IPMSM Torque Control Strategies based on LUTs and VCT feedback for Robust Control under Machine Parameter Variations E. Trancho 1 , E. Ibarra 1 , A. Arias 2 , C. Salazar 1 , I. Lopez 1 , A. Diaz de Guere˜ nu 1 , A. Pe˜ na 1 1 Tecnalia Research and Innovation, Industry and Transport Unit Parque Cient´ ıfico y Tecnol´ ogico de Bizkaia, c/ Geldo, Edif. 700, 48160 Derio (Spain) 2 Institut d’Organitzaci´ o i Control, Universitat Polit` ecnica de Catalunya. Diagonal, 647, 08028 Barcelona elena.trancho@tecnalia.com Abstract—In recent years, Interior Permanent Magnet Syn- chronous Machines (IPMSMs) have attracted a considerable attention in the scientific community and industry for Electric and Hybrid Electric Vehicle (HEV) propulsion systems. Look- up Table (LUT) based Field Oriented Control (FOC) strategies are widely used for IPMSM torque control. However, LUTs strongly depend on machine parameters. Deviations of these parameters due to machine ageing, temperature or manufac- turing inaccuracies can lead to control instabilities in the field weakening region. In this paper, two novel hybrid IPMSM control strategies combining the usage of LUTs and Voltage Constraint Tracking (VCT) feedbacks are proposed in order to overcome the aforementioned controllability issues. Simulation results that demonstrate the validity of the proposed approaches are presented. Index Terms—IPMSM, FOC, LUT, VCT I. I NTRODUCTION Nowadays, Interior Permanent Magnet Synchronous Ma- chines (IPMSMs) are receiving a considerable attention in a number of high performance applications, such as Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs) due to their high power density and high efficiency over wide speed and torque ranges [1]–[4]. A variety of torque control methods for IPMSMs can be found in the scientific literature [1], [5]–[15]. Look-up- Table (LUT) based Field Oriented Control (FOC) strategies (figure 1) are one of the most commonly used torque control techniques [6]–[8]. These techniques are relatively simple to implement and require low computational cost. However, the LUT approach has the following drawbacks: • LUTs can require a relatively high amount of memory, depending on their size and number of dimensions. • Machine electric parameters may vary due to manufactur- ing tolerances, machine ageing or temperature variations. Thus, the torque control may be affected by irregularities and unconsciousness during operation, leading to possible instabilities in the Field Weakening (FW) region. Taking the latter into account, this paper presents a ro- bust 2D-LUT based current control, ensuring controllability under electrical parameter variations and/or resolver offset 3 phase inverter PWM IPMSM PI PI i U i V W i UVW dq θ m θ m θ m ω m ω m , v V * v U * v W * V DC V DC dq UVW T em * i d i q ff q ff d i d * i q * Current setpoint gen. g 1-6 Temp Fig. 1. General diagram of a 4D-LUT based IPMSM field oriented control. determination errors. In order to achieve this goal, two novel Voltage-Constraint-Tracking (VCT) based feedback strategies are proposed to guarantee that the system remains under the maximum voltage constraint in the field weakening region. As far as the autors are concerned, hybrid solutions integrating both LUT-based control and voltage feedback have not been deeply studied in scientific literature. II. LUT BASED FOC CONTROL A. IPMSM control fundamentals The stator voltages of an IPMSM in the dq synchronous rotating reference frame can be obtained as [16]: v d = R s i d + dΨ d dt - ω e Ψ q , (1) v q = R s i q + dΨ q dt + ω e Ψ d , (2) where the magnetic fluxes are: Ψ d = L d i d +Ψ pm , (3) Ψ q = L q i q . (4) being v d , v q , i d and i q the stator voltages and currents; R s , L d and L q the stator resistance and inductances, Ψ pm the