603 lines
26 KiB
Matlab
603 lines
26 KiB
Matlab
%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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addpath('./src/'); % Path for Functions
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%% Colors for the figures
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colors = colororder;
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%% Nano-Hexapod on top of Micro-Station model
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mdl = 'nass_rotating_model';
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%% Load micro-station parameters
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load('uniaxial_micro_station_parameters.mat')
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%% Load controllers
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load('nass_controllers.mat');
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% System dynamics
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%% Nano-Hexapod
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mn = 15; % Nano-Hexapod mass [kg]
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%% Light Sample
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ms = 1; % Sample Mass [kg]
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%% General Configuration
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model_config = struct();
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model_config.controller = "open_loop"; % Default: Open-Loop
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model_config.Tuv_type = "normal"; % Default: 2DoF stage
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Forces [Fu, Fv]
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io(io_i) = linio([mdl, '/fd'], 1, 'openinput'); io_i = io_i + 1; % Direct Forces on Sample [Fdx, Fdy]
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io(io_i) = linio([mdl, '/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion [Dfx, Dfy]
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io(io_i) = linio([mdl, '/ft'], 1, 'openinput'); io_i = io_i + 1; % Micro-Station Disturbances [Ftx, Fty]
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io(io_i) = linio([mdl, '/nano_hexapod'], 1, 'openoutput'); io_i = io_i + 1; % [Fmu, Fmv]
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io(io_i) = linio([mdl, '/nano_hexapod'], 2, 'openoutput'); io_i = io_i + 1; % [Du, Dv]
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io(io_i) = linio([mdl, '/ext_metrology'],1, 'openoutput'); io_i = io_i + 1; % [Dx, Dy]
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% The dynamics of the undamped and damped plants are identified.
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% The active damping parameters used are the optimal ones previously identified (i.e. for the rotating nano-hexapod fixed on a rigid platform).
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%% Voice Coil (i.e. soft) Nano-Hexapod
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kn = 1e4; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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Wz = 0; % Rotating Velocity [rad/s]
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G_vc_norot = linearize(mdl, io, 0.0);
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G_vc_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_vc_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 2*pi; % Rotating Velocity [rad/s]
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G_vc_fast = linearize(mdl, io, 0.0);
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G_vc_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_vc_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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%% APA (i.e. relatively stiff) Nano-Hexapod
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kn = 1e6; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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Wz = 0; % Rotating Velocity [rad/s]
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G_md_norot = linearize(mdl, io, 0.0);
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G_md_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_md_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 2*pi; % Rotating Velocity [rad/s]
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G_md_fast = linearize(mdl, io, 0.0);
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G_md_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_md_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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%% Piezoelectric (i.e. stiff) Nano-Hexapod
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kn = 1e8; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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Wz = 0; % Rotating Velocity [rad/s]
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G_pz_norot = linearize(mdl, io, 0.0);
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G_pz_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_pz_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 2*pi; % Rotating Velocity [rad/s]
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G_pz_fast = linearize(mdl, io, 0.0);
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G_pz_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_pz_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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%% Identify plants with Parallel stiffnesses
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model_config.Tuv_type = "parallel_k"; % Default: 2DoF stage
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% Voice Coil
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kp = 1e3;
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cp = 2*0.001*sqrt((ms + mn)*kp);
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kn = 1e4-kp; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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% Identify dynamics
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Wz = 2*pi; % [rad/s]
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G_vc_kp_fast = linearize(mdl, io, 0);
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G_vc_kp_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_vc_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 0; % [rad/s]
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G_vc_kp_norot = linearize(mdl, io, 0);
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G_vc_kp_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_vc_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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% APA
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kp = 1e4;
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cp = 2*0.001*sqrt((ms + mn)*kp);
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kn = 1e6 - kp; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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% Identify dynamics
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Wz = 2*pi; % [rad/s]
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G_md_kp_fast = linearize(mdl, io, 0);
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G_md_kp_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_md_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 0; % [rad/s]
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G_md_kp_norot = linearize(mdl, io, 0);
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G_md_kp_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_md_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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% Piezo
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kp = 1e5;
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cp = 2*0.001*sqrt((ms + mn)*kp);
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kn = 1e8 - kp; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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% Identify dynamics
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Wz = 2*pi; % [rad/s]
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G_pz_kp_fast = linearize(mdl, io, 0);
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G_pz_kp_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_pz_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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Wz = 0; % [rad/s]
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G_pz_kp_norot = linearize(mdl, io, 0);
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G_pz_kp_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy', 'Ftx', 'Fty'};
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G_pz_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};
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%% Closed Loop Plants - IFF with HPF
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G_vc_norot_iff_hpf = feedback(G_vc_norot, Kiff_hpf_vc, 'name');
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G_vc_fast_iff_hpf = feedback(G_vc_fast, Kiff_hpf_vc, 'name');
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G_md_norot_iff_hpf = feedback(G_md_norot, Kiff_hpf_md, 'name');
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G_md_fast_iff_hpf = feedback(G_md_fast, Kiff_hpf_md, 'name');
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G_pz_norot_iff_hpf = feedback(G_pz_norot, Kiff_hpf_pz, 'name');
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G_pz_fast_iff_hpf = feedback(G_pz_fast, Kiff_hpf_pz, 'name');
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%% Closed Loop Plants - IFF with Parallel Stiffness
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G_vc_norot_iff_kp = feedback(G_vc_kp_norot, Kiff_kp_vc, 'name');
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G_vc_fast_iff_kp = feedback(G_vc_kp_fast, Kiff_kp_vc, 'name');
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G_md_norot_iff_kp = feedback(G_md_kp_norot, Kiff_kp_md, 'name');
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G_md_fast_iff_kp = feedback(G_md_kp_fast, Kiff_kp_md, 'name');
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G_pz_norot_iff_kp = feedback(G_pz_kp_norot, Kiff_kp_pz, 'name');
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G_pz_fast_iff_kp = feedback(G_pz_kp_fast, Kiff_kp_pz, 'name');
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%% Closed Loop Plants - RDC
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G_vc_norot_rdc = feedback(G_vc_norot, Krdc_vc, 'name');
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G_vc_fast_rdc = feedback(G_vc_fast, Krdc_vc, 'name');
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G_md_norot_rdc = feedback(G_md_norot, Krdc_md, 'name');
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G_md_fast_rdc = feedback(G_md_fast, Krdc_md, 'name');
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G_pz_norot_rdc = feedback(G_pz_norot, Krdc_pz, 'name');
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G_pz_fast_rdc = feedback(G_pz_fast, Krdc_pz, 'name');
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% The undamped and damped plants are shown in Figure ref:fig:rotating_nass_plant_comp_stiffness.
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% Three nano-hexapod velocities are shown (from left to right): $k_n = \SI{0.01}{\N\per\mu\m}$, $k_n = \SI{1}{\N\per\mu\m}$ and $k_n = \SI{100}{\N\per\mu\m}$.
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% The direct terms are shown by the solid curves while the coupling terms are shown by the shaded ones.
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% #+begin_important
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% It can be observed on Figure ref:fig:rotating_nass_plant_comp_stiffness that:
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% - Coupling (ratio between the off-diagonal and direct terms) is larger for the soft nano-hexapod
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% - Damping added by the three proposed techniques is quite high and the obtained plant is rather easy to control
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% - There is some coupling between nano-hexapod and micro-station dynamics for the stiff nano-hexapod (mode at 200Hz)
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% - The two proposed IFF modification yields similar results
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% #+end_important
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%% Bode plot of the transfer function from nano-hexapod actuator to measured motion by the external metrology
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freqs_vc = logspace(-1, 2, 1000);
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freqs_md = logspace(0, 3, 1000);
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freqs_pz = logspace(0, 3, 1000);
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figure;
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tiledlayout(3, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', zeros(1,3), ...
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'DisplayName', 'OL');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast('Dy', 'Fu'), freqs_vc, 'Hz'))), 'color', [zeros(1,3), 0.5], ...
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'DisplayName', 'Coupling');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(1,:), ...
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'DisplayName', 'IFF + $k_p$');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dy', 'Fu'), freqs_vc, 'Hz'))), 'color', [colors(1,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(2,:), ...
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'DisplayName', 'IFF + HPF');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dy', 'Fu'), freqs_vc, 'Hz'))), 'color', [colors(2,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_rdc('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(3,:), ...
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'DisplayName', 'RDC');
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plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_rdc('Dy', 'Fu'), freqs_vc, 'Hz'))), 'color', [colors(3,:), 0.5], ...
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'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
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ylim([1e-12, 1e-2])
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title('$k_n = 0.01\,N/\mu m$');
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ax2 = nexttile([2,1]);
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hold on;
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', zeros(1,3), ...
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'DisplayName', 'OL');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast('Dy', 'Fu'), freqs_md, 'Hz'))), 'color', [zeros(1,3), 0.5], ...
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'DisplayName', 'Coupling');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(1,:), ...
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'DisplayName', 'IFF + $k_p$');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dy', 'Fu'), freqs_md, 'Hz'))), 'color', [colors(1,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_kp('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(2,:), ...
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'DisplayName', 'IFF + HPF');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_kp('Dy', 'Fu'), freqs_md, 'Hz'))), 'color', [colors(2,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_rdc('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(3,:), ...
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'DisplayName', 'RDC');
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plot(freqs_md, abs(squeeze(freqresp(G_md_fast_rdc('Dy', 'Fu'), freqs_md, 'Hz'))), 'color', [colors(3,:), 0.5], ...
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'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
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ylim([1e-12, 1e-2])
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title('$k_n = 1\,N/\mu m$');
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ax3 = nexttile([2,1]);
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hold on;
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', zeros(1,3), ...
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'DisplayName', 'OL');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast('Dy', 'Fu'), freqs_pz, 'Hz'))), 'color', [zeros(1,3), 0.5], ...
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'DisplayName', 'Coupling');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(1,:), ...
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'DisplayName', 'IFF + $k_p$');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dy', 'Fu'), freqs_pz, 'Hz'))), 'color', [colors(1,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(2,:), ...
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'DisplayName', 'IFF + HPF');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dy', 'Fu'), freqs_pz, 'Hz'))), 'color', [colors(2,:), 0.5], ...
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'HandleVisibility', 'off');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_rdc('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(3,:), ...
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'DisplayName', 'RDC');
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plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_rdc('Dy', 'Fu'), freqs_pz, 'Hz'))), 'color', [colors(3,:), 0.5], ...
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'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
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ylim([1e-12, 1e-2])
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ldg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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ldg.ItemTokenSize = [20, 1];
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title('$k_n = 100\,N/\mu m$');
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ax1b = nexttile;
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hold on;
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plot(freqs_vc, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_fast('Dx', 'Fu'), freqs_vc, 'Hz')))), 'color', zeros(1,3));
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plot(freqs_vc, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_fast_iff_hpf('Dx', 'Fu'), freqs_vc, 'Hz')))), 'color', colors(1,:));
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plot(freqs_vc, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_fast_iff_kp('Dx', 'Fu'), freqs_vc, 'Hz')))), 'color', colors(2,:));
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plot(freqs_vc, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_fast_rdc('Dx', 'Fu'), freqs_vc, 'Hz')))), 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360);
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ylim([-270, 90]);
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ax2b = nexttile;
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hold on;
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plot(freqs_md, 180/pi*unwrap(angle(squeeze(freqresp(G_md_fast('Dx', 'Fu'), freqs_md, 'Hz')))), 'color', zeros(1,3));
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plot(freqs_md, 180/pi*unwrap(angle(squeeze(freqresp(G_md_fast_iff_hpf('Dx', 'Fu'), freqs_md, 'Hz')))), 'color', colors(1,:));
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plot(freqs_md, 180/pi*unwrap(angle(squeeze(freqresp(G_md_fast_iff_kp('Dx', 'Fu'), freqs_md, 'Hz')))), 'color', colors(2,:));
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plot(freqs_md, 180/pi*unwrap(angle(squeeze(freqresp(G_md_fast_rdc('Dx', 'Fu'), freqs_md, 'Hz')))), 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
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hold off;
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yticks(-360:90:360);
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ylim([-270, 90]);
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ax3b = nexttile;
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hold on;
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plot(freqs_pz, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_fast('Dx', 'Fu'), freqs_pz, 'Hz')))), 'color', zeros(1,3));
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plot(freqs_pz, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_fast_iff_hpf('Dx', 'Fu'), freqs_pz, 'Hz')))), 'color', colors(1,:));
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plot(freqs_pz, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_fast_iff_kp('Dx', 'Fu'), freqs_pz, 'Hz')))), 'color', colors(2,:));
|
|
plot(freqs_pz, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_fast_rdc('Dx', 'Fu'), freqs_pz, 'Hz')))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
hold off;
|
|
yticks(-360:90:360);
|
|
ylim([-270, 90]);
|
|
|
|
linkaxes([ax1,ax1b],'x');
|
|
xlim([freqs_vc(1), freqs_vc(end)]);
|
|
|
|
linkaxes([ax2,ax2b],'x');
|
|
xlim([freqs_md(1), freqs_md(end)]);
|
|
|
|
linkaxes([ax3,ax3b],'x');
|
|
xlim([freqs_pz(1), freqs_pz(end)]);
|
|
|
|
|
|
|
|
% #+name: fig:rotating_nass_plant_comp_stiffness
|
|
% #+caption: Bode plot of the transfer function from nano-hexapod actuator to measured motion by the external metrology
|
|
% #+RESULTS:
|
|
% [[file:figs/rotating_nass_plant_comp_stiffness.png]]
|
|
|
|
% To confirm that the coupling is smaller when the stiffness of the nano-hexapod is increase, the /coupling ratio/ for the three nano-hexapod stiffnesses are shown in Figure ref:fig:rotating_nass_plant_coupling_comp.
|
|
|
|
|
|
%% Coupling ratio for the proposed active damping techniques evaluated for the three nano-hexapod stiffnesses
|
|
figure;
|
|
freqs_vc = logspace(-1, 2, 1000);
|
|
freqs_md = logspace(0, 3, 1000);
|
|
freqs_pz = logspace(0, 3, 1000);
|
|
|
|
figure;
|
|
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile();
|
|
hold on;
|
|
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast('Dy', 'Fu')/G_vc_fast('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dy', 'Fu')/G_vc_fast_iff_hpf('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dy', 'Fu')/G_vc_fast_iff_kp('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_rdc('Dy', 'Fu')/G_vc_fast_rdc('Dx', 'Fu'), freqs_vc, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Coupling Ratio');
|
|
title('$k_n = 0.01\,N/\mu m$');
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs_md, abs(squeeze(freqresp(G_md_fast('Dy', 'Fu')/G_md_fast('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dy', 'Fu')/G_md_fast_iff_hpf('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_kp('Dy', 'Fu')/G_md_fast_iff_kp('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_rdc('Dy', 'Fu')/G_md_fast_rdc('Dx', 'Fu'), freqs_md, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
title('$k_n = 1\,N/\mu m$');
|
|
|
|
ax3 = nexttile();
|
|
hold on;
|
|
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast('Dy', 'Fu')/G_pz_fast('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dy', 'Fu')/G_pz_fast_iff_hpf('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dy', 'Fu')/G_pz_fast_iff_kp('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_rdc('Dy', 'Fu')/G_pz_fast_rdc('Dx', 'Fu'), freqs_pz, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
title('$k_n = 100\,N/\mu m$');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [20, 1];
|
|
|
|
linkaxes([ax1,ax2,ax3], 'y')
|
|
|
|
% Effect of disturbances
|
|
|
|
% The effect of three disturbances are considered:
|
|
% - Floor motion (Figure ref:fig:rotating_nass_effect_floor_motion)
|
|
% - Micro-Station vibrations (Figure ref:fig:rotating_nass_effect_stage_vibration)
|
|
% - Direct force applied on the payload (Figure ref:fig:rotating_nass_effect_direct_forces)
|
|
|
|
% #+begin_important
|
|
% Conclusions are similar than with the uniaxial (non-rotating) model:
|
|
% - Regarding the effect of floor motion and forces applied on the payload:
|
|
% - The stiffer, the better (magnitudes are lower for the right curves, Figures ref:fig:rotating_nass_effect_floor_motion and ref:fig:rotating_nass_effect_direct_forces)
|
|
% - Integral Force Feedback degrades the performances at low frequency compared to relative damping control
|
|
% - Regarding the effect of micro-station vibrations:
|
|
% - Having a soft nano-hexapod allows to filter these vibrations between the suspensions modes of the nano-hexapod and some flexible modes of the micro-station. Using relative damping control reduce this filtering (Figure ref:fig:rotating_nass_effect_stage_vibration, left).
|
|
% #+end_important
|
|
|
|
|
|
%% Effect of Floor motion on the position error - Comparison of active damping techniques for the three nano-hexapod stiffnesses
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast('Dx', 'Dfx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_rdc('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Magnitude $d_x/D_{f,x}$ [m/N]');
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 0.01\,N/\mu m$');
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast('Dx', 'Dfx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_kp('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_rdc('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 1\,N/\mu m$');
|
|
|
|
ax3 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast('Dx', 'Dfx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_rdc('Dx', 'Dfx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 100\,N/\mu m$');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [20, 1];
|
|
|
|
linkaxes([ax1,ax2,ax3], 'y')
|
|
|
|
|
|
|
|
% #+name: fig:rotating_nass_effect_floor_motion
|
|
% #+caption: Effect of Floor motion on the position error - Comparison of active damping techniques for the three nano-hexapod stiffnesses
|
|
% #+RESULTS:
|
|
% [[file:figs/rotating_nass_effect_floor_motion.png]]
|
|
|
|
|
|
%% Effect of micro-station vibrations on the position error - Comparison of active damping techniques for the three nano-hexapod stiffnesses
|
|
figure;
|
|
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast('Dx', 'Ftx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_rdc('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Magnitude $d_x/f_{t,x}$ [m/N]');
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 0.01\,N/\mu m$');
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast('Dx', 'Ftx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_kp('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_rdc('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 1\,N/\mu m$');
|
|
|
|
ax3 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast('Dx', 'Ftx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_rdc('Dx', 'Ftx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 100\,N/\mu m$');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [20, 1];
|
|
|
|
linkaxes([ax1,ax2,ax3], 'y')
|
|
|
|
|
|
|
|
% #+name: fig:rotating_nass_effect_stage_vibration
|
|
% #+caption: Effect of micro-station vibrations on the position error - Comparison of active damping techniques for the three nano-hexapod stiffnesses
|
|
% #+RESULTS:
|
|
% [[file:figs/rotating_nass_effect_stage_vibration.png]]
|
|
|
|
|
|
%% Effect of sample forces on the position error - Comparison of active damping techniques for the three nano-hexapod stiffnesses
|
|
figure;
|
|
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast('Dx', 'Fdx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_hpf('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_iff_kp('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_fast_rdc('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Magnitude $d_x/f_{s,x}$ [m/N]');
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 0.01\,N/\mu m$');
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast('Dx', 'Fdx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_hpf('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_iff_kp('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_md_fast_rdc('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 1\,N/\mu m$');
|
|
|
|
ax3 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast('Dx', 'Fdx'), freqs, 'Hz'))), 'color', zeros(1,3), ...
|
|
'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_hpf('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF + $k_p$');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_iff_kp('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(2,:), ...
|
|
'DisplayName', 'IFF + HPF');
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_fast_rdc('Dx', 'Fdx'), freqs, 'Hz'))), 'color', colors(3,:), ...
|
|
'DisplayName', 'RDC');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
|
|
xtickangle(0)
|
|
title('$k_n = 100\,N/\mu m$');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [20, 1];
|
|
|
|
linkaxes([ax1,ax2,ax3], 'y')
|