\) is used such
stewart = initializeStewartPlatform(); @@ -382,8 +382,8 @@ references = initializeReferences(stewart);
Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{L}\). @@ -406,8 +406,8 @@ G.OutputName = {'L1', '
The diagonal terms of the plant is shown in Figure 2. @@ -441,8 +441,8 @@ We see that the plant is decoupled at low frequency which indicate that decentra
The controller consists of: @@ -472,8 +472,8 @@ Kl = diag(1./diag(abs(freqresp(G, wc))))
t = linspace(0, 10, 1000); @@ -518,8 +518,8 @@ simout_D = simout;
Such control architecture is easy to implement and give good results. @@ -540,8 +540,8 @@ However, as \(\mathcal{X}\) is not directly measured, it is possible that import
The centralized controller takes the position error \(\bm{\epsilon}_\mathcal{X}\) as an inputs and generate actuator forces \(\bm{\tau}\) (see Figure 7). @@ -551,7 +551,7 @@ The signals are:
stewart = initializeStewartPlatform(); @@ -612,8 +612,8 @@ references = initializeReferences(stewart);
Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{L}\). @@ -643,8 +643,8 @@ G.OutputName = {'Dx', '
The pose error \(\bm{\epsilon}_\mathcal{X}\) is first converted in the frame of the leg by using the Jacobian matrix. @@ -665,8 +665,8 @@ Note here that the transformation from the pose error \(\bm{\epsilon}_\mathcal{X
We now multiply the plant by the Jacobian matrix as shown in Figure 8 to obtain a more diagonal plant. @@ -716,8 +716,8 @@ Thus \(J \cdot G(\omega = 0) = J \cdot \frac{\delta\bm{\mathcal{X}}}{\delta\bm{\
The controller consists of: @@ -755,8 +755,8 @@ The controller \(\bm{K} = \bm{K}_\mathcal{L} \bm{J}\) is computed.
A diagonal controller \(\bm{K}_\mathcal{X}\) take the pose error \(\bm{\epsilon}_\mathcal{X}\) and generate cartesian forces \(\bm{\mathcal{F}}\) that are then converted to actuators forces using the Jacobian as shown in Figure e 12. @@ -816,8 +816,8 @@ The final implemented controller is \(\bm{K} = \bm{J}^{-T} \cdot \bm{K}_\mathcal
We now multiply the plant by the Jacobian matrix as shown in Figure 12 to obtain a more diagonal plant. @@ -939,8 +939,8 @@ This control architecture can also give a dynamically decoupled plant if the Cen
The controller consists of: @@ -978,8 +978,8 @@ The controller \(\bm{K} = \bm{J}^{-T} \bm{K}_\mathcal{X}\) is computed.
The plant \(\bm{G}\) is pre-multiply by \(\bm{G}^{-1}(\omega = 0)\) such that the “shaped plant” \(\bm{G}_0 = \bm{G} \bm{G}^{-1}(\omega = 0)\) is diagonal at low frequency. @@ -1043,8 +1043,8 @@ The control architecture is shown in Figure 16.
The plant is pre-multiplied by \(\bm{G}^{-1}(\omega = 0)\).
@@ -1072,8 +1072,8 @@ The diagonal elements of the shaped plant are shown in Figure
-
We have that:
@@ -1147,8 +1147,8 @@ This error is much lower when using the diagonal control in the frame of the leg
Both control architecture gives similar results even tough the control in the Leg’s frame gives slightly better results.
@@ -1231,8 +1231,8 @@ Thus, this method should be quite robust against parameter variation (e.g. the p
Created: 2020-03-11 mer. 19:00 Created: 2020-03-11 mer. 19:012.6.3 Controller Design
+2.6.3 Controller Design
2.8 Conclusion
+2.8 Conclusion
3.1 Control Schematic
+3.1 Control Schematic