Applications of Sliding Mode Control to Benchmark Problems

J.C. Wu (Civil Engineering, Tamkang University, Taiwan)
J.N. Yang (Civil and Environmental Engineering, University of California Irvine)
A.K. Agrawal (Civil and Environmental Engineering, University of California Irvine)

paper (PDF, 1087KB); abstract

Active Mass Driver (AMD) Results

	LQG						CSMC						CSMC&C
	sensor: a₃		sensors: a₁, a₂, a₃		sensors: x_m, a₁, a₂, a₃, a_m		sensor: a₃		sensors: a₁, a₂, a₃		sensors: x_m, a₁, a₂, a₃, a_m		sensor: a₃		sensors: a₁, a₂, a₃		sensors: x_m, a₁, a₂, a₃, a_m
J1	0.211194		0.194251		0.187818		0.211423		0.196320		0.197868		0.266055		0.194808		0.211395
J2	0.323352		0.295638		0.284573		0.323463		0.295591		0.293641		0.409300		0.293937		0.318274
J3	0.769583		0.812623		0.844419		0.765006		0.811035		0.822149		0.548999		0.828617		0.778301
J4	0.759950		0.798370		0.825886		0.752395		0.797007		0.804220		0.542843		0.794520		0.755979
J5	0.780486		0.828740		0.832666		0.767664		0.800385		0.777477		0.530915		0.740851		0.644339
J6	0.319619	0.384433	0.316367	0.381805	0.308265	0.377927	0.316670	0.378405	0.311179	0.375960	0.307699	0.373821	0.373861	0.417904	0.306794	0.370004	0.327493	0.375717
J7	0.495660	0.691478	0.488802	0.669092	0.472473	0.661634	0.516771	0.682410	0.488757	0.669491	0.472963	0.667404	0.718762	0.700086	0.555904	0.626916	0.620065	0.628698
J8	1.145109	1.364268	1.178333	1.502241	1.247948	1.623979	1.135990	1.474050	1.205135	1.581921	1.233771	1.683200	0.698253	0.936601	1.241495	1.866337	1.197120	1.729242
J9	1.144221	1.564398	1.160820	1.437649	1.209752	1.481112	1.130565	1.397370	1.187024	1.405960	1.218260	1.490262	0.724057	0.915431	1.234478	1.573891	1.209736	1.454986
J10	1.170644	1.879942	1.102575	1.751496	1.107770	1.649072	1.181723	1.412342	1.120408	1.464746	1.074897	1.567258	0.867454	0.906429	1.181716	1.521713	1.107086	1.282066
uRMS	0.247263		0.256735		0.270982		0.245432		0.259933		0.266832		0.171029		0.274172		0.263722
amRMS	1.397070		1.483444		1.490471		1.374118		1.432690		1.391684		0.950339		1.326123		1.153367
xmRMS	1.008154		1.064536		1.106188		1.002157		1.062455		1.077016		0.719189		1.085488		1.019575
uMAX	1.063787	0.651697	1.098927	0.707124	1.160118	0.753863	1.060666	0.684417	1.126701	0.734966	1.148066	0.781797	0.698391	0.440540	1.190553	0.868649	1.161229	0.808696
amMAX	5.911751	4.850251	5.568005	4.518860	5.594239	4.254606	5.967703	3.643842	5.658059	3.779043	5.428229	4.043526	4.380640	2.338586	5.967667	3.926020	5.590783	3.307731
xmMAX	3.859017	2.264685	3.970981	2.493720	4.205585	2.695804	3.828285	2.446923	4.061305	2.625988	4.157809	2.794111	2.353112	1.554757	4.183839	3.098120	4.034294	2.870542
	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe

The Kanai-Tajimi results were performed using w_g =37.3 rads/sec, z_g =0.3, T_f =300 secs.

Active Tendon (TEN) Results

	LQG						CSMC						CSMC&C
	sensor: a₃		sensors: a₁, a₂, a₃		sensors: x_p, a₁, a₂, a₃, f		sensor: a₃		sensors: a₁, a₂, a₃		sensors: x_p, a₁, a₂, a₃, f		sensor: f		sensors: x_p, a₃, f		sensors: x_p, a₁, a₂, a₃, f
J1	0.161995		0.168092		0.164620		0.157550		0.156774		0.157236		0.190519		0.183082		0.172685
J2	0.340909		0.354484		0.347204		0.338982		0.337664		0.338666		0.392666		0.380207		0.366910
J3	0.034708		0.032830		0.032940		0.031234		0.031180		0.030816		0.039393		0.036677		0.031735
J4	0.036236		0.034140		0.034268		0.033048		0.033103		0.032809		0.039787		0.036983		0.030747
J5	0.008639		0.009061		0.008894		0.009436		0.009435		0.009467		0.008971		0.008999		0.009678
J6	0.249740	0.325564	0.255939	0.327622	0.250646	0.322342	0.240353	0.318990	0.240824	0.316575	0.242109	0.315707	0.279817	0.336725	0.270486	0.333336	0.258310	0.324548
J7	0.518823	0.857773	0.531607	0.860309	0.525230	0.851359	0.488782	0.835655	0.493495	0.843832	0.494217	0.843681	0.574841	0.816232	0.552209	0.812632	0.497379	0.809748
J8	0.053124	0.064036	0.049545	0.060639	0.049091	0.066186	0.047264	0.066569	0.046752	0.067536	0.046345	0.067413	0.058838	0.064036	0.055901	0.063140	0.052012	0.061131
J9	0.055828	0.071651	0.051524	0.066555	0.053927	0.067726	0.056340	0.071475	0.060237	0.073746	0.059425	0.072904	0.053032	0.064757	0.049562	0.060953	0.043092	0.054888
J10	0.034641	0.027345	0.035407	0.027124	0.035016	0.026931	0.037297	0.029284	0.037489	0.029361	0.037341	0.029539	0.035443	0.023339	0.035213	0.024151	0.038150	0.026582
uRMS	0.629665		0.594763		0.597800		0.584773		0.584633		0.578044		0.693047		0.649522		0.581140
amRMS	2.496748		2.618724		2.570340		2.726927		2.726777		2.736044		2.592688		2.600809		2.796886
xmRMS	0.081216		0.076822		0.077079		0.073087		0.072960		0.072108		0.092179		0.085825		0.074259
uMAX	2.667679	1.886880	2.466915	1.790466	2.473741	1.953977	2.397563	2.015744	2.421991	2.045687	2.418822	2.042422	2.848799	1.823298	2.725608	1.808357	2.610929	1.822409
amMAX	10.011174	7.902565	10.232543	7.838951	10.119577	7.783054	10.778825	8.463162	10.834250	8.485392	10.791571	8.536705	10.242924	6.744878	10.176466	6.979608	11.025216	7.682122
xmMAX	0.342649	0.242056	0.319567	0.229216	0.316635	0.250183	0.304854	0.251633	0.301547	0.255286	0.298923	0.254822	0.379504	0.242056	0.360562	0.238669	0.335475	0.231074
	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe	ElCentro	Hachinohe

The Kanai-Tajimi results were performed using w_g =14.5 rads/sec, z_g =0.3, T_f =750 secs.

Numbers in this face represent violated constraints.
Numbers in this face are the larger of the ElCentro/Hachinohe values.

Sensor labels are:

x_m active mass displacement

x_p active tendon displacement

a₁ first floor acceleration

a₂ second floor acceleration

a₃ third floor acceleration

a_m active mass acceleration

f active tendon force

Page designed by Erik A. Johnson (JohnsonE@usc.edu).