**5. Conclusions**

From simulation and experimental analysis performed on induction motor control some interesting conclusions can be drawn. In APBC strategies an important simplification of control scheme based on FOC principle can be attained when using the TFCP, allowing an effective control of the system without the necessity of having a rotor flux sensor or implementing a rotor flux observer to orientate the field. For APBC strategy the use of timevarying adaptive gains noticeably improves the transient behavior of controlled system, both for tracking as well as for regulation, when compared with the APBC strategy with fixed adaptive gains and also when compared with classical control strategies. Results are very similar for both the SISO and the MIMO approaches when using APBC. Compared with other control schemes proposed in the literature such as those based on traditional PI (Chee-Mun, 19998), sliding modes (Chan & Wang, 1996 ; Dunningan et al, 1998 ; Taoutaou & Castro-Linares, 2000; Araujo & Freitas, 2000), artificial intelligence (Bose, 1997 ; Vas, 1999) and non adaptive passivity (Taoutaou & Castro-Linares, 2000; Espinosa & Ortega, 1995), we have been able to develop four simple and novel controllers. They have adaptive characteristics, being robust in the presence of load parameter variations. Simple proportional controllers are used for the rotor speed, rotor flux and stator current control loops. They are also robust for a large range of proportional gain variations.

In the case of energy shaping strategy, IDA-PBC, a novel control scheme was studied and implemented. Since the original strategy was only designed for speed control, the addition of an outer speed loop of proportional-integral type, allowed obtaining certain robustness with respect to torque perturbations. In this strategy was necessary the design and implementation of a rotor flux observer, adding certain complexity to the complete system.

Since the BCS has fixed controller parameters its behavior is not as good as the adaptive strategies studied and presented here.

From simulation results obtained in this study it is possible to state that the integration order of FOPI controller plays a central role in speed control of an IM, when compared with the BCS. Choosing a suitable value of the integration order allows obtaining fast/slow responses and over/under damped responses. For this particular case of IM speed control , it was observed that for integration orders lesser than 1 the stabilization time is rather large and the controlled variable may not present overshoot. On the contrary, for values over 1 the stabilization time is small (and diminishes as integration order increases); the overshoot increases as the integration order does, reaching instability for integration order equal to 2. It was observed that the best results obtained from this study correspond to integration orders near to 1.40, presenting small rise and stabilization times, though with certain degree of overshoot.

In conclusion, the adaptive strategies studied present clear advantages with respect to the BCS used as basis of comparison. Amongst the adaptive schemes the APBC with timevarying adaptive gains is the one that behaves better.
