The Structural Robustness of the Induction Motor Stator Currents Subsystem

Abstract

Stator-currents control is essential for several high-performance induction motor control schemes such as field oriented control. There are numerous reports dealing with sophisticated control schemes for this subsystem. However, classical linear controllers remain widely used due to their experimental success and simplicity. Considering that the induction motor stator currents subsystem is normally represented by a fifth order non-linear multivariable model, it is remarkable that simple fixed linear controllers, such as typical proportional integral schemes, are able to provide adequate robustness and performance in practice. In fact, it is normally assumed that this subsystem is "easy" to control, and the difficulties are mostly technical. Moreover, it is common practice to consider a stable first order linear single input single output (SISO) system as a design model. On the other hand, it is widely known that stable and minimum phase uncertain SISO systems are also "easy" to control. In this article it is formally demonstrated that the stator currents subsystem of the induction motor is the multivariable equivalent of such SISO systems. That is, it is formally demonstrated that this process is "easy" to control. This result may assist with better induction motor control and may serve as an example of the evaluation of similar multivariable systems. Real time experimental results are included.

Fundamental Analysis of the Perturbation Rejection Characteristics of Single-Input-Multiple-Output Systems Subject to Multiple Perturbations

“…In the first case ℎ 3 ( )/ 1 ( ) = 0 according to (21) which properly indicates that ℎ 3 is not affected by 1 . In the other case ℎ 3 ( )/ 2 ( ) = 1/( + 1/2) which confirms that the third tank is only affected in open-loop by 2 .…”

“…This function is inherent to the nature of the process and reveals important dynamical characteristics related to the existence of robust controllers satisfying arbitrary specifications. The main characteristics of the MSF are as follows [17,21,26]: (i) It determines the cross-coupling characteristics of each input-output configuration. In particular, its magnitude quantifies the coupling between channels.…”

“…In this context, it is pertinent to recall that the MSF has been historically used to measure the structural robustness of multivariable systems [8][9][10][11][12][13][14][16][17][18][19][20][21]. As such, ( 0 ) → 1 is a sign of low structural robustness and it is undesired, since in that case the transmission zeros may change from minimum phase to nonminimum phase.…”

“…Calculating (21) for this output and perturbation configuration yields ℎ 2 ( )/ 2 ( ) = 0.25/( + 1/2)( + 3/4). This case is interesting as the calculation of the actual perturbation rejection using controller (36) results in …”

“…The ICAD framework allows using classical single input single output (SISO) measures of robustness and performance for multiple input multiple output (MIMO) systems. The ICAD framework allows the interpretation of complex control problems in the context of engineering systems [8,16,[18][19][20][21]. Although ICAD was originally proposed as a decentralized control design tool, in this article ICAD is adapted for the study of the SIMO perturbation rejection problem.…”