From 1d4af33d53813a9f5c1d9bc2af55746ca973e2c3 Mon Sep 17 00:00:00 2001 From: Marvin Date: Mon, 24 Nov 2025 23:17:46 +0100 Subject: [PATCH 1/7] new file: toolbox/examples/friction_model/F_fric.m new file: toolbox/examples/friction_model/friction_model_RHS.m new file: toolbox/examples/friction_model/friction_model_test.m modified: toolbox/examples/liveExamples/canonicalExRHS_test_live.mlx --- toolbox/examples/friction_model/F_fric.m | 8 +++ .../friction_model/friction_model_RHS.m | 17 ++++++ .../friction_model/friction_model_test.m | 54 ++++++++++++++++++ .../liveExamples/canonicalExRHS_test_live.mlx | Bin 131154 -> 82974 bytes 4 files changed, 79 insertions(+) create mode 100644 toolbox/examples/friction_model/F_fric.m create mode 100644 toolbox/examples/friction_model/friction_model_RHS.m create mode 100644 toolbox/examples/friction_model/friction_model_test.m diff --git a/toolbox/examples/friction_model/F_fric.m b/toolbox/examples/friction_model/F_fric.m new file mode 100644 index 0000000..21f0c5c --- /dev/null +++ b/toolbox/examples/friction_model/F_fric.m @@ -0,0 +1,8 @@ +function res = F_fric(x, mu_rel, epsilon, F_s, k, delta) + if abs(mu_rel) <= epsilon % epsilon small (mu rel = 0 numerically) + res = min(abs(k * x(1)), F_s) * sign(k * x(1)); + else + res = -( (F_s * sign(mu_rel)) / (1 + delta * abs(mu_rel)) ); + end +end + diff --git a/toolbox/examples/friction_model/friction_model_RHS.m b/toolbox/examples/friction_model/friction_model_RHS.m new file mode 100644 index 0000000..01a658c --- /dev/null +++ b/toolbox/examples/friction_model/friction_model_RHS.m @@ -0,0 +1,17 @@ +function dx = friction_model_RHS(t, x, p) +% p = (k, m, mu_b, F_s, delta, epsilon) +k = p(1); +m = p(2); +mu_b = p(3); +F_s = p(4); +delta = p(5); +epsilon = p(6); +mu_rel = x(2) - mu_b; + +dx = zeros(2,1); +dx(1) = x(2); + +dx(2) = -(k / m) * x(1) + F_fric(x, mu_rel, epsilon, F_s, k, delta) / m; + +end + diff --git a/toolbox/examples/friction_model/friction_model_test.m b/toolbox/examples/friction_model/friction_model_test.m new file mode 100644 index 0000000..77fff1b --- /dev/null +++ b/toolbox/examples/friction_model/friction_model_test.m @@ -0,0 +1,54 @@ +integrator = @ode45; +t0 = 0; +tf = 12; +timeinterval = [t0,tf]; +initstates = [1.133944669704 0 ]; +p(1) = 1.0; %k +p(2) = 1.0; %m +p(3) = 0.2; %mu_b +p(4) = 1; %F_s +p(5) = 3; %delta +p(6) = 1e-15; %epsilon +p = reshape(p, [], 1); + +%% preprocessing +fprintf('Preprocessing...\n '); +odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-6); +filename = 'friction_model_RHS'; +dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions); +fprintf('Done, now integrate...\n'); + +%% integrate +sol_ifdiff = solveODE(dhandle, timeinterval, initstates, p); +fprintf('Done \n'); + +%% results +disp(sol_ifdiff); +T = 0:0.01:12; +Y = deval(sol_ifdiff, T); +switches = sol_ifdiff.switches; + +figure; hold on; box on; + +a = zeros(length(sol_ifdiff.x)); + +plot(T, Y(1,:), 'LineWidth', 2); +plot(T, Y(2,:), 'LineWidth', 2); +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +%plot(switches, Ys(2,:), 'rx', 'MarkerSize', 8, 'LineWidth', 1.5); + +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end + +xlabel('Time (s)', 'FontSize', 12); +ylabel('States', 'FontSize', 12); +title('ODE Solution to Friction Model', 'FontSize', 14); + +legend({'State 1','State 2'}, 'Location', 'best'); +grid on; + +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +disp(sol_ifdiff.idata); +disp(sol_ifdiff.stats); diff --git a/toolbox/examples/liveExamples/canonicalExRHS_test_live.mlx b/toolbox/examples/liveExamples/canonicalExRHS_test_live.mlx index 9ea3ef8696d8f537c0a9c0eff4535dfeadd90146..843d025dd5735f1af1c05661aedac1ee25250fd8 100644 GIT binary patch delta 78797 zcmV(nK=QxRfC!$51+du-f5=p}?SL-<03^!+01*HH0BvD(Y++(AZ*_EVb#yLxZEUQ& z*RtzKmZo{1PZ3rZV^xEyf>x7J(FUzG2!On3GiWUcN#N-R+>sR-nbX}@L$h->0f%t+ 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Bin 127972 -> 128005 bytes toolbox/examples/friction_model/F_fric_mod.m | 22 ++ toolbox/examples/friction_model/F_fric_mod2.m | 8 + .../friction_model/friction_model_RHSmod.m | 18 ++ .../friction_model/friction_model_RHSmod2.m | 16 ++ .../friction_model/friction_model_mod_test.m | 213 ++++++++++++++++++ .../liveExamples/CanonicalSensitivities.mlx | Bin 165495 -> 143775 bytes 7 files changed, 277 insertions(+) create mode 100644 toolbox/examples/friction_model/F_fric_mod.m create mode 100644 toolbox/examples/friction_model/F_fric_mod2.m create mode 100644 toolbox/examples/friction_model/friction_model_RHSmod.m create mode 100644 toolbox/examples/friction_model/friction_model_RHSmod2.m create mode 100644 toolbox/examples/friction_model/friction_model_mod_test.m diff --git a/toolbox/doc/GettingStarted.mlx b/toolbox/doc/GettingStarted.mlx index 1257698a7d504c58dd7d0032283fa54bb7283f6b..a46e906cee0599ddf5174426829f27bd0ccf3092 100644 GIT binary patch delta 66647 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b/toolbox/examples/friction_model/F_fric_mod.m new file mode 100644 index 0000000..d52871b --- /dev/null +++ b/toolbox/examples/friction_model/F_fric_mod.m @@ -0,0 +1,22 @@ +function res = F_fric_mod(x, mu_rel, epsilon, F_s, k, delta) +if mu_rel <= -epsilon + res = F_s / (1 - delta * mu_rel); + %res = -F_s * mu_rel; +else + if mu_rel >= epsilon + res = (-F_s) / (1 + delta * mu_rel); + %res = -F_s * mu_rel; + else + if k*x(1) <= -F_s + res = F_s; + else + if k*x(1) >= F_s + res = F_s; + else + res = k*x(1); + end + end + end +end +end + diff --git a/toolbox/examples/friction_model/F_fric_mod2.m b/toolbox/examples/friction_model/F_fric_mod2.m new file mode 100644 index 0000000..b7c8c68 --- /dev/null +++ b/toolbox/examples/friction_model/F_fric_mod2.m @@ -0,0 +1,8 @@ +function res = F_fric_mod2(x, mu_rel, epsilon, F_s, k, delta) +if mu_rel <= 0 + res = F_s / (1 - delta * mu_rel); +else + res = -F_s / (1 + delta * mu_rel); +end +end + diff --git a/toolbox/examples/friction_model/friction_model_RHSmod.m b/toolbox/examples/friction_model/friction_model_RHSmod.m new file mode 100644 index 0000000..13923b1 --- /dev/null +++ b/toolbox/examples/friction_model/friction_model_RHSmod.m @@ -0,0 +1,18 @@ +function dx = friction_model_RHSmod(t, x, p) +% p = (k, m, mu_b, F_s, delta, epsilon) +k = p(1); +m = p(2); +mu_b = p(3); +F_s = p(4); +delta = p(5); +epsilon = p(6); +mu_rel = x(2) - mu_b; + +dx = zeros(2,1); +dx(1) = x(2); + + + +dx(2) = -(k / m) * x(1) + F_fric_mod(x, mu_rel, epsilon, F_s, k, delta) / m; + +end \ No newline at end of file diff --git a/toolbox/examples/friction_model/friction_model_RHSmod2.m b/toolbox/examples/friction_model/friction_model_RHSmod2.m new file mode 100644 index 0000000..5633e2c --- /dev/null +++ b/toolbox/examples/friction_model/friction_model_RHSmod2.m @@ -0,0 +1,16 @@ +function dx = friction_model_RHSmod2(t, x, p) +% p = (k, m, mu_b, F_s, delta, epsilon) +k = p(1); +m = p(2); +mu_b = p(3); +F_s = p(4); +delta = p(5); +epsilon = p(6); +mu_rel = x(2) - mu_b; + +dx = zeros(2,1); +dx(1) = x(2); + +dx(2) = -(k / m) * x(1) + F_fric_mod2(x, mu_rel, epsilon, F_s, k, delta) / m; + +end diff --git a/toolbox/examples/friction_model/friction_model_mod_test.m b/toolbox/examples/friction_model/friction_model_mod_test.m new file mode 100644 index 0000000..2c0eef0 --- /dev/null +++ b/toolbox/examples/friction_model/friction_model_mod_test.m @@ -0,0 +1,213 @@ +integrator = @ode45; +t0 = 0; +tf = 12; +timeinterval = [t0,tf]; +initstates = [1.133944669704 0 ]; +p(1) = 1.0; %k +p(2) = 1.0; %m +p(3) = 0.2; %mu_b +p(4) = 1; %F_s +p(5) = 3; %delta +epsilon = 1e-11; +p(6) = epsilon; %epsilon +p = reshape(p, [], 1); + +%% Solving the friction model variant without filippov mode +% %preprocessing +fprintf('Preprocessing...\n '); +odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-6); +filename = 'friction_model_RHSmod'; +dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions); +fprintf('Done, now integrate...\n'); + +% integrate +sol_ifdiff = solveODE(dhandle, timeinterval, initstates, p); +fprintf('Done \n'); + +% results +disp(sol_ifdiff); +T = 0:0.01:12; +Y = deval(sol_ifdiff, T); +switches = sol_ifdiff.switches; + +figure(1); hold on; box on; + +a = zeros(length(sol_ifdiff.x)); + +plot(T, Y(1,:), 'LineWidth', 2); +plot(T, Y(2,:), 'LineWidth', 2); +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); + +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end + +xlabel('Time (s)', 'FontSize', 12); +ylabel('States', 'FontSize', 12); +title('ODE Solution to Friction Model', 'FontSize', 14); + +legend({'State 1','State 2'}, 'Location', 'best'); +grid on; + +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +%disp(sol_ifdiff.idata); +%disp(sol_ifdiff.stats); + +%% Computing VDE-sensitivities + +dim_y = size(sol_ifdiff.y, 1); +dim_p = length(p); +FDstep = generateFDstep(dim_y, dim_p); +integrator_options = odeset('AbsTol', 1e-14, 'RelTol', 1e-12); +sensitivities_function_VDE = generateSensitivityFunction(dhandle, sol_ifdiff, FDstep, 'integrator_options', integrator_options); +sens = sensitivities_function_VDE(T); +Gy11 = arrayfun(@(x) x.Gy(1, 1), sens); +Gy12 = arrayfun(@(x) x.Gy(1, 2), sens); +Gy21 = arrayfun(@(x) x.Gy(2, 1), sens); +Gy22 = arrayfun(@(x) x.Gy(2, 2), sens); + +figure(500); box on; +subplot(2, 2, 1); +plot(T, Gy11, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end +xlabel('Time (s)', 'FontSize', 12); +ylabel('Gy11', 'FontSize', 12); +title('Gy11', 'FontSize', 14); +legend({'Gy11'}, 'Location', 'best'); +grid on; +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +subplot(2, 2, 2); +plot(T, Gy12, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end +xlabel('Time (s)', 'FontSize', 12); +ylabel('Gy12', 'FontSize', 12); +title('Gy12', 'FontSize', 14); +legend({'Gy12'}, 'Location', 'best'); +grid on; +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +subplot(2, 2, 3); +plot(T, Gy21, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end +xlabel('Time (s)', 'FontSize', 12); +ylabel('Gy21', 'FontSize', 12); +title('Gy21', 'FontSize', 14); +legend({'Gy21'}, 'Location', 'best'); +grid on; +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +subplot(2, 2, 4); +plot(T, Gy22, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end +xlabel('Time (s)', 'FontSize', 12); +ylabel('Gy22', 'FontSize', 12); +title('Gy22', 'FontSize', 14); +legend({'Gy22'}, 'Location', 'best'); +grid on; +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + + + +%% Solving the friction model variant with filippov mode +% %preprocessing +fprintf('Preprocessing...\n '); +filename2 = 'friction_model_RHSmod2'; +dhandle2 = prepareDatahandleForIntegration(filename2, 'integrator', func2str(integrator), 'options', odeoptions); +fprintf('Done, now integrate...\n'); + +% integrate +sol_ifdiff2 = solveODE(dhandle2, timeinterval, initstates, p); +fprintf('Done \n'); + +% results +disp(sol_ifdiff2); +T = 0:0.01:12; +Y2 = deval(sol_ifdiff2, T); +switches2 = sol_ifdiff2.switches; + +figure(2); hold on; box on; + +a2 = zeros(length(sol_ifdiff2.x)); + +plot(T, Y2(1,:), 'LineWidth', 2); +plot(T, Y2(2,:), 'LineWidth', 2); +plot(sol_ifdiff2.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); + +for s = switches2 + xline(s, '--r', 'LineWidth', 1.5); +end + +xlabel('Time (s)', 'FontSize', 12); +ylabel('States', 'FontSize', 12); +title('ODE Solution to Friction Model (Filippov)', 'FontSize', 14); + +legend({'State 1','State 2'}, 'Location', 'best'); +grid on; + +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +%disp(sol_ifdiff2.idata); +%disp(sol_ifdiff2.stats); + +%% creating difference plot + +figure(3); hold on; box on; + +% remove zeros from err for log-plot +a2 = epsilon * ones(length(sol_ifdiff2.x)); +fildiff1 = abs(Y2(1,:) - Y(1,:)); +fildiff2 = abs(Y2(2,:) - Y(2,:)); + +plot(T, fildiff1, 'LineWidth', 2); +plot(T, fildiff2, 'LineWidth', 2); +plot(sol_ifdiff2.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); + +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end + +xlabel('Time (s)', 'FontSize', 12); +ylabel('Difference', 'FontSize', 12); +title('Difference of filippov and non-filippov integrations', 'FontSize', 14); + +legend({'Diff State 1','Diff State 2'}, 'Location', 'best'); +grid on; + +set(gca, 'FontSize', 12, 'LineWidth', 1.2, 'YScale', 'log'); + + +%% 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z1^FB`|HG+cMH}@G=^|m-Af0n|eI`8#VwL1im(}FAQ7i%m0tAtoT4$GAE&?`xOAmrD z5QOjiij{k5S;Rn6%gvh?b_h1VZeM) zUD20ycU}93{e~odCOp0%1ddY*>h99(R*p_v1zR~*r(WL-?2zH|3_H~*X%rA*H)l8h zT*=+O@BsJ+2wVmjumDqxSi(3#{c@MlQkIsMMgE0rm9J-A22VJPLOV8!V#eWxrJ zTd4sPuqClgIO43LQpL^OTMSgke4Pf z0yPDAl=A!=mtZgg6$93P0+$*q0vwm$Fai*lq%Z;+0xE%*z%T+y0yBb_z%T+EmnJa+ z9UPIGT4%xl001`u001Ze000000003100000A%mB|FajHwfGz?Lmx(a~5C$oP0ssI2 D From 25ecd1ca235c7a7c7607c441d7853b4a41bd9e9b Mon Sep 17 00:00:00 2001 From: Marvin Date: Tue, 16 Dec 2025 13:51:43 +0100 Subject: [PATCH 3/7] modified: toolbox/examples/friction_model/friction_model_mod_test.m --- .../friction_model/friction_model_mod_test.m | 38 ++++++++++++++----- 1 file changed, 29 insertions(+), 9 deletions(-) diff --git a/toolbox/examples/friction_model/friction_model_mod_test.m b/toolbox/examples/friction_model/friction_model_mod_test.m index 2c0eef0..559636c 100644 --- a/toolbox/examples/friction_model/friction_model_mod_test.m +++ b/toolbox/examples/friction_model/friction_model_mod_test.m @@ -69,7 +69,7 @@ figure(500); box on; subplot(2, 2, 1); -plot(T, Gy11, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +scatter(T, Gy11, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -82,7 +82,7 @@ set(gca, 'FontSize', 12, 'LineWidth', 1.2); subplot(2, 2, 2); -plot(T, Gy12, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +scatter(T, Gy12, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -95,7 +95,7 @@ set(gca, 'FontSize', 12, 'LineWidth', 1.2); subplot(2, 2, 3); -plot(T, Gy21, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +scatter(T, Gy21, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -108,7 +108,7 @@ set(gca, 'FontSize', 12, 'LineWidth', 1.2); subplot(2, 2, 4); -plot(T, Gy22, 'LineWidth', 2, 'Color', [0, 0.5, 0]); hold on; +scatter(T, Gy22, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -192,20 +192,40 @@ %% Display of the switching functions -nu_rel = Y(2,:) - p(3); +nu_rel = (Y(2,:) - p(3)); -figure(4); hold on; box on; +figure(4); +subplot(2, 1, 1); hold on; box on; -plot(T, nu_rel, 'LineWidth', 2); -plot(sol_ifdiff2.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); +plot(sol_ifdiff2.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); + +for s = switches + xline(s, '--r', 'LineWidth', 1.5); +end + +xlabel('Time (s)', 'FontSize', 12); +ylabel('\nu_{rel} (switching function)', 'FontSize', 12); +title('Evolution of first switching condition', 'FontSize', 14); + +legend({'\nu_{rel}'}, 'Location', 'best'); +grid on; + +set(gca, 'FontSize', 12, 'LineWidth', 1.2); + +subplot(2, 1, 2); hold on; box on; + +scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); +plot(sol_ifdiff2.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); end xlabel('Time (s)', 'FontSize', 12); -ylabel('nu_rel (switching function)', 'FontSize', 12); +ylabel('\nu_{rel} (switching function)', 'FontSize', 12); title('Evolution of first switching condition', 'FontSize', 14); +ylim([-2 * epsilon 2 * epsilon]); legend({'\nu_{rel}'}, 'Location', 'best'); grid on; From 98bcb06c2619f74eaba6914fa14bd5347ccb9334 Mon Sep 17 00:00:00 2001 From: Marvin Date: Wed, 17 Dec 2025 14:32:04 +0100 Subject: [PATCH 4/7] modified: toolbox/examples/friction_model/friction_model_mod_test.m --- toolbox/examples/friction_model/friction_model_mod_test.m | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/toolbox/examples/friction_model/friction_model_mod_test.m b/toolbox/examples/friction_model/friction_model_mod_test.m index 559636c..4cbab85 100644 --- a/toolbox/examples/friction_model/friction_model_mod_test.m +++ b/toolbox/examples/friction_model/friction_model_mod_test.m @@ -1,6 +1,6 @@ integrator = @ode45; t0 = 0; -tf = 12; +tf = 30; timeinterval = [t0,tf]; initstates = [1.133944669704 0 ]; p(1) = 1.0; %k @@ -26,7 +26,7 @@ % results disp(sol_ifdiff); -T = 0:0.01:12; +T = t0:0.01:tf; Y = deval(sol_ifdiff, T); switches = sol_ifdiff.switches; @@ -135,7 +135,7 @@ % results disp(sol_ifdiff2); -T = 0:0.01:12; +T = t0:0.01:tf; Y2 = deval(sol_ifdiff2, T); switches2 = sol_ifdiff2.switches; @@ -167,7 +167,6 @@ figure(3); hold on; box on; -% remove zeros from err for log-plot a2 = epsilon * ones(length(sol_ifdiff2.x)); fildiff1 = abs(Y2(1,:) - Y(1,:)); fildiff2 = abs(Y2(2,:) - Y(2,:)); From ec9d4574d223fab62506e58088f49286601d6d5b Mon Sep 17 00:00:00 2001 From: Marvin Date: Tue, 24 Feb 2026 17:49:07 +0100 Subject: [PATCH 5/7] Reworked the friction model code (variable names) and file structure deleted: toolbox/examples/friction_model/F_fric.m renamed: toolbox/examples/friction_model/friction_model_RHSmod.m -> toolbox/examples/friction_model/friction_RHS_filippov.m renamed: toolbox/examples/friction_model/friction_model_RHSmod2.m -> toolbox/examples/friction_model/friction_RHS_no_filippov.m deleted: toolbox/examples/friction_model/friction_model_RHS.m renamed: toolbox/examples/friction_model/friction_model_mod_test.m -> toolbox/examples/friction_model/friction_model_comparison.m deleted: toolbox/examples/friction_model/friction_model_test.m renamed: toolbox/examples/friction_model/F_fric_mod2.m -> toolbox/examples/friction_model/helpers/F_fric_fil.m renamed: toolbox/examples/friction_model/F_fric_mod.m -> toolbox/examples/friction_model/helpers/F_fric_no_fil.m --- toolbox/examples/friction_model/F_fric.m | 8 -- ...model_RHSmod.m => friction_RHS_filippov.m} | 8 +- ...l_RHSmod2.m => friction_RHS_no_filippov.m} | 7 +- .../friction_model/friction_model_RHS.m | 17 ----- ...mod_test.m => friction_model_comparison.m} | 76 ++++++++++--------- .../friction_model/friction_model_test.m | 54 ------------- .../{F_fric_mod2.m => helpers/F_fric_fil.m} | 2 +- .../{F_fric_mod.m => helpers/F_fric_no_fil.m} | 2 +- 8 files changed, 48 insertions(+), 126 deletions(-) delete mode 100644 toolbox/examples/friction_model/F_fric.m rename toolbox/examples/friction_model/{friction_model_RHSmod.m => friction_RHS_filippov.m} (64%) rename toolbox/examples/friction_model/{friction_model_RHSmod2.m => friction_RHS_no_filippov.m} (59%) delete mode 100644 toolbox/examples/friction_model/friction_model_RHS.m rename toolbox/examples/friction_model/{friction_model_mod_test.m => friction_model_comparison.m} (70%) delete mode 100644 toolbox/examples/friction_model/friction_model_test.m rename toolbox/examples/friction_model/{F_fric_mod2.m => helpers/F_fric_fil.m} (63%) rename toolbox/examples/friction_model/{F_fric_mod.m => helpers/F_fric_no_fil.m} (86%) diff --git a/toolbox/examples/friction_model/F_fric.m b/toolbox/examples/friction_model/F_fric.m deleted file mode 100644 index 21f0c5c..0000000 --- a/toolbox/examples/friction_model/F_fric.m +++ /dev/null @@ -1,8 +0,0 @@ -function res = F_fric(x, mu_rel, epsilon, F_s, k, delta) - if abs(mu_rel) <= epsilon % epsilon small (mu rel = 0 numerically) - res = min(abs(k * x(1)), F_s) * sign(k * x(1)); - else - res = -( (F_s * sign(mu_rel)) / (1 + delta * abs(mu_rel)) ); - end -end - diff --git a/toolbox/examples/friction_model/friction_model_RHSmod.m b/toolbox/examples/friction_model/friction_RHS_filippov.m similarity index 64% rename from toolbox/examples/friction_model/friction_model_RHSmod.m rename to toolbox/examples/friction_model/friction_RHS_filippov.m index 13923b1..b14fbaa 100644 --- a/toolbox/examples/friction_model/friction_model_RHSmod.m +++ b/toolbox/examples/friction_model/friction_RHS_filippov.m @@ -1,4 +1,4 @@ -function dx = friction_model_RHSmod(t, x, p) +function dx = friction_RHS_filippov(t, x, p) % p = (k, m, mu_b, F_s, delta, epsilon) k = p(1); m = p(2); @@ -11,8 +11,6 @@ dx = zeros(2,1); dx(1) = x(2); +dx(2) = -(k / m) * x(1) + F_fric_fil(x, mu_rel, epsilon, F_s, k, delta) / m; - -dx(2) = -(k / m) * x(1) + F_fric_mod(x, mu_rel, epsilon, F_s, k, delta) / m; - -end \ No newline at end of file +end diff --git a/toolbox/examples/friction_model/friction_model_RHSmod2.m b/toolbox/examples/friction_model/friction_RHS_no_filippov.m similarity index 59% rename from toolbox/examples/friction_model/friction_model_RHSmod2.m rename to toolbox/examples/friction_model/friction_RHS_no_filippov.m index 5633e2c..fbdd538 100644 --- a/toolbox/examples/friction_model/friction_model_RHSmod2.m +++ b/toolbox/examples/friction_model/friction_RHS_no_filippov.m @@ -1,4 +1,4 @@ -function dx = friction_model_RHSmod2(t, x, p) +function dx = friction_RHS_no_filippov(t, x, p) % p = (k, m, mu_b, F_s, delta, epsilon) k = p(1); m = p(2); @@ -10,7 +10,6 @@ dx = zeros(2,1); dx(1) = x(2); +dx(2) = -(k / m) * x(1) + F_fric_no_fil(x, mu_rel, epsilon, F_s, k, delta) / m; -dx(2) = -(k / m) * x(1) + F_fric_mod2(x, mu_rel, epsilon, F_s, k, delta) / m; - -end +end \ No newline at end of file diff --git a/toolbox/examples/friction_model/friction_model_RHS.m b/toolbox/examples/friction_model/friction_model_RHS.m deleted file mode 100644 index 01a658c..0000000 --- a/toolbox/examples/friction_model/friction_model_RHS.m +++ /dev/null @@ -1,17 +0,0 @@ -function dx = friction_model_RHS(t, x, p) -% p = (k, m, mu_b, F_s, delta, epsilon) -k = p(1); -m = p(2); -mu_b = p(3); -F_s = p(4); -delta = p(5); -epsilon = p(6); -mu_rel = x(2) - mu_b; - -dx = zeros(2,1); -dx(1) = x(2); - -dx(2) = -(k / m) * x(1) + F_fric(x, mu_rel, epsilon, F_s, k, delta) / m; - -end - diff --git a/toolbox/examples/friction_model/friction_model_mod_test.m b/toolbox/examples/friction_model/friction_model_comparison.m similarity index 70% rename from toolbox/examples/friction_model/friction_model_mod_test.m rename to toolbox/examples/friction_model/friction_model_comparison.m index 4cbab85..d35a9e6 100644 --- a/toolbox/examples/friction_model/friction_model_mod_test.m +++ b/toolbox/examples/friction_model/friction_model_comparison.m @@ -12,31 +12,33 @@ p(6) = epsilon; %epsilon p = reshape(p, [], 1); +warning('off', 'IFDIFF:chattering'); + %% Solving the friction model variant without filippov mode % %preprocessing fprintf('Preprocessing...\n '); odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-6); -filename = 'friction_model_RHSmod'; +filename = 'friction_RHS_no_filippov'; dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions); fprintf('Done, now integrate...\n'); % integrate -sol_ifdiff = solveODE(dhandle, timeinterval, initstates, p); +sol_no_filippov = solveODE(dhandle, timeinterval, initstates, p); fprintf('Done \n'); % results -disp(sol_ifdiff); +disp(sol_no_filippov); T = t0:0.01:tf; -Y = deval(sol_ifdiff, T); -switches = sol_ifdiff.switches; +Y_no_fil = deval(sol_no_filippov, T); +switches = sol_no_filippov.switches; figure(1); hold on; box on; -a = zeros(length(sol_ifdiff.x)); +a = zeros(length(sol_no_filippov.x)); -plot(T, Y(1,:), 'LineWidth', 2); -plot(T, Y(2,:), 'LineWidth', 2); -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(T, Y_no_fil(1,:), 'LineWidth', 2); +plot(T, Y_no_fil(2,:), 'LineWidth', 2); +plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -56,11 +58,11 @@ %% Computing VDE-sensitivities -dim_y = size(sol_ifdiff.y, 1); +dim_y = size(sol_no_filippov.y, 1); dim_p = length(p); FDstep = generateFDstep(dim_y, dim_p); integrator_options = odeset('AbsTol', 1e-14, 'RelTol', 1e-12); -sensitivities_function_VDE = generateSensitivityFunction(dhandle, sol_ifdiff, FDstep, 'integrator_options', integrator_options); +sensitivities_function_VDE = generateSensitivityFunction(dhandle, sol_no_filippov, FDstep, 'integrator_options', integrator_options); sens = sensitivities_function_VDE(T); Gy11 = arrayfun(@(x) x.Gy(1, 1), sens); Gy12 = arrayfun(@(x) x.Gy(1, 2), sens); @@ -70,7 +72,7 @@ figure(500); box on; subplot(2, 2, 1); scatter(T, Gy11, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); end @@ -83,7 +85,7 @@ subplot(2, 2, 2); scatter(T, Gy12, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); end @@ -96,7 +98,7 @@ subplot(2, 2, 3); scatter(T, Gy21, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); end @@ -109,7 +111,7 @@ subplot(2, 2, 4); scatter(T, Gy22, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); end @@ -125,29 +127,29 @@ %% Solving the friction model variant with filippov mode % %preprocessing fprintf('Preprocessing...\n '); -filename2 = 'friction_model_RHSmod2'; -dhandle2 = prepareDatahandleForIntegration(filename2, 'integrator', func2str(integrator), 'options', odeoptions); +filenamefil = 'friction_RHS_filippov'; +dhandle_filippov = prepareDatahandleForIntegration(filenamefil, 'integrator', func2str(integrator), 'options', odeoptions); fprintf('Done, now integrate...\n'); % integrate -sol_ifdiff2 = solveODE(dhandle2, timeinterval, initstates, p); +sol_filippov = solveODE(dhandle_filippov, timeinterval, initstates, p); fprintf('Done \n'); % results -disp(sol_ifdiff2); +disp(sol_filippov); T = t0:0.01:tf; -Y2 = deval(sol_ifdiff2, T); -switches2 = sol_ifdiff2.switches; +Y_filippov = deval(sol_filippov, T); +switches_fil = sol_filippov.switches; figure(2); hold on; box on; -a2 = zeros(length(sol_ifdiff2.x)); +a2 = zeros(length(sol_filippov.x)); -plot(T, Y2(1,:), 'LineWidth', 2); -plot(T, Y2(2,:), 'LineWidth', 2); -plot(sol_ifdiff2.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(T, Y_filippov(1,:), 'LineWidth', 2); +plot(T, Y_filippov(2,:), 'LineWidth', 2); +plot(sol_filippov.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches2 +for s = switches_fil xline(s, '--r', 'LineWidth', 1.5); end @@ -163,17 +165,20 @@ %disp(sol_ifdiff2.idata); %disp(sol_ifdiff2.stats); +%% Compute filippov sensitivities +% to do + %% creating difference plot figure(3); hold on; box on; -a2 = epsilon * ones(length(sol_ifdiff2.x)); -fildiff1 = abs(Y2(1,:) - Y(1,:)); -fildiff2 = abs(Y2(2,:) - Y(2,:)); +a2 = epsilon * ones(length(sol_filippov.x)); +fildiff1 = abs(Y_filippov(1,:) - Y_no_fil(1,:)); +fildiff2 = abs(Y_filippov(2,:) - Y_no_fil(2,:)); plot(T, fildiff1, 'LineWidth', 2); plot(T, fildiff2, 'LineWidth', 2); -plot(sol_ifdiff2.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_filippov.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -188,16 +193,15 @@ set(gca, 'FontSize', 12, 'LineWidth', 1.2, 'YScale', 'log'); - %% Display of the switching functions -nu_rel = (Y(2,:) - p(3)); +nu_rel = (Y_no_fil(2,:) - p(3)); figure(4); subplot(2, 1, 1); hold on; box on; scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); -plot(sol_ifdiff2.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_filippov.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -215,7 +219,7 @@ subplot(2, 1, 2); hold on; box on; scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); -plot(sol_ifdiff2.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_filippov.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); for s = switches xline(s, '--r', 'LineWidth', 1.5); @@ -225,8 +229,8 @@ ylabel('\nu_{rel} (switching function)', 'FontSize', 12); title('Evolution of first switching condition', 'FontSize', 14); ylim([-2 * epsilon 2 * epsilon]); - legend({'\nu_{rel}'}, 'Location', 'best'); grid on; +set(gca, 'FontSize', 12, 'LineWidth', 1.2); -set(gca, 'FontSize', 12, 'LineWidth', 1.2); \ No newline at end of file +warning('on', 'IFDIFF:chattering'); \ No newline at end of file diff --git a/toolbox/examples/friction_model/friction_model_test.m b/toolbox/examples/friction_model/friction_model_test.m deleted file mode 100644 index 77fff1b..0000000 --- a/toolbox/examples/friction_model/friction_model_test.m +++ /dev/null @@ -1,54 +0,0 @@ -integrator = @ode45; -t0 = 0; -tf = 12; -timeinterval = [t0,tf]; -initstates = [1.133944669704 0 ]; -p(1) = 1.0; %k -p(2) = 1.0; %m -p(3) = 0.2; %mu_b -p(4) = 1; %F_s -p(5) = 3; %delta -p(6) = 1e-15; %epsilon -p = reshape(p, [], 1); - -%% preprocessing -fprintf('Preprocessing...\n '); -odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-6); -filename = 'friction_model_RHS'; -dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions); -fprintf('Done, now integrate...\n'); - -%% integrate -sol_ifdiff = solveODE(dhandle, timeinterval, initstates, p); -fprintf('Done \n'); - -%% results -disp(sol_ifdiff); -T = 0:0.01:12; -Y = deval(sol_ifdiff, T); -switches = sol_ifdiff.switches; - -figure; hold on; box on; - -a = zeros(length(sol_ifdiff.x)); - -plot(T, Y(1,:), 'LineWidth', 2); -plot(T, Y(2,:), 'LineWidth', 2); -plot(sol_ifdiff.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -%plot(switches, Ys(2,:), 'rx', 'MarkerSize', 8, 'LineWidth', 1.5); - -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end - -xlabel('Time (s)', 'FontSize', 12); -ylabel('States', 'FontSize', 12); -title('ODE Solution to Friction Model', 'FontSize', 14); - -legend({'State 1','State 2'}, 'Location', 'best'); -grid on; - -set(gca, 'FontSize', 12, 'LineWidth', 1.2); - -disp(sol_ifdiff.idata); -disp(sol_ifdiff.stats); diff --git a/toolbox/examples/friction_model/F_fric_mod2.m b/toolbox/examples/friction_model/helpers/F_fric_fil.m similarity index 63% rename from toolbox/examples/friction_model/F_fric_mod2.m rename to toolbox/examples/friction_model/helpers/F_fric_fil.m index b7c8c68..1078deb 100644 --- a/toolbox/examples/friction_model/F_fric_mod2.m +++ b/toolbox/examples/friction_model/helpers/F_fric_fil.m @@ -1,4 +1,4 @@ -function res = F_fric_mod2(x, mu_rel, epsilon, F_s, k, delta) +function res = F_fric_fil(x, mu_rel, epsilon, F_s, k, delta) if mu_rel <= 0 res = F_s / (1 - delta * mu_rel); else diff --git a/toolbox/examples/friction_model/F_fric_mod.m b/toolbox/examples/friction_model/helpers/F_fric_no_fil.m similarity index 86% rename from toolbox/examples/friction_model/F_fric_mod.m rename to toolbox/examples/friction_model/helpers/F_fric_no_fil.m index d52871b..6563491 100644 --- a/toolbox/examples/friction_model/F_fric_mod.m +++ b/toolbox/examples/friction_model/helpers/F_fric_no_fil.m @@ -1,4 +1,4 @@ -function res = F_fric_mod(x, mu_rel, epsilon, F_s, k, delta) +function res = F_fric_no_fil(x, mu_rel, epsilon, F_s, k, delta) if mu_rel <= -epsilon res = F_s / (1 - delta * mu_rel); %res = -F_s * mu_rel; From 580714ce5ab4606c99311cd3f0be51c70997d688 Mon Sep 17 00:00:00 2001 From: Marvin Date: Tue, 3 Mar 2026 12:01:23 +0100 Subject: [PATCH 6/7] Modified files according to comments by Lev modified: toolbox/examples/friction_model/friction_model_comparison.m modified: toolbox/examples/friction_model/helpers/F_fric_no_fil.m --- .../friction_model_comparison.m | 181 ++++++++---------- .../friction_model/helpers/F_fric_no_fil.m | 2 - 2 files changed, 82 insertions(+), 101 deletions(-) diff --git a/toolbox/examples/friction_model/friction_model_comparison.m b/toolbox/examples/friction_model/friction_model_comparison.m index d35a9e6..ac30634 100644 --- a/toolbox/examples/friction_model/friction_model_comparison.m +++ b/toolbox/examples/friction_model/friction_model_comparison.m @@ -1,3 +1,20 @@ +%% Source: Stick-Slip Vibrations Induced by Alternate Friction Models +% paper by: R. Leine, D. van Campen, A. de Kraker, and L. van den Steen +% doi: 10.1023/A:1008289604683 + +% The system describes dry friction of a spring suspended weight sitting on a +% constantly moving conveyor belt. The weight moves along with the belt +% until spring tension becomes too high and the weight is pushed back. +% This creates a switched periodic motion. + +% The corresponding ODE can be formulated in a filippov and non-filippov +% variant and serves as a perfect example to test the accuracy of not only +% the filippov integration but also the resulting sensitivities. + +% Both formulations can be found in "Numerical Solution of Optimal Control +% Problems with Explicit and Implicit Switches" by Andreas Meyer +% chapter: 15.3 + integrator = @ode45; t0 = 0; tf = 30; @@ -10,161 +27,134 @@ p(5) = 3; %delta epsilon = 1e-11; p(6) = epsilon; %epsilon -p = reshape(p, [], 1); +% saving current warning state for filippov detection (then turn off warning) +initial_filippov_warning_state = warning('query', 'IFDIFF:chattering').state; warning('off', 'IFDIFF:chattering'); %% Solving the friction model variant without filippov mode -% %preprocessing +% preprocessing fprintf('Preprocessing...\n '); odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-6); filename = 'friction_RHS_no_filippov'; -dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions); +dhandle = prepareDatahandleForIntegration(filename, 'integrator', integrator, 'options', odeoptions); fprintf('Done, now integrate...\n'); % integrate -sol_no_filippov = solveODE(dhandle, timeinterval, initstates, p); +try + sol_no_filippov = solveODE(dhandle, timeinterval, initstates, p); +catch ME + warning(initial_filippov_warning_state, 'IFDIFF:chattering'); + warning('Problem integrating model variant wihtout filippov behaviour...'); + rethrow(ME); +end fprintf('Done \n'); % results -disp(sol_no_filippov); T = t0:0.01:tf; Y_no_fil = deval(sol_no_filippov, T); -switches = sol_no_filippov.switches; figure(1); hold on; box on; -a = zeros(length(sol_no_filippov.x)); +integrator_steps_marker_vals = zeros(length(sol_no_filippov.x)); plot(T, Y_no_fil(1,:), 'LineWidth', 2); plot(T, Y_no_fil(2,:), 'LineWidth', 2); -plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); - -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end +plot(sol_no_filippov.x, integrator_steps_marker_vals, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +xline(sol_no_filippov.switches, '--r', 'LineWidth', 1.5); xlabel('Time (s)', 'FontSize', 12); ylabel('States', 'FontSize', 12); title('ODE Solution to Friction Model', 'FontSize', 14); -legend({'State 1','State 2'}, 'Location', 'best'); +legend({'Position of Weight','Velocity of Weight'}, 'Location', 'best'); grid on; set(gca, 'FontSize', 12, 'LineWidth', 1.2); -%disp(sol_ifdiff.idata); -%disp(sol_ifdiff.stats); - %% Computing VDE-sensitivities dim_y = size(sol_no_filippov.y, 1); dim_p = length(p); FDstep = generateFDstep(dim_y, dim_p); integrator_options = odeset('AbsTol', 1e-14, 'RelTol', 1e-12); -sensitivities_function_VDE = generateSensitivityFunction(dhandle, sol_no_filippov, FDstep, 'integrator_options', integrator_options); -sens = sensitivities_function_VDE(T); +try + sensitivities_function_VDE = generateSensitivityFunction(dhandle, sol_no_filippov, FDstep, 'integrator_options', integrator_options); + sens = sensitivities_function_VDE(T); +catch ME + warning(initial_filippov_warning_state, 'IFDIFF:chattering'); + warning('Problem with sensitivities in model variant wihtout filippov behaviour...'); + rethrow(ME) +end Gy11 = arrayfun(@(x) x.Gy(1, 1), sens); Gy12 = arrayfun(@(x) x.Gy(1, 2), sens); Gy21 = arrayfun(@(x) x.Gy(2, 1), sens); Gy22 = arrayfun(@(x) x.Gy(2, 2), sens); figure(500); box on; -subplot(2, 2, 1); -scatter(T, Gy11, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end -xlabel('Time (s)', 'FontSize', 12); -ylabel('Gy11', 'FontSize', 12); -title('Gy11', 'FontSize', 14); -legend({'Gy11'}, 'Location', 'best'); -grid on; -set(gca, 'FontSize', 12, 'LineWidth', 1.2); -subplot(2, 2, 2); -scatter(T, Gy12, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); +Gy = {Gy11, Gy12, Gy21, Gy22}; +names = {'Gy11','Gy12','Gy21','Gy22'}; + +% plot the sensitivities w.r.t. the initial states +for k = 1:4 + subplot(2,2,k) + hold on + + scatter(T, Gy{k}, 'LineWidth',0.5,'Color',[0 0.5 0],'Marker','.') + plot(sol_no_filippov.x, integrator_steps_marker_vals, 'rx','MarkerSize',8,'LineWidth',1,'Color',[0 0 0.5]) + + xline(sol_no_filippov.switches,'--r','LineWidth',1.5); + + xlabel('Time (s)','FontSize',12) + ylabel(names{k},'FontSize',12) + title(names{k},'FontSize',14) + legend(names{k},'Location','best') + grid on + set(gca,'FontSize',12,'LineWidth',1.2) end -xlabel('Time (s)', 'FontSize', 12); -ylabel('Gy12', 'FontSize', 12); -title('Gy12', 'FontSize', 14); -legend({'Gy12'}, 'Location', 'best'); -grid on; -set(gca, 'FontSize', 12, 'LineWidth', 1.2); - -subplot(2, 2, 3); -scatter(T, Gy21, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end -xlabel('Time (s)', 'FontSize', 12); -ylabel('Gy21', 'FontSize', 12); -title('Gy21', 'FontSize', 14); -legend({'Gy21'}, 'Location', 'best'); -grid on; -set(gca, 'FontSize', 12, 'LineWidth', 1.2); - -subplot(2, 2, 4); -scatter(T, Gy22, 'LineWidth', 0.5, 'Color', [0, 0.5, 0], Marker='.'); hold on; -plot(sol_no_filippov.x, a, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end -xlabel('Time (s)', 'FontSize', 12); -ylabel('Gy22', 'FontSize', 12); -title('Gy22', 'FontSize', 14); -legend({'Gy22'}, 'Location', 'best'); -grid on; -set(gca, 'FontSize', 12, 'LineWidth', 1.2); - %% Solving the friction model variant with filippov mode -% %preprocessing +% preprocessing fprintf('Preprocessing...\n '); filenamefil = 'friction_RHS_filippov'; -dhandle_filippov = prepareDatahandleForIntegration(filenamefil, 'integrator', func2str(integrator), 'options', odeoptions); +dhandle_filippov = prepareDatahandleForIntegration(filenamefil, 'integrator', integrator, 'options', odeoptions); fprintf('Done, now integrate...\n'); % integrate -sol_filippov = solveODE(dhandle_filippov, timeinterval, initstates, p); +try + sol_filippov = solveODE(dhandle_filippov, timeinterval, initstates, p); +catch + warning(initial_filippov_warning_state, 'IFDIFF:chattering'); + warning('Problem integrating model variant wiht filippov behaviour...'); + rethrow(ME); +end fprintf('Done \n'); % results -disp(sol_filippov); T = t0:0.01:tf; Y_filippov = deval(sol_filippov, T); -switches_fil = sol_filippov.switches; figure(2); hold on; box on; -a2 = zeros(length(sol_filippov.x)); +integrator_steps_marker_fil = zeros(length(sol_filippov.x)); plot(T, Y_filippov(1,:), 'LineWidth', 2); plot(T, Y_filippov(2,:), 'LineWidth', 2); -plot(sol_filippov.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(sol_filippov.x, integrator_steps_marker_fil, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches_fil - xline(s, '--r', 'LineWidth', 1.5); -end +xline(sol_filippov.switches, '--r', 'LineWidth', 1.5); xlabel('Time (s)', 'FontSize', 12); ylabel('States', 'FontSize', 12); title('ODE Solution to Friction Model (Filippov)', 'FontSize', 14); -legend({'State 1','State 2'}, 'Location', 'best'); +legend({'Position of Weight','Velocity of Weight'}, 'Location', 'best'); grid on; set(gca, 'FontSize', 12, 'LineWidth', 1.2); -%disp(sol_ifdiff2.idata); -%disp(sol_ifdiff2.stats); - %% Compute filippov sensitivities % to do @@ -172,23 +162,19 @@ figure(3); hold on; box on; -a2 = epsilon * ones(length(sol_filippov.x)); -fildiff1 = abs(Y_filippov(1,:) - Y_no_fil(1,:)); -fildiff2 = abs(Y_filippov(2,:) - Y_no_fil(2,:)); +integrator_steps_marker_fil = epsilon * ones(length(sol_filippov.x)); +fildiff = abs(Y_filippov - Y_no_fil); -plot(T, fildiff1, 'LineWidth', 2); -plot(T, fildiff2, 'LineWidth', 2); -plot(sol_filippov.x, a2, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); +plot(T, fildiff(1,:), T, fildiff(2,:), 'LineWidth', 2); +plot(sol_filippov.x, integrator_steps_marker_fil, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end +xline(sol_no_filippov.switches, '--r', 'LineWidth', 1.5); xlabel('Time (s)', 'FontSize', 12); ylabel('Difference', 'FontSize', 12); title('Difference of filippov and non-filippov integrations', 'FontSize', 14); -legend({'Diff State 1','Diff State 2'}, 'Location', 'best'); +legend({'Diff Position','Diff Velocity'}, 'Location', 'best'); grid on; set(gca, 'FontSize', 12, 'LineWidth', 1.2, 'YScale', 'log'); @@ -203,9 +189,7 @@ scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); plot(sol_filippov.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end +xline(sol_no_filippov.switches, '--r', 'LineWidth', 1.5); xlabel('Time (s)', 'FontSize', 12); ylabel('\nu_{rel} (switching function)', 'FontSize', 12); @@ -221,9 +205,7 @@ scatter(T, nu_rel, 'LineWidth', 0.5, Marker='.'); plot(sol_filippov.x, 0, 'rx', 'MarkerSize', 8, 'LineWidth', 1, 'Color', [0, 0, 0.5]); -for s = switches - xline(s, '--r', 'LineWidth', 1.5); -end +xline(sol_no_filippov.switches, '--r', 'LineWidth', 1.5); xlabel('Time (s)', 'FontSize', 12); ylabel('\nu_{rel} (switching function)', 'FontSize', 12); @@ -233,4 +215,5 @@ grid on; set(gca, 'FontSize', 12, 'LineWidth', 1.2); -warning('on', 'IFDIFF:chattering'); \ No newline at end of file +% return warining state to what it was before running the code +warning(initial_filippov_warning_state, 'IFDIFF:chattering'); \ No newline at end of file diff --git a/toolbox/examples/friction_model/helpers/F_fric_no_fil.m b/toolbox/examples/friction_model/helpers/F_fric_no_fil.m index 6563491..5b8a81a 100644 --- a/toolbox/examples/friction_model/helpers/F_fric_no_fil.m +++ b/toolbox/examples/friction_model/helpers/F_fric_no_fil.m @@ -1,11 +1,9 @@ function res = F_fric_no_fil(x, mu_rel, epsilon, F_s, k, delta) if mu_rel <= -epsilon res = F_s / (1 - delta * mu_rel); - %res = -F_s * mu_rel; else if mu_rel >= epsilon res = (-F_s) / (1 + delta * mu_rel); - %res = -F_s * mu_rel; else if k*x(1) <= -F_s res = F_s; From b4180eb517361b924a713230ae5da8f67e9ece68 Mon Sep 17 00:00:00 2001 From: Marvin Date: Tue, 3 Mar 2026 12:34:12 +0100 Subject: [PATCH 7/7] Restore unintentionally modified .mlx files --- toolbox/doc/GettingStarted.mlx | Bin 128005 -> 127972 bytes .../liveExamples/CanonicalSensitivities.mlx | Bin 143775 -> 165495 bytes .../liveExamples/canonicalExRHS_test_live.mlx | Bin 82974 -> 131154 bytes 3 files 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