5. Conclusions
The mechatronic elevator system driven by a PMSM is mathematically modeled, and the energy equations in the electrical and mechanical parts are also formulated. The 7-R profile is discussed and the optimal fraction σ = 0.5 has been obtained with minimizing the IAEE by the SLPSO method. In other words, trajectory with σ = 0.5 has the non-maximum acceleration (deceleration) region, the minimum IAEE and longest flight time. On the contrary, the simple 3-R profile is proposed by a 7-D polynomial trajectory with the same constraint conditions. The optimal fraction η = 0.4 is found by the SLPSO with the minimum IAEE. Specially, the different parameters, groups 1 and 2, are compared, and it is found the 7-R profile with σ = 0.5 and 3-R profile with η = 0.4 also have the minimum IAEE for the same system model. It means that the optimal solutions are insensitive to the system model. Finally, the new 5-R and 3-R profiles are compared and their relative errors of the IAEE and flight time are small. In summary, when the final position, maximum velocity and acceleration are specified for any mechatronic system, the proposed trajectory design method can also be applied for a PTP multi-region profile with the minimum IAEE.