Fig 1.
SAE tire axis coordinate system.
Fig 2.
Inputs and outputs of TM-easy tire model [7].
Fig 3.
Generalized tire parameters [6].
Fig 4.
Response of tire force to slip [6].
Fig 5.
Four-wheel SSV dynamic model [6].
Table 1.
Parameters of P-3AT robots for displaced CG.
Table 2.
Tire model parameters for μx = 0.5 and μy = 0.4.
Table 3.
Tire model parameters for μx = 0.4 and μy = 0.2.
Table 4.
Tire model parameters for μx = 0.6 and μy = 0.4.
Table 5.
Tire model parameters for μx = 0.7 and μy = 0.5.
Table 6.
Tire model parameters for μx = 0.9 and μy = 0.5.
Table 7.
Tire model parameters for μx = 0.3 and μy = 0.2.
Fig 6.
Block diagram of four-wheel SSV.
Fig 7.
Proposed control architecture.
Fig 8.
Fuzzy membership function for yaw with .
Fig 9.
Fuzzy membership functions for yaw with Δρu.
Fig 10.
Fuzzy membership function for the longitudinal velocity with s.
Fig 11.
Fuzzy membership functions for longitudinal velocity with Δρθ.
Table 8.
Gains of SMC.
Fig 12.
Yaw tracking comparison.
Fig 13.
Longitudinal velocity tracking comparison.
Fig 14.
Comparison of yaw errors in case of SMC, FSMC and fractional FSMC.
Fig 15.
Comparison of velocity errors in case of SMC FSMC and fractional FSMC.
Table 9.
Yaw and velocity errors comparison.
Fig 16.
Control torque response generated by SMC, FSMC and fractional FSMC based laws.
Fig 17.
Yaw control torque response generated by SMC, FSMC and fractional FSMC based laws.
Fig 18.
Velocity control torque response generated by SMC, FSMC and fractional FSMC based laws.
Fig 19.
Yaw tracking comparison with ramp yaw rate as reference trajectory.
Fig 20.
Comparison of yaw errors in case of SMC, FSMC and fractional FSMC under ramp yaw rate as reference.
Fig 21.
Comparison of yaw torque in case of SMC, FSMC and fractional FSMC under ramp yaw rate as reference.
Fig 22.
Longitudinal velocity tracking comparison under ramp yaw rate as reference.
Fig 23.
Longitudinal velocity error tracking comparison under ramp yaw rate as reference.
Fig 24.
Longitudinal velocity torque comparison under ramp yaw rate as reference.
Table 10.
Yaw and velocity errors comparison with ramp yaw rate as reference.
Fig 25.
Velocity error at different coefficient of friction.
Fig 26.
Yaw control error at different coefficient of friction.
Table 11.
Maximum yaw and velocity control errors at different friction coefficient for FSMC scheme.
Fig 27.
Control torque time response for SMC, FSMC and fractional FSMC.
Fig 28.
Velocity control torque time response for SMC, FSMC and fractional FSMC.
Fig 29.
Yaw control torque time response for SMC, FSMC and fractional FSMC.