A Simplified Speed Control Of Induction Motor based on a Low Cost FPGA

ABSTRACT


INTRODUCTION
The Field Oriented Control (FOC) or vector control has seen rapid expansion in recent years. The FOC can be used to vary the speed of an induction motor over a wide range. It was initially developed by Blaschke in the beginning of 1970s [1]. The FOC can be implemented in two ways Indirect and Direct control scheme. The technique described in this work is based on indirect FOC because there is no direct access to the rotor currents. Indirect vector control of the rotor currents is accomplished using the following data: a. Rotor mechanical velocity b. Instantaneous stator phase currents c. Rotor electrical time constant The motor must be equipped with stator currents sensors and a rotor velocity feedback device. Traditional indirect vector control consists of the ten blocks [2], [ [4], TMS320C24x family from Texas Instruments [5] and STM32 family from STMicroelectronics [6]. Nevertheless, hardware solutions such as FPGAs have already been used with success in AC motor control and drive applications such as pulse width modulation (PWM) [7], [8], Direct Torque Control of induction motor [9][10][11] and FOC [12], [13] drives.
In this paper, a simplified speed control of an induction motor based a low cost FPGA is proposed. The FPGA implementation is outlined by an efficient design methodology which is based on modularity and reusability concepts [14], [15].
The major benefit for using FPGA is the achievement of the digital control algorithm within a few µ second [16]. The calculation time, including the A/D conversion time of 2.4 µs, for the proposed FPGA based controller is only equal to 3.135 µs. So, for a 20 KHz power converter, the digital control feedback can be approximated quite closely to an analogue one because the effects of sampling and delay in the feedback loop are small compared to the process time scale improving therefore the performances of the control.
The first section will detail the simplified speed control strategy of an induction motor. This strategy is based on indirect FOC. The second section will present the hardware architecture design based FPGA. Finally, in a third section, some experimental results carried on a prototyping platform will be shown for the validation of the developed control system.

SIMPLIFIED SPEED CONTROL STRATEGY 2.1. Principle of the Proposed Control Strategy
The well-known discrete-time model of a squirrel-cage induction motor in the dq reference frame is used for this study. The voltage, the stator flux linkage and the electromagnetic torque Equations expressed in the rotor reference frame (d-q coordinates, with d-axis linked to the inductor) are: ( − ) = (10) Where Rs is the stator resistance, R r is the rotor resistance, Lm the stator/rotor mutual inductance, L s and L r the stator-rotor inductances, p the number of pole pairs, ω e the electrical velocity, ω r is the angular velocity of the rotor, ω sl is the slip velocity, usd and usq the d-q components of the stator voltage, i sd and i sq the d-q components of the stator current, urd and urq the d-q components of the rotor voltage, i rd and i rq the d- ISSN: 2088-8708 q components of the rotor current, ψ sd and ψ sq the d-q components of the stator flux linkage , ψ rd and ψ rq the d-q components of the rotor flux linkage and Te the electromagnetic torque. The rotor flux is allowed to be aligned with the d-axis so that This constraint can be represented by the vector diagram in Figure 1. Setting ψ rq to zero in Equations (9), the new torque Equation becomes.
If Equations (3) and (7) are combined using the constraint (12), the rotor flux Equation becomes = Where s denotes the differential operator d/dt and τ r the rotor time constant. Equation (14) implies that the rotor flux depends only on the stator current. If Equations (4) and (8) are combined using the constraint (12), the slip velocity becomes Using Equations (6) and (10) So, the slip angle is estimated by the following relation: Where θ sl0 is the initial slip angle which can be set to zero Equation (10) gives Using Equations (2), (6) and (15), the q-component stator voltage usq can be expressed with i sd , i sq and ψ rd  (14), the d-component of the rotor flux linkage ψ rd becomes constant in steadystate. Then, controlling isd implies controlling the torque. The related control scheme is shown in Figure 2.

PI-P Controller Design
The PI-P regulator is introduced into the control scheme in order to achieve a second order system with a damping coefficient ζ=0.7.
The dynamic model of the speed induction motor drive is significantly simplified, and can be reasonably represented by the block diagram shown in Figure 3. τ represents the time constant for the desired current i sq  The goal of the P regulator is to obtain a second order system with real poles in closed loop. In order to simplify the calculation we neglect the viscous friction coefficient f. Figure 4 shows the simplified block diagram of the P regulator with the process.
The P coefficient k v is selected to obtain a double real pole called ω n = Then, the transfer function becomes Where ω n =1/2τ The PI regulator is introduced before the P regulator in order to compensate the real pole ω n and to obtain a second order system in closed loop To compensate the real pole ω n , PI coefficients must obeys this rule = Using Equation (23), the global closed loop transfer function becomes Then, for a desired damping coefficient ζ, k p is expressed by the following Equation

ARCHITECTURE DESIGN
The purpose of this section is to develop a discrete-time and an optimized architecture based FPGA for the control algorithm. The most used discretization method is based on Forward shift approximation [17]. The shift form approximation is given by Where T is the sampling period. As shown in Figure 2, the control algorithm is divided into four modules. The description of the different modules is detailed below.
PI-P controller block: This module generates the digital values of the stator component references i sq * through the rotor angular velocity error. The discretization of the PI-P algorithm using the Forward shift approximation gives Where = The rotor velocity is obtained from the rotor angle using the following Equation: Where ( − ) is the rotor angle at instant + . Figure Figure 6 shows the DFG corresponding to the dq-to-abc transformation module.

Experimental Set-up
For this project, the used FPGA target is a XC2s100 from Xilinx Inc. The FPGA based hardware control system includes the speed controller, an AD converter interface and a serial interface in one FPGA chip. Figure 7 shows the corresponding implemented architecture.  To test the FPGA based controller, a test bed for the control of an induction machine was assembled. Figure 8 shows the prototyping platform. The test bed is composed of a 0.75 Kw induction motor provided with a 1024 points encoder, current sensors and a controlled load for load torque generation. The VSI module includes a three phase IGBT based inverter, a 2200 µF capacitance and a three phase diode rectifier. An AD conversion circuit board is used to convert the measured currents and an inverter interface circuit board allows the voltage level adaptation of the switching states for the control of the inverter. During experimentation, the DC voltage source E of the three phase inverter is set to 400V. Figure 9 presents the experimental results of the stator current isa for an hysteresis controller band width equal to 0% of the rated line current, a sampling frequency F s equal to 10KHz and different values of the speed input. Figure 10 presents the speed response of the system for ramp input. It shows the speed response after a torque load perturbation. The speed response is provided by the serial interface to a host PC.
Experimental results shown in Figure 9 and Figure 10 give proof that the control system satisfy the basic requirements of the control strategy and validate therefore the good functionality of the system. The same experiment has been done in the literature [20] with the indirect FOC which gave similar performances. Table 1 shows the variation of the time response for the indirect FOC and the simplified indirect FOC.

CONCLUSION
This paper presents the implementation on a FPGA of a simplified speed control for induction machine. The control algorithm is based on indirect FOC. It uses only six blocks instead of ten blocks. A PI-P regulator is designed to obtain good performances for speed tracking. The algorithm was implemented on a low cost FPGA. The implementation has rigorously followed an efficient design methodology. This methodology was used with success for the speed control of induction machine using FPGA based controller and it can be considered as a part of a process whose target is the creation of a specific electrical system library of optimized reusable modules which will ensure a great flexibility for the design development.