Fig 1.
The flow chart of the MSIBWO algorithm.
Table 1.
Benchmark functions.
Table 2.
The parameter settings for each algorithm.
Table 3.
Test results.
Table 4.
The results of Friedman test.
Fig 2.
Convergence curves for unimodal function test.
(a): Convergence curves of seven algorithms for F1. (b): Convergence curves of seven algorithms for F2. (c): Convergence curves of seven algorithms for F3. (d): Convergence curves of seven algorithms for F4.
Fig 3.
Convergence curves for multimodal function test.
(a): Convergence curves of seven algorithms for F5. (b): Convergence curves of seven algorithms for F6. (c): Convergence curves of seven algorithms for F7. (d): Convergence curves of seven algorithms for F8.
Table 5.
Comparison of computational complexity of algorithms.
Fig 4.
Model of electrohydraulic servo actuator.
Fig 5.
Half-vehicle model.
Fig 6.
The FOPID parameter optimization flow chart based on the MSIBWO algorithm.
Fig 7.
The control system for the electrohydraulic servo actuator.
Table 6.
The parameters of the electrohydraulic servo actuator.
Fig 8.
The iterative curves of the algorithms.
Table 7.
The values corresponding to the three controllers.
Fig 9.
Dynamic force-response curve of the system under step signal.
Table 8.
The system response performance indicators.
Table 9.
Test results for step response.
Table 10.
Results of Kruskal-Wallis test under step signal.
Fig 10.
The force-response curves of the system under different frequency sine signals.
(a) The force-response curve of the system at a sine signal frequency of 0.1 Hz. (b) The force-response curve of the system at a sine signal frequency of 0.5 Hz. (c) The force-response curve of the system at a sine signal frequency of 1.0 Hz. (d) The force-response curve of the system at a sine signal frequency of 2.0Hz. (e) The force-response curve of the system at a sine signal frequency of 4.0 Hz.
Table 11.
The RMSE for the system under different frequency sine signals.
Table 12.
Test results for sine response.
Table 13.
Results of Kruskal-Wallis test under sine signals.
Fig 11.
The force-response curves of the system with external disturbance forces.
Fig 12.
The force-tracking error curves.
Table 14.
The RMSE for the system under the different controllers.
Fig 13.
The half-vehicle model is established in MATLAB/Simulink.
Table 15.
The parameters of the half-vehicle model.
Fig 14.
The vertical acceleration curve of the vehicle body.
Fig 15.
The pitch acceleration curve of the vehicle body.
Table 16.
The ride comfort indicators.