function [sys] = identifyPlant(opts_param) %% Default values for opts opts = struct(); %% Populate opts with input parameters if exist('opts_param','var') for opt = fieldnames(opts_param)' opts.(opt{1}) = opts_param.(opt{1}); end end %% Options for Linearized options = linearizeOptions; options.SampleTime = 0; %% Name of the Simulink File mdl = 'sim_nano_station_id'; %% Input/Output definition io(1) = linio([mdl, '/Fn'], 1, 'input'); % Cartesian forces applied by NASS io(2) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion io(3) = linio([mdl, '/Fs'], 1, 'input'); % External forces on the sample io(4) = linio([mdl, '/Fnl'], 1, 'input'); % Forces applied on the NASS's legs io(5) = linio([mdl, '/Fd'], 1, 'input'); % Disturbance Forces io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs io(9) = linio([mdl, '/Es'], 1, 'output'); % Position Error w.r.t. NASS base io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the legs %% Run the linearization G = linearize(mdl, io, options); G.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz', ... 'Dgx', 'Dgy', 'Dgz', ... 'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz', ... 'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ... 'Frzz', 'Ftyx', 'Ftyz'}; G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', ... 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6', ... 'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', ... 'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz', ... 'Vm1', 'Vm2', 'Vm3', 'Vm4', 'Vm5', 'Vm6'}; %% Create the sub transfer functions minreal_tol = sqrt(eps); % From forces applied in the cartesian frame to displacement of the sample in the cartesian frame sys.G_cart = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'}), minreal_tol, false); % From ground motion to Sample displacement sys.G_gm = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Dgx', 'Dgy', 'Dgz'}), minreal_tol, false); % From direct forces applied on the sample to displacement of the sample sys.G_fs = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz'}), minreal_tol, false); % From forces applied on NASS's legs to force sensor in each leg sys.G_iff = minreal(G({'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), minreal_tol, false); % From forces applied on NASS's legs to displacement of each leg sys.G_dleg = minreal(G({'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), minreal_tol, false); % From forces/torques applied by the NASS to position error sys.G_plant = minreal(G({'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'}), minreal_tol, false); % From forces/torques applied by the NASS to velocity of the actuator sys.G_geoph = minreal(G({'Vm1', 'Vm2', 'Vm3', 'Vm4', 'Vm5', 'Vm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), minreal_tol, false); % From various disturbance forces to position error sys.G_dist = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Frzz', 'Ftyx', 'Ftyz'}), minreal_tol, false); %% We remove low frequency and high frequency dynamics that are usually unstable % using =freqsep= is risky as it may change the shape of the transfer functions % f_min = 0.1; % [Hz] % f_max = 1e4; % [Hz] % [~, sys.G_cart] = freqsep(freqsep(sys.G_cart, 2*pi*f_max), 2*pi*f_min); % [~, sys.G_gm] = freqsep(freqsep(sys.G_gm, 2*pi*f_max), 2*pi*f_min); % [~, sys.G_fs] = freqsep(freqsep(sys.G_fs, 2*pi*f_max), 2*pi*f_min); % [~, sys.G_iff] = freqsep(freqsep(sys.G_iff, 2*pi*f_max), 2*pi*f_min); % [~, sys.G_dleg] = freqsep(freqsep(sys.G_dleg, 2*pi*f_max), 2*pi*f_min); % [~, sys.G_plant] = freqsep(freqsep(sys.G_plant, 2*pi*f_max), 2*pi*f_min); %% We finally verify that the system is stable if ~isstable(sys.G_cart) || ~isstable(sys.G_gm) || ~isstable(sys.G_fs) || ~isstable(sys.G_iff) || ~isstable(sys.G_dleg) || ~isstable(sys.G_plant) warning('One of the identified system is unstable'); end end