Cedrat Actuator

1. Documentation
2. Parameters
3. Identification
4. Integral Force Feedback
5. Damped System

1 Documentation

Blocked force: \(1400\ N\)
Stiffness: \(10.8\ N/\mu m\)
Resonance (free-free): \(6450\ Hz\)
Resonance (blocked-free): \(1750\ Hz\)
Height: \(45\ mm\)
Length: \(80\ mm\)
Width: \(22\ mm\)
Mass: \(160\ g\)

2 Parameters

cedrat.L = 80; % Total Width of the Actuator[mm]
cedrat.H = 45; % Total Height of the Actuator [mm]
cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
cedrat.mtot = 0.160; % Total mass of the Actuator [kg]
cedrat.m = cedrat.mtot/6; % Mass of each single element [kg]

cedrat.k = 1e9; % Linear Stiffness of each "blade" [N/m]
cedrat.c = 0.1*sqrt(cedrat.mtot*cedrat.k); % [N/(m/s)]

cedrat.ka = 5e7; % Linear Stiffness of the stack [N/m]
cedrat.ca = 0.1*sqrt(cedrat.mtot*cedrat.ka); % [N/(m/s)]

cedrat.kr = 10; % Rotation Stiffness [N*m/(deg)]
cedrat.cr = 0.0001; % Rotation Damping [N*m/(deg/s)]

K_iff = tf(0);

% dummy_mass = 140; % [kg]
dummy_mass = 1; % [kg]

3 Identification

%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;

%% Name of the Simulink File
mdl = 'cedrat_piezo';

%% Input/Output definition
io(1)  = linio([mdl, '/F'],  1, 'input');
io(2)  = linio([mdl, '/Fz'], 1, 'input');
io(3)  = linio([mdl, '/Dw'], 1, 'input');
io(4)  = linio([mdl, '/Dz'], 1, 'output');
io(5)  = linio([mdl, '/Fm'], 1, 'output');

%% Run the linearization
G = linearize(mdl, io, options);
G.InputName  = {'F', 'Fz', 'Dw'};
G.OutputName = {'Dz', 'Fm'};

Figure 1: Identified Transfer function (png, pdf)

4 Integral Force Feedback

Figure 2: Transfer function from \(F\) to \(F_m\) (png, pdf)

K_iff = -100000/s*(s/2/pi/100)/(1 + s/2/pi/100)*(s/2/pi/100)/(1 + s/2/pi/100);

Figure 3: Open Loop Gain Transfer Function - Cedrat (png, pdf)

5 Damped System

%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;

%% Name of the Simulink File
mdl = 'cedrat_piezo';

%% Input/Output definition
io(1)  = linio([mdl, '/F'],  1, 'input');
io(2)  = linio([mdl, '/Fz'],  1, 'input');
io(3)  = linio([mdl, '/Dw'], 1, 'input');
io(4)  = linio([mdl, '/Dz'], 1, 'output');
io(5)  = linio([mdl, '/Fm'], 1, 'output');

%% Run the linearization
G_iff = linearize(mdl, io, options);
G_iff.InputName  = {'F', 'Fz', 'Dw'};
G_iff.OutputName = {'Dz', 'Fm'};

Figure 4: Identified Transfer function (png, pdf)