Original Benchmark for sensorless induction motor drives at low frequencies and validation of high gain observer Malek Ghanes, Alexis Girin and Tarik Saheb Abstract— An original benchmark for the validation of sensorless induction motor observers is proposed to evaluate them particularly in the well known case where the motor state could be unobservable. Due to the complexity of observation at low frequencies (specifically on our benchmark) we present an improvement of a high gain observer which has been tested and validated on the reference trajectories of this benchmark. I. INTRODUCTION For industrial applications, the reduction of the sensors number is an important problem. Indeed, the sensors con- tribute to increase the complexity of machineries and the cost of the installation (additional wiring and maintenance). In the field of the induction machine control, the most efficient control strategies such as field oriented control and nonlinear control require velocity measurement. Thus the sensorless control (involving an estimation of speed and position) becomes a major subject of concern. Several approaches for the sensorless control of induction machines have been proposed in the literature. Generally, using the induction motor state equations, the flux and speed can be calculated from the stator voltage and current values [5], [8], [12]. A model reference adaptive system (MRAS) [9], [11] is also an alternative method for sensorless induction motor control. In another proposed scheme [5], the flux is obtained by a full order Luenberger observer. In this case, the adaptation law to estimate the speed uses the cross product of the current error vector and the observed flux vector as input. The methods above perform well except at very low speeds, near zero stator frequency [7]. The main difficulty is the observability problem of the induction machine at low frequencies. Indeed, observability problems at low frequency have not often been taken into account in motor control design. A possibility to circumvent the difficulty is to inject high frequency signals in the stator voltage [6]. Nevertheless, few works have addressed this observability problem. In [1] a sufficient condition for lost of observability is that the excitation voltage frequency is zero and the motor is operating at constant speed. From this point of view, the first purpose of this paper is to propose a dedicated benchmark, in which the reference trajectories are defined to drive the motor from high to low frequencies, with the aim to test and validate observers M. Ghanes and A. Girin are with the Communications and Cy- bernetic Research Institute of Nantes (IRCCyN), Ecole Centrale de Nantes, BP 92101, 1 rue de la noe, 44321 Nantes Cedex 03, France. Malek.Ghanes@irccyn.ec-nantes.fr T. Saheb is with the GE44, CRTT, 44602 Saint-Nazaire cedex saheb@ge44.univ-nantes.fr without mechanical sensors. The second purpose of this paper is to use this benchmark to test a high gain observer which is an improved version of the one presented in [10]. Robustness tests are defined in the setting of the benchmark with given inductance and resistance variations. This paper is organized as follows: in section 2, the model of induction machine is reminded. The third section presents our benchmark. In the fourth section we derive a high gain observer and report simulation results. Some conclusions are drawn finally. II. INDUCTION MOTOR MODEL The equations of the induction motor model can be written using the Concordia and Park transformations [2]. The resulting dynamic equations are given in the rotor flux reference frame (d-q). Applying this transformation, the model of the motor can be described by (1)       ˙ Ω ˙ ρ ˙ i d ˙ i q ˙ ψ d       =        μψ d i d − F v J Ω pΩ+ α r Msr ψ d i q −Υi d + α r βψ d + pΩi q + α r Msr ψ d i 2 q −Υi q − βpΩψ d − pΩi d + α r M sr ψ d i d i q −α r ψ d + α r M sr i d        +       0 0 − 1 J 0 0 0 γ 0 0 0 γ 0 0 0 0         V d V q T l   (1) where i d , i q , ψ d , ρ, V d , V q , Ω and T l denote the stator currents, the rotor flux magnitude, the rotor field frame angle (rotor flux direction), the stator voltage components, the angular speed and the torque load, respectively. The subscripts s and r refer to the stator and rotor. R s and R r are the stator and rotor resistances. L s and L r are the self-inductances, M sr is the mutual inductance between the stator and rotor windings. p is the number of pole-pairs. J is the inertia of the system (motor and load) and f v is the viscous damping coefficient. Furthermore, we define α r = Rr Lr , α s = Rs Ls , β = Msr σLsLr , γ = 1 σLs , η = 1 σ , μ = pM sr JL r , σ =1 − M 2 sr L s L r , Υ=(α s η + α r βM sr ). Only stator currents and stator voltages are measured. III. OBSERVER BENCHMARK As mentioned in [1], the observability problem of induc- tion motor has been underlined by many authors. In [1], observability issues concerning this problem have been clarified and formally stated. The authors of this paper have Proceeding of the 2004 American Control Conference Boston, Massachusetts June 30 - July 2, 2004 0-7803-8335-4/04/$17.00 ©2004 AACC WeA03.3 71