Update sensor/actuator constants
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@ -602,18 +602,18 @@ Also, the off diagonal terms are quite small compared to the diagonal terms.
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The bode plot is shown in Figure [[fig:nano_hexapod_struts_2dof_iff_plant]].
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#+begin_src matlab :exports none
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freqs = 5*logspace(0, 2, 1000);
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freqs = 2*logspace(1, 3, 1000);
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Giff(1,1), freqs, 'Hz'))), '-', ...
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plot(freqs, 20*abs(squeeze(freqresp(Giff(1,1), freqs, 'Hz'))), '-', ...
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'DisplayName', '$F_{m,i}/\tau_i$')
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for i = 1:6
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(Giff(i,i), freqs, 'Hz'))), '-', ...
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plot(freqs, 20*abs(squeeze(freqresp(Giff(i,i), freqs, 'Hz'))), '-', ...
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'HandleVisibility', 'off');
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end
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% Off diagonal terms
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@ -1502,6 +1502,10 @@ exportFig('figs/nano_hexapod_iff_root_locus.pdf', 'width', 'wide', 'height', 'ta
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#+RESULTS:
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[[file:figs/nano_hexapod_iff_root_locus.png]]
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#+begin_question
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Are the zeros shown in the Root Locus (Figure [[fig:nano_hexapod_iff_root_locus]]) are the poles of the nano-hexapod when the active part of the strut ($k_e$ and $k_a$) is removed?
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This will be checked in the next section.
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#+end_question
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The obtained controller is then:
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#+begin_src matlab
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@ -1553,6 +1557,41 @@ exportFig('figs/nano_hexapod_iff_loop_gain.pdf', 'width', 'wide', 'height', 'tal
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#+RESULTS:
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[[file:figs/nano_hexapod_iff_loop_gain.png]]
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** Frequency of the zeros of the IFF plant
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In order to find the zeros of the IFF plant, the hexapod is initialized with quasi null actuator stiffness and the system is identified.
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#+begin_src matlab
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n_hexapod = initializeNanoHexapodFinal('flex_bot_type', '4dof', ...
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'flex_top_type', '4dof', ...
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'motion_sensor_type', 'struts', ...
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'actuator_type', '2dof', ...
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'actuator_ke', ones(6,1)*1e-1, ...
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'actuator_ka', ones(6,1)*1e-1);
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Giff_z = linearize(mdl, io, 0.0, options);
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Giff_z.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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Giff_z.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
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#+end_src
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Then, we can look at the frequency of the poles.
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#+begin_src matlab :results value replace :exports results :tangle no
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G_z = pole(Giff_z);
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ans = sort(imag(G_z(imag(G_z)>0)))
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#+end_src
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#+name: tab:iff_frequency_zero
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#+caption: Frequency of the poles corresponding to the IFF zeros (Hz).
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#+attr_latex: :environment tabularx :width 0.2\linewidth :align c
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#+attr_latex: :center t :booktabs t :float t
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| 50.750 |
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| 51.483 |
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| 117.94 |
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| 157.79 |
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| 197.21 |
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| 198.47 |
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And we indeed find the frequency of the zeros for the IFF plant.
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** Effect of IFF on the plant
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<<sec:iff_effect_plant>>
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@ -3421,15 +3460,15 @@ arguments
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args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts'
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%% Actuators
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args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible'
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args.actuator_Ga (6,1) double {mustBeNumeric} = ones(6,1)*1 % Actuator gain [N/V]
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args.actuator_Gs (6,1) double {mustBeNumeric} = ones(6,1)*1 % Sensor gain [V/m]
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args.actuator_Ga (6,1) double {mustBeNumeric} = zeros(6,1) % Actuator gain [N/V]
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args.actuator_Gs (6,1) double {mustBeNumeric} = zeros(6,1) % Sensor gain [V/m]
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% For 2DoF
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args.actuator_k (6,1) double {mustBeNumeric} = ones(6,1)*0.35e6 % [N/m]
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args.actuator_ke (6,1) double {mustBeNumeric} = ones(6,1)*1.5e6 % [N/m]
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args.actuator_ka (6,1) double {mustBeNumeric} = ones(6,1)*43e6 % [N/m]
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args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e1 % [N/(m/s)]
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args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
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args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
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args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e0 % [N/(m/s)]
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args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e0 % [N/(m/s)]
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args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e0 % [N/(m/s)]
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args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
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% For Flexible Frame
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args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
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@ -3545,8 +3584,33 @@ end
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#+end_src
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#+begin_src matlab
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nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
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nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
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%% Actuator gain [N/V]
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if all(args.actuator_Ga == 0)
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switch args.actuator_type
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case '2dof'
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nano_hexapod.actuator.Ga = ones(6,1)*(-46.4);
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case 'flexible frame'
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nano_hexapod.actuator.Ga = ones(6,1); % TODO
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case 'flexible'
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nano_hexapod.actuator.Ga = ones(6,1)*23.4;
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end
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else
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nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
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end
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%% Sensor gain [V/m]
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if all(args.actuator_Gs == 0)
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switch args.actuator_type
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case '2dof'
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nano_hexapod.actuator.Gs = ones(6,1)*0.098;
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case 'flexible frame'
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nano_hexapod.actuator.Gs = ones(6,1); % TODO
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case 'flexible'
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nano_hexapod.actuator.Gs = ones(6,1)*(-4674824);
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end
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else
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nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
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end
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#+end_src
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2dof
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@ -27,20 +27,20 @@ arguments
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args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts'
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%% Actuators
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args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible'
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args.actuator_Ga (6,1) double {mustBeNumeric} = ones(6,1)*1 % Actuator gain [N/V]
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args.actuator_Gs (6,1) double {mustBeNumeric} = ones(6,1)*1 % Sensor gain [V/m]
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args.actuator_Ga (6,1) double {mustBeNumeric} = zeros(6,1) % Actuator gain [N/V]
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args.actuator_Gs (6,1) double {mustBeNumeric} = zeros(6,1) % Sensor gain [V/m]
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% For 2DoF
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args.actuator_k (6,1) double {mustBeNumeric} = ones(6,1)*0.35e6 % [N/m]
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args.actuator_ke (6,1) double {mustBeNumeric} = ones(6,1)*1.5e6 % [N/m]
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args.actuator_ka (6,1) double {mustBeNumeric} = ones(6,1)*43e6 % [N/m]
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args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e1 % [N/(m/s)]
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args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
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args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
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args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e0 % [N/(m/s)]
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args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e0 % [N/(m/s)]
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args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e0 % [N/(m/s)]
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args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
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% For Flexible Frame
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args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
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args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m]
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% For Flexible
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args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio
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%% Controller
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args.controller_type char {mustBeMember(args.controller_type,{'none', 'iff', 'dvf'})} = 'none'
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@ -114,8 +114,33 @@ switch args.actuator_type
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nano_hexapod.actuator.type = 3;
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end
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nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
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nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
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%% Actuator gain [N/V]
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if all(args.actuator_Ga == 0)
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switch args.actuator_type
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case '2dof'
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nano_hexapod.actuator.Ga = ones(6,1)*(-46.4);
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case 'flexible frame'
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nano_hexapod.actuator.Ga = ones(6,1); % TODO
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case 'flexible'
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nano_hexapod.actuator.Ga = ones(6,1)*23.4;
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end
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else
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nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
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end
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%% Sensor gain [V/m]
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if all(args.actuator_Gs == 0)
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switch args.actuator_type
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case '2dof'
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nano_hexapod.actuator.Gs = ones(6,1)*0.098;
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case 'flexible frame'
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nano_hexapod.actuator.Gs = ones(6,1); % TODO
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case 'flexible'
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nano_hexapod.actuator.Gs = ones(6,1)*(-4674824);
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end
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else
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nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
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end
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nano_hexapod.actuator.k = args.actuator_k; % [N/m]
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nano_hexapod.actuator.ke = args.actuator_ke; % [N/m]
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