test-bench-apa/matlab/simscape_model.m

%% Clear Workspace and Close figures
clear; close all; clc;

%% Intialize Laplace variable
s = zpk('s');

addpath('./mat/');

% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
% We first extract the stiffness and mass matrices.

K = readmatrix('APA95ML_K.CSV');
M = readmatrix('APA95ML_M.CSV');



% #+caption: First 10x10 elements of the Mass matrix
% #+RESULTS:
% |    0.03 |   7e-08 |  2e-06 | -3e-09 | -0.0002 | -6e-08 | -0.001 |   8e-07 |  6e-07 | -8e-09 |
% |   7e-08 |    0.02 | -1e-06 |  9e-05 |  -3e-09 | -4e-09 | -1e-06 | -0.0006 | -4e-08 |  5e-06 |
% |   2e-06 |  -1e-06 |   0.02 | -3e-08 |  -4e-08 |  1e-08 |  1e-07 |  -2e-07 | 0.0003 |  1e-09 |
% |  -3e-09 |   9e-05 | -3e-08 |  1e-06 |  -3e-11 | -3e-13 | -7e-09 |  -5e-06 | -3e-10 |  3e-08 |
% | -0.0002 |  -3e-09 | -4e-08 | -3e-11 |   2e-06 |  6e-10 |  2e-06 |  -7e-09 | -2e-09 |  7e-11 |
% |  -6e-08 |  -4e-09 |  1e-08 | -3e-13 |   6e-10 |  1e-06 |  1e-08 |   3e-09 | -2e-09 |  2e-13 |
% |  -0.001 |  -1e-06 |  1e-07 | -7e-09 |   2e-06 |  1e-08 |   0.03 |   4e-08 | -2e-06 |  8e-09 |
% |   8e-07 | -0.0006 | -2e-07 | -5e-06 |  -7e-09 |  3e-09 |  4e-08 |    0.02 | -9e-07 | -9e-05 |
% |   6e-07 |  -4e-08 | 0.0003 | -3e-10 |  -2e-09 | -2e-09 | -2e-06 |  -9e-07 |   0.02 |  2e-08 |
% |  -8e-09 |   5e-06 |  1e-09 |  3e-08 |   7e-11 |  2e-13 |  8e-09 |  -9e-05 |  2e-08 |  1e-06 |

% Then, we extract the coordinates of the interface nodes.

[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA95ML_out_nodes_3D.txt');

% Simscape Model
% The flexible element is imported using the =Reduced Order Flexible Solid= Simscape block.

% To model the actuator, an =Internal Force= block is added between the nodes 3 and 12.
% A =Relative Motion Sensor= block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo.

% One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame.

m = 5.5;

load('apa95ml_params.mat', 'ga', 'gs');

% Dynamics from Actuator Voltage to Vertical Mass Displacement
% The identified dynamics is shown in Figure [[fig:dynamics_act_disp_comp_mass]].


%% Name of the Simulink File
mdl = 'piezo_amplified_3d';

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Actuator Voltage [V]
io(io_i) = linio([mdl, '/y'],  1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]

Ghm = linearize(mdl, io);

freqs = logspace(0, 4, 5000);

figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

% Dynamics from Actuator Voltage to Force Sensor Voltage
% The obtained dynamics is shown in Figure [[fig:dynamics_force_force_sensor_comp_mass]].


%% Name of the Simulink File
mdl = 'piezo_amplified_3d';

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Voltage Actuator [V]
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage [V]

Gfm = linearize(mdl, io);

freqs = logspace(1, 5, 1000);

figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(Gfm, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm, freqs, 'Hz')))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360); ylim([-360, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

save('mat/fem_simscape_models.mat', 'Ghm', 'Gfm')