Predictive Versus Vector Control Of The Induction Motor

The paper deals with the vector control and predictive control of the induction motor. For the vector control, the rotor flux oriented one is pointed out, with highlight on the voltage source inverter type. The influence of the most important parameter variations (e.g. stator resistance) is discussed. A simple (and practical) method for avoiding these influences is presented, based on proper simulation models. Following the basics of the predictive control, a simulation model for this type of command is presented, together with simulations results. Finally, the results are cross analysed and further actions are proposed the work continuation. INTRODUCTION On one hand, since the basic work concerning torque and field control due to Leonhard, Blaschke and their followers in the 1970s, the AC drives became a competitive technology with respect to the traditional one, based on DC drives. In rotating references, solidar with the rotor flux, stator flux or magnetizing flux respectively, there is an obvious decoupling between the two components of the stator current: while the direct component acts on the flux modulus only and produces the reactive component, the quadrature component generates the torque, being the active component. The two components of the stator current may be thus controlled independently and the flux and torque generation are thus decoupled, similarly to the DC motor. Due to results simplicity, the rotor flux orriented control has imposed almost as a standard. From here, two types of control were engineered. On one hand we have the direct control drives, where flux position and modulus are known while the reactive and active components of the stator current are computed in the proper reference frame using the set-point torque and flux. On the other hand we have the indirect control drives, where the slip frequency is computed and imposed without direct knowledge of the flux, while the reference system change from the flux-reference to stator-reference one is performed by integration of the sum of the motor speed and the speed corresponding to the computed slip (Casadei et al. 2002, Vas 1998). A very simple method for the toque control is also the Direct Torque Control (DTC), suited for electrical traction applications (Takahashi and Noguchi 1986, Baader et al. 1992, Ehsani et al. 1997, Faiz et al. 1999, Haddoun et al. 2007, Ivanov 2009, Ivanov 2010). On the other hand, the increased computational capabilities of the existing DSP allow the implementation of the predictive control at the level of the converters which induce the hybrid character of the overall control system of the drive. We infer that predictive control has established itself in the last 5-7 years as a very proficient form of controlling highly nonlinear and uncertain systems; moreover the most recent results show its applicability to fast processes among which drives and their converters have a central position (Seo et al. 2009, Prieur and Tarbouriech 2011, Geyer et al. 2008, Mariethoz et al. 2010, Geyer et al. 2009, Trabelsi et al. 2008, Shi et al. 2007, Rodriguez et al. 2007, Larrinaga et al. 2007, Richter et al. 2010, Almer et al. 2010). The paper will briefly present in the first section the basics of the vector control for the rotor flux oriented control for voltage source inverter, with highlight on the influence of the parameters variations on the drive performance. A simple method for reducing these influences will be discussed based on appropriated models. The basics of the predictive control will be presented in Section 2. Section 3 will analyse the predictive control applied to the induction motor, based also on a Simulink model. Finally, conclusions will be issued and ideas for continuation will be pointed out. VECTOR CONTROL OF INDUCTION MOTOR As stated above, the vector control strategy most often used is the rotor flux oriented one. The reasons reside in the simplicity of the expressions resulted from the rotor voltage equation which mainly gives the rotor flux speed and further, by integration, the rotor flux position, used Proceedings 27th European Conference on Modelling and Simulation ©ECMS Webjørn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Editors) ISBN: 978-0-9564944-6-7 / ISBN: 978-0-9564944-7-4 (CD) at its turn for the transformation of the reference currents/voltages from the rotary frame to the stationary one. For the squirrel cage induction motor, the rotor voltages equation in terms of phasors is ( ) 0 r r r mr r r r r r d R i j P dt Ψ Ψ Ψ Ψ = + + ω − ω Ψ , (1) where Rr is the rotor resistance, r r i Ψ is the rotor current, m ω is the rotor flux speed, ω is the mechanical speed of the rotor and P is the number of pairs of poles. The Ψ subscript highlights that (1) is expressed in the rotary frame synchronous with the rotor flux r r Ψ Ψ . By assuming unsaturated operation (realistic hypothesis when the stator currents are precisely controlled), the rotor flux expressed in terms of magnetizing inductance Lm and rotor magnetizing current mr i is m r mr L i Ψ = ⋅ Consequently, (1) becomes ( ) 0 mr r m mr r m r r mr d i R i L j P i L dt Ψ = + + ω − ω ⋅ ⋅ . (2) The rotor current r r i Ψ , being immeasurable for the squirrel cage motor, is expressed in terms of the stator current s r i Ψ and the magnetizing one. By denoting the rotor time constant / r r r T L R = , (2) becomes ( ) mr r mr r r mr s r mr d i T i i j P T i dt Ψ + = − ω − ω , (3) Lr being the total rotor inductance which includes the leakages ( r m r L L Lσ = + ). By identifying the terms on each of the axes d, q, the following two expressions result which are the simplest among all the vector control types mr r sd mr d i T i i dt + = , (4) sq mr r r mr i P T i ω = ω + . (5) We notice from (4) that if the flux is kept constant ( ct. mr i = ), then = ct. sd mr i i = As the electromagnetic torque expressed in the rotor flux oriented frame is 2 3 2 m e sd sq r L t P i i L = ⋅ , (6) from (5) and (6) results that the slip speed (term 2 in (5)) is proportional with the torque and further, the mechanical characteristic of the induction motor are straight lines, quite similar to the DC motor. When the motor is supplied by a voltage source inverter, the necessary voltages are obtained by considering the stator voltages equation expressed in the same rotary frame synchronous with the rotor flux r r Ψ Ψ : s r r r s s m s r s r mr s r m s r r r d i di u R i L L dt dt j L i j L i Ψ Ψ Ψ Ψ