Figure 1.
Disc D in the left of the complex plane.
Figure 1.
Disc D in the left of the complex plane.
Figure 2.
Time response of for the initial condition , .
Figure 2.
Time response of for the initial condition , .
Figure 3.
Time response of for the initial condition , .
Figure 3.
Time response of for the initial condition , .
Figure 4.
Location of the closed-loop eigenvalues in the SDREAM-FDR (, ).
Figure 4.
Location of the closed-loop eigenvalues in the SDREAM-FDR (, ).
Figure 5.
Location of the closed-loop eigenvalues for Update Algorithm 1 (, ).
Figure 5.
Location of the closed-loop eigenvalues for Update Algorithm 1 (, ).
Figure 6.
Location of the closed-loop eigenvalues for Update Algorithm 2 (, ).
Figure 6.
Location of the closed-loop eigenvalues for Update Algorithm 2 (, ).
Figure 7.
Disc region and eigenvalue location samples for the Update Algorithm 1 (, ).
Figure 7.
Disc region and eigenvalue location samples for the Update Algorithm 1 (, ).
Figure 8.
Disc region and eigenvalue location samples for Update Algorithm 2 (, ).
Figure 8.
Disc region and eigenvalue location samples for Update Algorithm 2 (, ).
Figure 9.
Time response of for the initial condition , .
Figure 9.
Time response of for the initial condition , .
Figure 10.
Time response of for the initial condition , .
Figure 10.
Time response of for the initial condition , .
Figure 11.
Location of the closed-loop eigenvalues in the SDREAM-FDR (, ).
Figure 11.
Location of the closed-loop eigenvalues in the SDREAM-FDR (, ).
Figure 12.
Location of the closed-loop eigenvalues for Update Algorithm 1 (, ).
Figure 12.
Location of the closed-loop eigenvalues for Update Algorithm 1 (, ).
Figure 13.
Location of the closed-loop eigenvalues for Update Algorithm 2 (, ).
Figure 13.
Location of the closed-loop eigenvalues for Update Algorithm 2 (, ).
Figure 14.
Disc region and eigenvalue location samples for Update Algorithm 1 (, ).
Figure 14.
Disc region and eigenvalue location samples for Update Algorithm 1 (, ).
Figure 15.
Disc region and eigenvalue location samples for Update Algorithm 2 (, ).
Figure 15.
Disc region and eigenvalue location samples for Update Algorithm 2 (, ).
Figure 16.
Three-DOF Helicopter Experimental Setup.
Figure 16.
Three-DOF Helicopter Experimental Setup.
Figure 17.
Free-body diagram of 3-DOF Helicopter.
Figure 17.
Free-body diagram of 3-DOF Helicopter.
Figure 18.
Location of the closed-loop eigenvalues in the SDREAM-FDR in the simulation.
Figure 18.
Location of the closed-loop eigenvalues in the SDREAM-FDR in the simulation.
Figure 19.
Location of the closed-loop eigenvalues for Update Algorithm 1 in the simulation.
Figure 19.
Location of the closed-loop eigenvalues for Update Algorithm 1 in the simulation.
Figure 20.
Location of the closed-loop eigenvalues for Update Algorithm 2 in the simulation.
Figure 20.
Location of the closed-loop eigenvalues for Update Algorithm 2 in the simulation.
Figure 21.
Disc region and eigenvalue location samples for Update Algorithm 1 in the simulation.
Figure 21.
Disc region and eigenvalue location samples for Update Algorithm 1 in the simulation.
Figure 22.
Disc region and eigenvalue location samples for Update Algorithm 2 in the simulation.
Figure 22.
Disc region and eigenvalue location samples for Update Algorithm 2 in the simulation.
Figure 23.
Elevation response of the helicopter controlled by three different approaches in simulations.
Figure 23.
Elevation response of the helicopter controlled by three different approaches in simulations.
Figure 24.
Travel response of the helicopter controlled by three different approaches in simulations.
Figure 24.
Travel response of the helicopter controlled by three different approaches in simulations.
Figure 25.
Motion of the location of the closed-loop eigenvalues in the SDREAM-FDR.
Figure 25.
Motion of the location of the closed-loop eigenvalues in the SDREAM-FDR.
Figure 26.
Motion of the location of the closed-loop eigenvalues for Update Algorithm 1.
Figure 26.
Motion of the location of the closed-loop eigenvalues for Update Algorithm 1.
Figure 27.
Motion of the location of the closed-loop eigenvalues for Update Algorithm 2.
Figure 27.
Motion of the location of the closed-loop eigenvalues for Update Algorithm 2.
Figure 28.
Disc region and eigenvalue location samples for Update Algorithm 1.
Figure 28.
Disc region and eigenvalue location samples for Update Algorithm 1.
Figure 29.
Disc region and eigenvalue location samples for Update Algorithm 2.
Figure 29.
Disc region and eigenvalue location samples for Update Algorithm 2.
Figure 30.
Elevation response of the helicopter controlled by three different approaches.
Figure 30.
Elevation response of the helicopter controlled by three different approaches.
Figure 31.
Travel response of the helicopter controlled by three different approaches.
Figure 31.
Travel response of the helicopter controlled by three different approaches.
Figure 32.
Pitch response of the helicopter controlled by three different approaches.
Figure 32.
Pitch response of the helicopter controlled by three different approaches.
Figure 33.
Controller gains of the SDREAM-FDR.
Figure 33.
Controller gains of the SDREAM-FDR.
Figure 34.
Controller gains of the approach using Update Algorithm 1.
Figure 34.
Controller gains of the approach using Update Algorithm 1.
Figure 35.
Controller gains of the approach using Update Algorithm 2.
Figure 35.
Controller gains of the approach using Update Algorithm 2.
Figure 36.
Front motor input of the helicopter controlled by three different approaches.
Figure 36.
Front motor input of the helicopter controlled by three different approaches.
Figure 37.
Back motor input of the helicopter controlled by three different approaches.
Figure 37.
Back motor input of the helicopter controlled by three different approaches.
Table 1.
Performance Indices for the initial condition , .
Table 1.
Performance Indices for the initial condition , .
States | Algorithms | ISE | IAE | ITAE | ITSE |
---|
| SDREAM-FDR | 2.913 | 2.238 | 2.023 | 1.153 |
| Algorithm 1 | 2.313 | 1.561 | 0.815 | 0.597 |
| Algorithm 2 | 1.518 | 0.958 | 0.282 | 0.224 |
| SDREAM-FDR | 2.896 | 3.970 | 11.279 | 3.677 |
| Algorithm 1 | 2.526 | 2.817 | 4.423 | 1.962 |
| Algorithm 2 | 2.127 | 1.962 | 1.754 | 0.966 |
Table 2.
Performance Indices for the initial condition , .
Table 2.
Performance Indices for the initial condition , .
States | Algorithms | ISE | IAE | ITAE | ITSE |
---|
| SDREAM-FDR | 0.440 | 0.951 | 1.011 | 0.251 |
| Algorithm 1 | 0.118 | 0.321 | 0.175 | 0.026 |
| Algorithm 2 | 0.059 | 0.084 | 0.010 | 9.551 × |
| SDREAM-FDR | 2.298 | 3.233 | 9.046 | 3.711 × |
| Algorithm 1 | 1.537 | 1.852 | 2.674 | 2.280 × |
| Algorithm 2 | 0.833 | 0.827 | 0.567 | 0.119 × |
Table 3.
Units of variables.
Table 3.
Units of variables.
Variables | Units |
---|
| radian |
| radian |
| radian |
| radian/s |
| radian/s |
| radian/s |
| voltage |
| voltage |
Table 4.
Parameter Values of the Three-DOF Helicopter Model.
Table 4.
Parameter Values of the Three-DOF Helicopter Model.
Parameter | Constant Coefficient |
---|
| 0.2517 |
| 0.2105 |
| 0.3290 |
| 1.5664 |
| 16.200 |
| 7.3200 |
| 1.000 |
| 0.1011 |
| 0.5040 |
| 1.3400 |
| 6.1600 |
| 1.000 |
| 4.000 |
Table 5.
Performance Indices for simulation studies.
Table 5.
Performance Indices for simulation studies.
States | Algorithms | ISE | IAE | ITAE | ITSE |
---|
| SDREAM-FDR | 256.695 | 33.875 | 84.218 | 344.201 |
Elevation Motion | Algorithm 1 | 228.111 | 30.576 | 70.882 | 269.844 |
| Algorithm 2 | 182.148 | 24.618 | 47.330 | 168.824 |
| SDREAM-FDR | 1334.8 | 134.334 | 5150.8 | 50,763 |
Travel Motion | Algorithm 1 | 1103 | 120.303 | 4590.41 | 41,716 |
| Algorithm 2 | 713.817 | 92.053 | 3472.6 | 26,673 |
Table 6.
Performance indices for experimental studies.
Table 6.
Performance indices for experimental studies.
States | Algorithms | ISE | IAE | ITAE | ITSE |
---|
| SDREAM-FDR | 735.023 | 88.734 | 585.259 | 1981 |
Elevation Motion | Algorithm 1 | 483.564 | 62.43 | 387.902 | 897.356 |
| Algorithm 2 | 196.272 | 27.179 | 163.415 | 142.37 |
| SDREAM-FDR | 755.611 | 129.584 | 4552.8 | 27,696 |
Travel Motion | Algorithm 1 | 745.19 | 122.759 | 4474.6 | 25,689 |
| Algorithm 2 | 369.362 | 74.125 | 2418.9 | 12,845 |