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# Cedrat Actuator

## Table of Contents

- 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: \(H = 45\ mm\)
- Length: \(L = 80\ mm\)
- 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 2: Identified Transfer function (png, pdf)

## 4 Integral Force Feedback

Figure 3: 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 4: 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 5: Identified Transfer function (png, pdf)

Author: Dehaeze Thomas

Created: 2019-10-29 mar. 11:06

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