From cdecb2447035a3bd2b25e52a50731827ff9a2df8 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 16 Mar 2020 11:23:15 +0100 Subject: [PATCH] Merge few figures --- docs/control-tracking.html | 357 ++++++++---------- ...=> decentralized_reference_tracking_L.pdf} | Bin ...=> decentralized_reference_tracking_L.png} | Bin docs/figs/hybrid_control_Kl_plant.pdf | Bin 0 -> 276119 bytes docs/figs/hybrid_control_Kl_plant.png | Bin 0 -> 145970 bytes .../figs/hybrid_control_Kl_plant_diagonal.pdf | Bin 47059 -> 0 bytes .../figs/hybrid_control_Kl_plant_diagonal.png | Bin 72935 -> 0 bytes .../hybrid_control_Kl_plant_off_diagonal.pdf | Bin 186717 -> 0 bytes .../hybrid_control_Kl_plant_off_diagonal.png | Bin 92036 -> 0 bytes docs/figs/plant_centralized_L.pdf | Bin 0 -> 276119 bytes docs/figs/plant_centralized_L.png | Bin 0 -> 145970 bytes docs/figs/plant_centralized_SD.pdf | Bin 0 -> 318676 bytes docs/figs/plant_centralized_SD.png | Bin 0 -> 173379 bytes docs/figs/plant_centralized_X.pdf | Bin 0 -> 303984 bytes docs/figs/plant_centralized_X.png | Bin 0 -> 160859 bytes docs/figs/plant_centralized_diagonal_L.pdf | Bin 65816 -> 0 bytes docs/figs/plant_centralized_diagonal_L.png | Bin 81847 -> 0 bytes docs/figs/plant_centralized_diagonal_SD.pdf | Bin 88808 -> 0 bytes docs/figs/plant_centralized_diagonal_SD.png | Bin 107653 -> 0 bytes docs/figs/plant_centralized_diagonal_X.pdf | Bin 93718 -> 0 bytes docs/figs/plant_centralized_diagonal_X.png | Bin 97440 -> 0 bytes .../figs/plant_centralized_off_diagonal_L.pdf | Bin 187391 -> 0 bytes .../figs/plant_centralized_off_diagonal_L.png | Bin 91894 -> 0 bytes .../plant_centralized_off_diagonal_SD.pdf | Bin 212918 -> 0 bytes .../plant_centralized_off_diagonal_SD.png | Bin 113989 -> 0 bytes .../figs/plant_centralized_off_diagonal_X.pdf | Bin 188167 -> 0 bytes .../figs/plant_centralized_off_diagonal_X.png | Bin 97961 -> 0 bytes docs/figs/plant_decentralized_L.pdf | Bin 0 -> 275990 bytes docs/figs/plant_decentralized_L.png | Bin 0 -> 147593 bytes docs/figs/plant_decentralized_diagonal.pdf | Bin 47059 -> 0 bytes docs/figs/plant_decentralized_diagonal.png | Bin 72935 -> 0 bytes .../figs/plant_decentralized_off_diagonal.pdf | Bin 186717 -> 0 bytes .../figs/plant_decentralized_off_diagonal.png | Bin 92036 -> 0 bytes org/control-tracking.org | 269 +++++-------- 34 files changed, 252 insertions(+), 374 deletions(-) rename docs/figs/{control_measure_rotating_2dof.pdf => decentralized_reference_tracking_L.pdf} (100%) rename docs/figs/{control_measure_rotating_2dof.png => decentralized_reference_tracking_L.png} (100%) create mode 100644 docs/figs/hybrid_control_Kl_plant.pdf create mode 100644 docs/figs/hybrid_control_Kl_plant.png delete mode 100644 docs/figs/hybrid_control_Kl_plant_diagonal.pdf delete mode 100644 docs/figs/hybrid_control_Kl_plant_diagonal.png delete mode 100644 docs/figs/hybrid_control_Kl_plant_off_diagonal.pdf delete mode 100644 docs/figs/hybrid_control_Kl_plant_off_diagonal.png create mode 100644 docs/figs/plant_centralized_L.pdf create mode 100644 docs/figs/plant_centralized_L.png create mode 100644 docs/figs/plant_centralized_SD.pdf create mode 100644 docs/figs/plant_centralized_SD.png create mode 100644 docs/figs/plant_centralized_X.pdf create mode 100644 docs/figs/plant_centralized_X.png delete mode 100644 docs/figs/plant_centralized_diagonal_L.pdf delete mode 100644 docs/figs/plant_centralized_diagonal_L.png delete mode 100644 docs/figs/plant_centralized_diagonal_SD.pdf delete mode 100644 docs/figs/plant_centralized_diagonal_SD.png delete mode 100644 docs/figs/plant_centralized_diagonal_X.pdf delete mode 100644 docs/figs/plant_centralized_diagonal_X.png delete mode 100644 docs/figs/plant_centralized_off_diagonal_L.pdf delete mode 100644 docs/figs/plant_centralized_off_diagonal_L.png delete mode 100644 docs/figs/plant_centralized_off_diagonal_SD.pdf delete mode 100644 docs/figs/plant_centralized_off_diagonal_SD.png delete mode 100644 docs/figs/plant_centralized_off_diagonal_X.pdf delete mode 100644 docs/figs/plant_centralized_off_diagonal_X.png create mode 100644 docs/figs/plant_decentralized_L.pdf create mode 100644 docs/figs/plant_decentralized_L.png delete mode 100644 docs/figs/plant_decentralized_diagonal.pdf delete mode 100644 docs/figs/plant_decentralized_diagonal.png delete mode 100644 docs/figs/plant_decentralized_off_diagonal.pdf delete mode 100644 docs/figs/plant_decentralized_off_diagonal.png diff --git a/docs/control-tracking.html b/docs/control-tracking.html index 2b89ab4..22f7fbd 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"> - + Stewart Platform - Tracking Control @@ -248,42 +248,42 @@
  • 3. Hybrid Control Architecture - HAC-LAC with relative DVF
  • 4. Comparison of all the methods
  • @@ -351,11 +351,11 @@ The control configuration are compare in section 4.

    -
    -

    1.1 Control Schematic

    +
    +

    1.1 Control Schematic

    -The control architecture is shown in Figure 1. +The control architecture is shown in Figure 1.

    @@ -367,16 +367,16 @@ Then, a diagonal (decentralized) controller \(\bm{K}_\mathcal{L}\) is used such

    -
    -

    control_measure_rotating_2dof.png +

    +

    decentralized_reference_tracking_L.png

    Figure 1: Decentralized control for reference tracking

    -
    -

    1.2 Initialize the Stewart platform

    +
    +

    1.2 Initialize the Stewart platform

    % Stewart Platform
    @@ -407,8 +407,8 @@ references = initializeReferences(stewart);
     
    -
    -

    1.3 Identification of the plant

    +
    +

    1.3 Identification of the plant

    Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{\mathcal{L}}\). @@ -431,43 +431,29 @@ G.OutputName = {'L1', '

    -
    -

    1.4 Plant Analysis

    +
    +

    1.4 Plant Analysis

    -The diagonal terms of the plant is shown in Figure 2. +The diagonal and off-diagonal terms of the plant are shown in Figure 2.

    All the diagonal terms are equal. -

    - - -
    -

    plant_decentralized_diagonal.png -

    -

    Figure 2: Diagonal Elements of the Plant (png, pdf)

    -
    - -

    -The off-diagonal terms are shown in Figure 3. -

    - -

    We see that the plant is decoupled at low frequency which indicate that decentralized control may be a good idea.

    -
    -

    plant_decentralized_off_diagonal.png +

    +

    plant_decentralized_L.png

    -

    Figure 3: Diagonal Elements of the Plant (png, pdf)

    +

    Figure 2: Obtain Diagonal and off diagonal dynamics (png, pdf)

    -
    -

    1.5 Controller Design

    +
    +

    1.5 Controller Design

    The controller consists of: @@ -478,7 +464,7 @@ The controller consists of:

    -The obtained loop gains corresponding to the diagonal elements are shown in Figure 4. +The obtained loop gains corresponding to the diagonal elements are shown in Figure 3.

    @@ -491,13 +477,13 @@ Kl = diag(1./diag(abs(freqresp(G, wc))))

    loop_gain_decentralized_L.png

    -

    Figure 4: Loop Gain of the diagonal elements (png, pdf)

    +

    Figure 3: Loop Gain of the diagonal elements (png, pdf)

    -
    -

    1.6 Simulation

    +
    +

    1.6 Simulation

    Let’s define some reference path to follow. @@ -516,7 +502,7 @@ references = initializeReferences(stewart, 't',

    -The reference path is shown in Figure 5. +The reference path is shown in Figure 4.

    @@ -532,7 +518,7 @@ zlabel('Z [m]');

    tracking_control_reference_path.png

    -

    Figure 5: Reference path used for Tracking control (png, pdf)

    +

    Figure 4: Reference path used for Tracking control (png, pdf)

    @@ -558,7 +544,7 @@ simout_D = simout;

    1.7 Results

    -The reference path and the position of the mobile platform are shown in Figure 6. +The reference path and the position of the mobile platform are shown in Figure 5.

    @@ -577,27 +563,27 @@ zlim([0, inf]);

    decentralized_control_3d_pos.png

    -

    Figure 6: Reference path and Obtained Position (png, pdf)

    +

    Figure 5: Reference path and Obtained Position (png, pdf)

    decentralized_control_Ex.png

    -

    Figure 7: Position error \(\bm{\epsilon}_\mathcal{X}\) (png, pdf)

    +

    Figure 6: Position error \(\bm{\epsilon}_\mathcal{X}\) (png, pdf)

    decentralized_control_El.png

    -

    Figure 8: Position error \(\bm{\epsilon}_\mathcal{L}\) (png, pdf)

    +

    Figure 7: Position error \(\bm{\epsilon}_\mathcal{L}\) (png, pdf)

    -
    -

    1.8 Conclusion

    +
    +

    1.8 Conclusion

    Such control architecture is easy to implement and give good results. @@ -618,11 +604,11 @@ However, as \(\mathcal{X}\) is not directly measured, it is possible that import

    -
    -

    2.1 Control Schematic

    +
    +

    2.1 Control Schematic

    -The centralized controller takes the position error \(\bm{\epsilon}_\mathcal{X}\) as an inputs and generate actuator forces \(\bm{\tau}\) (see Figure 9). +The centralized controller takes the position error \(\bm{\epsilon}_\mathcal{X}\) as an inputs and generate actuator forces \(\bm{\tau}\) (see Figure 8). The signals are:

      @@ -636,7 +622,7 @@ The signals are:

      centralized_reference_tracking.png

      -

      Figure 9: Centralized Controller

      +

      Figure 8: Centralized Controller

      @@ -649,7 +635,7 @@ We can think of two ways to make the plant more diagonal that are described in s

      -Note here that the subtraction shown in Figure 9 is not a real subtraction. +Note here that the subtraction shown in Figure 8 is not a real subtraction. It is indeed a more complex computation explained in section 5.

      @@ -657,8 +643,8 @@ It is indeed a more complex computation explained in section -

      2.2 Initialize the Stewart platform

      +
      +

      2.2 Initialize the Stewart platform

      % Stewart Platform
      @@ -689,8 +675,8 @@ references = initializeReferences(stewart);
       
      -
      -

      2.3 Identification of the plant

      +
      +

      2.3 Identification of the plant

      -
      -

      2.4.1 Control Architecture

      +
      +

      2.4.1 Control Architecture

      The pose error \(\bm{\epsilon}_\mathcal{X}\) is first converted in the frame of the leg by using the Jacobian matrix. Then a diagonal controller \(\bm{K}_\mathcal{L}\) is designed. -The final implemented controller is \(\bm{K} = \bm{K}_\mathcal{L} \cdot \bm{J}\) as shown in Figure 10 +The final implemented controller is \(\bm{K} = \bm{K}_\mathcal{L} \cdot \bm{J}\) as shown in Figure 9

      @@ -737,16 +723,16 @@ Note here that the transformation from the pose error \(\bm{\epsilon}_\mathcal{X

      centralized_reference_tracking_L.png

      -

      Figure 10: Controller in the frame of the legs

      +

      Figure 9: Controller in the frame of the legs

      -
      -

      2.4.2 Plant Analysis

      +
      +

      2.4.2 Plant Analysis

      -We now multiply the plant by the Jacobian matrix as shown in Figure 10 to obtain a more diagonal plant. +We now multiply the plant by the Jacobian matrix as shown in Figure 9 to obtain a more diagonal plant.

      @@ -755,27 +741,17 @@ Gl.OutputName = {'D1',
      - -
      -

      plant_centralized_diagonal_L.png -

      -

      Figure 11: Diagonal Elements of the plant \(\bm{J} \bm{G}\) (png, pdf)

      -
      -

      -All the diagonal elements are identical. +The bode plot of the plant is shown in Figure 10. +We can see that the diagonal elements are identical. This will simplify the design of the controller as all the elements of the diagonal controller can be made identical.

      -

      -The off-diagonal terms of the controller are shown in Figure 12. -

      - -
      -

      plant_centralized_off_diagonal_L.png +

      +

      plant_centralized_L.png

      -

      Figure 12: Off Diagonal Elements of the plant \(\bm{J} \bm{G}\) (png, pdf)

      +

      Figure 10: Diagonal and off-diagonal elements of the plant \(\bm{K}\bm{G}\) (png, pdf)

      @@ -793,8 +769,8 @@ Thus \(J \cdot G(\omega = 0) = J \cdot \frac{\delta\bm{\mathcal{X}}}{\delta\bm{\

      -
      -

      2.4.3 Controller Design

      +
      +

      2.4.3 Controller Design

      The controller consists of: @@ -805,7 +781,7 @@ The controller consists of:

    -The obtained loop gains corresponding to the diagonal elements are shown in Figure 13. +The obtained loop gains corresponding to the diagonal elements are shown in Figure 11.

    @@ -818,7 +794,7 @@ Kl = diag(1./diag(abs(freqresp(Gl, wc))))

    loop_gain_centralized_L.png

    -

    Figure 13: Loop Gain of the diagonal elements (png, pdf)

    +

    Figure 11: Loop Gain of the diagonal elements (png, pdf)

    @@ -831,8 +807,8 @@ The controller \(\bm{K} = \bm{K}_\mathcal{L} \bm{J}\) is computed.

    -
    -

    2.4.4 Simulation

    +
    +

    2.4.4 Simulation

    We specify the reference path to follow. @@ -876,11 +852,11 @@ save('./mat/control_tracking.mat',

    -
    -

    2.5.1 Control Architecture

    +
    +

    2.5.1 Control Architecture

    -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 14. +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.

    @@ -891,16 +867,16 @@ The final implemented controller is \(\bm{K} = \bm{J}^{-T} \cdot \bm{K}_\mathcal

    centralized_reference_tracking_X.png

    -

    Figure 14: Controller in the cartesian frame

    +

    Figure 12: Controller in the cartesian frame

    -
    -

    2.5.2 Plant Analysis

    +
    +

    2.5.2 Plant Analysis

    -We now multiply the plant by the Jacobian matrix as shown in Figure 14 to obtain a more diagonal plant. +We now multiply the plant by the Jacobian matrix as shown in Figure 12 to obtain a more diagonal plant.

    @@ -910,10 +886,10 @@ Gx.InputName = {'Fx',
    -
    -

    plant_centralized_diagonal_X.png +

    +

    plant_centralized_X.png

    -

    Figure 15: Diagonal Elements of the plant \(\bm{G} \bm{J}^{-T}\) (png, pdf)

    +

    Figure 13: Diagonal and off-diagonal elements of the plant \(\bm{G} \bm{J}^{-T}\) (png, pdf)

    @@ -922,13 +898,6 @@ The resonances of the system are “decoupled”. For instance, the vertical resonance of the system is only present on the diagonal term corresponding to \(D_z/\mathcal{F}_z\).

    - -
    -

    plant_centralized_off_diagonal_X.png -

    -

    Figure 16: Off Diagonal Elements of the plant \(\bm{G} \bm{J}^{-T}\) (png, pdf)

    -
    -

    Here the system is almost decoupled at all frequencies except for the transfer functions \(\frac{R_y}{\mathcal{F}_x}\) and \(\frac{R_x}{\mathcal{F}_y}\).

    @@ -1019,8 +988,8 @@ This control architecture can also give a dynamically decoupled plant if the Cen
    -
    -

    2.5.3 Controller Design

    +
    +

    2.5.3 Controller Design

    The controller consists of: @@ -1031,7 +1000,7 @@ The controller consists of:

    -The obtained loop gains corresponding to the diagonal elements are shown in Figure 17. +The obtained loop gains corresponding to the diagonal elements are shown in Figure 14.

    @@ -1044,7 +1013,7 @@ Kx = diag(1./diag(abs(freqresp(Gx, wc))))

    loop_gain_centralized_X.png

    -

    Figure 17: Loop Gain of the diagonal elements (png, pdf)

    +

    Figure 14: Loop Gain of the diagonal elements (png, pdf)

    @@ -1057,8 +1026,8 @@ The controller \(\bm{K} = \bm{J}^{-T} \bm{K}_\mathcal{X}\) is computed.

    -
    -

    2.5.4 Simulation

    +
    +

    2.5.4 Simulation

    We specify the reference path to follow. @@ -1102,8 +1071,8 @@ save('./mat/control_tracking.mat',

    -
    -

    2.6.1 Control Architecture

    +
    +

    2.6.1 Control Architecture

    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. @@ -1114,24 +1083,24 @@ Then a diagonal controller \(\bm{K}_0\) is designed.

    -The control architecture is shown in Figure 18. +The control architecture is shown in Figure 15.

    centralized_reference_tracking_S.png

    -

    Figure 18: Static Decoupling of the Plant

    +

    Figure 15: Static Decoupling of the Plant

    -
    -

    2.6.2 Plant Analysis

    +
    +

    2.6.2 Plant Analysis

    The plant is pre-multiplied by \(\bm{G}^{-1}(\omega = 0)\). -The diagonal elements of the shaped plant are shown in Figure 19. +The diagonal and off-diagonal elements of the shaped plant are shown in Figure 16.

    @@ -1140,23 +1109,16 @@ The diagonal elements of the shaped plant are shown in Figure -

    plant_centralized_diagonal_SD.png +

    - - -
    -

    plant_centralized_off_diagonal_SD.png -

    -

    Figure 20: Off Diagonal Elements of the plant \(\bm{G} \bm{J}^{-T}\) (png, pdf)

    +

    Figure 16: Diagonal and off-diagonal elements of the plant \(\bm{G} \bm{G}^{-1}(\omega = 0)\) (png, pdf)

    -
    -

    2.6.3 Controller Design

    +
    +

    2.6.3 Controller Design

    We have that: @@ -1188,7 +1150,7 @@ We have that \(\bm{K}_0(s)\) commutes with \(\bm{G}^{-1}(\omega = 0)\) and thus

    centralized_control_comp_K.png

    -

    Figure 21: Comparison of the MIMO controller \(\bm{K}\) for both centralized architectures (png, pdf)

    +

    Figure 17: Comparison of the MIMO controller \(\bm{K}\) for both centralized architectures (png, pdf)

    @@ -1197,11 +1159,11 @@ We have that \(\bm{K}_0(s)\) commutes with \(\bm{G}^{-1}(\omega = 0)\) and thus

    2.7.2 Simulation Results

    -The position error \(\bm{\epsilon}_\mathcal{X}\) for both centralized architecture are shown in Figure 22. +The position error \(\bm{\epsilon}_\mathcal{X}\) for both centralized architecture are shown in Figure 18.

    -Based on Figure 22, we can see that: +Based on Figure 18, we can see that:

    • There is some tracking error \(\epsilon_x\)
    • @@ -1216,14 +1178,14 @@ This error is much lower when using the diagonal control in the frame of the leg

      centralized_control_comp_Ex.png

      -

      Figure 22: Comparison of the position error \(\bm{\epsilon}_\mathcal{X}\) for both centralized controllers (png, pdf)

      +

      Figure 18: Comparison of the position error \(\bm{\epsilon}_\mathcal{X}\) for both centralized controllers (png, pdf)

    -
    -

    2.8 Conclusion

    +
    +

    2.8 Conclusion

    Both control architecture gives similar results even tough the control in the Leg’s frame gives slightly better results. @@ -1306,11 +1268,11 @@ Thus, this method should be quite robust against parameter variation (e.g. the p

    -
    -

    3.1 Control Schematic

    +
    +

    3.1 Control Schematic

    -Let’s consider the control schematic shown in Figure 23. +Let’s consider the control schematic shown in Figure 19.

    @@ -1343,13 +1305,13 @@ This second loop is responsible for the reference tracking.

    hybrid_reference_tracking.png

    -

    Figure 23: Hybrid Control Architecture

    +

    Figure 19: Hybrid Control Architecture

    -
    -

    3.2 Initialize the Stewart platform

    +
    +

    3.2 Initialize the Stewart platform

    % Stewart Platform
    @@ -1384,8 +1346,8 @@ references = initializeReferences(stewart);
     

    3.3 First Control Loop - \(\bm{K}_\mathcal{L}\)

    -
    -

    3.3.1 Identification

    +
    +

    3.3.1 Identification

    Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{L}\). @@ -1408,31 +1370,24 @@ Gl.OutputName = {'L1',

    -
    -

    3.3.2 Obtained Plant

    +
    +

    3.3.2 Obtained Plant

    -The diagonal elements of the plant are shown in Figure 24 while the off diagonal terms are shown in Figure 25. +The obtained plant is shown in Figure 20.

    -
    -

    hybrid_control_Kl_plant_diagonal.png +

    +

    hybrid_control_Kl_plant.png

    -

    Figure 24: Diagonal elements of the plant for the design of \(\bm{K}_\mathcal{L}\) (png, pdf)

    -
    - - -
    -

    hybrid_control_Kl_plant_off_diagonal.png -

    -

    Figure 25: Off-diagonal elements of the plant for the design of \(\bm{K}_\mathcal{L}\) (png, pdf)

    +

    Figure 20: Diagonal and off-diagonal elements of the plant for the design of \(\bm{K}_\mathcal{L}\) (png, pdf)

    -
    -

    3.3.3 Controller Design

    +
    +

    3.3.3 Controller Design

    We apply a decentralized (diagonal) direct velocity feedback. @@ -1442,7 +1397,7 @@ The gain of the controller is chosen such that the resonances are critically dam

    -The obtain loop gain is shown in Figure 26. +The obtain loop gain is shown in Figure 21.

    @@ -1454,7 +1409,7 @@ The obtain loop gain is shown in Figure 26.

    hybrid_control_Kl_loop_gain.png

    -

    Figure 26: Obtain Loop Gain for the DVF control loop (png, pdf)

    +

    Figure 21: Obtain Loop Gain for the DVF control loop (png, pdf)

    @@ -1464,8 +1419,8 @@ The obtain loop gain is shown in Figure 26.

    3.4 Second Control Loop - \(\bm{K}_\mathcal{X}\)

    -
    -

    3.4.1 Identification

    +
    +

    3.4.1 Identification

    Kx = tf(zeros(6));
    @@ -1492,8 +1447,8 @@ G.OutputName = {'Dx', '
     
    -
    -

    3.4.2 Obtained Plant

    +
    +

    3.4.2 Obtained Plant

    We use the Jacobian matrix to apply forces in the cartesian frame. @@ -1505,19 +1460,19 @@ Gx.InputName = {'Fx',

    -The obtained plant is shown in Figure 27. +The obtained plant is shown in Figure 22.

    hybrid_control_Kx_plant.png

    -

    Figure 27: Diagonal and Off-diagonal elements of the plant for the design of \(\bm{K}_\mathcal{L}\) (png, pdf)

    +

    Figure 22: Diagonal and Off-diagonal elements of the plant for the design of \(\bm{K}_\mathcal{L}\) (png, pdf)

    -
    -

    3.4.3 Controller Design

    +
    +

    3.4.3 Controller Design

    The controller consists of: @@ -1545,7 +1500,7 @@ Kx = Kx.*diag(1./dia

    hybrid_control_Kx_loop_gain.png

    -

    Figure 28: Obtained Loop Gain for the controller \(\bm{K}_\mathcal{X}\) (png, pdf)

    +

    Figure 23: Obtained Loop Gain for the controller \(\bm{K}_\mathcal{X}\) (png, pdf)

    @@ -1590,20 +1545,20 @@ save('./mat/control_tracking.mat', 29. +The obtained position error is shown in Figure 24.

    hybrid_control_Ex.png

    -

    Figure 29: Obtained position error \(\bm{\epsilon}_\mathcal{X}\) (png, pdf)

    +

    Figure 24: Obtained position error \(\bm{\epsilon}_\mathcal{X}\) (png, pdf)

    -
    -

    3.6 Conclusion

    +
    +

    3.6 Conclusion

    @@ -1615,7 +1570,7 @@ The obtained position error is shown in Figure 29.

    -Let’s load the simulation results and compare them in Figure 30. +Let’s load the simulation results and compare them in Figure 25.

    load('./mat/control_tracking.mat', 'simout_D', 'simout_L', 'simout_X', 'simout_H');
    @@ -1626,7 +1581,7 @@ Let’s load the simulation results and compare them in Figure 
     

    reference_tracking_performance_comparison.png

    -

    Figure 30: Comparison of the position errors for all the Control architecture used (png, pdf)

    +

    Figure 25: Comparison of the position errors for all the Control architecture used (png, pdf)

    @@ -1767,7 +1722,7 @@ Erz = atan2(-T(1, 2)/

    Author: Dehaeze Thomas

    -

    Created: 2020-03-13 ven. 13:23

    +

    Created: 2020-03-16 lun. 11:22

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