**1. Introduction**

The design of suitable control algorithms for induction motors (IM) has been widely investigated for more than two decades. Since the beginning of field oriented control (FOC) of AC drives, seen as a viable replacement of the traditional DC drives, several techniques from linear control theory have been used in the different control loops of the FOC scheme, such as Proportional Integral (PI) regulators, and exact feedback linearization (Bose, 1997, 2002; Vas, 1998). Due to their linear characteristics, these techniques do not guarantee suitable machine operation for the whole operation range, and do not consider the parameter variations of the motor-load set.

Several nonlinear control techniques have also been proposed to overcome the problems mentioned above, such as sliding mode techniques (Williams & Green, 1991; Al-Nimma & Williams, 1980; Araujo & Freitas, 2000) and artificial intelligence techniques using fuzzy logic, neuronal networks or a combination of them (Vas, 1999; Al-Nimma & Williams, 1980; Bose, 2002). All these techniques are based on complex control strategies differing of the advanced control techniques described here.

In this chapter we present a collection of advanced control strategies for induction motors, developed by the authors during the last ten years, which overcome some of the disadvantages of the previously mentioned control techniques. The techniques studied and presented in this chapter are based on equivalent passivity by adaptive feedback, passivity by interconnection and damping assignment (IDA-PCB) and fractional order proportionalintegral controller (FOPIC) in the standard field oriented control scheme (FOC).

All of the control strategies described here guarantee high performance control, such as high starting torque at low speed and during the transient period, accuracy in steady state, a wide range of speed control, and good response under speed and load changes. For all of

© 2012 Duarte-Mermoud and Travieso-Torres, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Duarte-Mermoud and Travieso-Torres, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

the control strategies developed throughout the chapter, after a brief theoretical description of each one of them, simulation as well as experimental results of their application to control IM are presented and discussed.

Advanced Control Techniques for Induction Motors 297

*sx i*

*sy i*

*sx i*

*sy i*

*s*

 *s* 

**Figure 2.** Basic control scheme with field oriented block (BCS)

**2.1. SISO Adaptive Passivity Based Control (ABPC) theory** 

(Byrnes et al, 1991), with explicit linear parametric dependence

 

guaranteeing stability described in the following section.

*T*

\* *sx*

\* *sx*

with *z n, y , u , A(y, z)* 

*a m, b , 0 nxn, p*  

*s*

 *s* 

**Figure 1.** Proposed control scheme with field oriented block (APBC)

\* *sd i*

\* *sq i*

*sd i*

*sq i*

The SISO APBC approach was proposed in Castro-Linares & Duarte-Mermoud (1998) and Duarte-Mermoud et al (2001), for systems parameterized in the following normal form

, ,

,

(1)

 *n, P(y, z)* 

 *nxn.* The function 0 0 *z fz* ( ) is known as zero dynamics

  *<sup>n</sup>*; and the parameters

<sup>0</sup>

 *, f0* 

(Isidori, 1995; Nijmiejer & Van der Shaft, 1996). Besides, it is necessary to check that the system is locally weakly minimum phase by finding a positive definite differentiable function *W0(z)* satisfying <sup>0</sup> 0 0 <sup>0</sup> ( ) / ( ) 0, *<sup>T</sup> Wz z fz* (Byrnes et al, 1991)*.* According to the theory presented in the original papers, for locally weakly minimum phase systems of the form (1) with matrix *B(y,z)* being invertible, there exist two adaptive controllers

*a b o p*

 

 *m, B(y, z)* 

*y Ayz Byzu z f z Pyzy*

\* *sd i*

*sd*

*sd u*

*sq u*

*sd i*

*sq i*

*sd u*

*sq u*

*sd i*

*sq i*

*sq*

\* *sq i*

*sd i*

*sq i*

The main contribution of this Chapter is to show that IM control techniques based on passivity, IDA-PCB and FOPIC can be successfully used in a FOC scheme, presenting some advantages over the classical techniques.
