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Internal Model Control Approach to PI Tunning in Vector Control of Induction Motor

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Internal Model Control Approach to PI Tunning in Vector Control of Induction Motor International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 Internal Model Control Approach to PI Tunning in Vector Control of Induction Motor Vipul G. Pagrut, Ragini V. Meshram, Bharat N. Gupta , Pranao Walekar Department of Electrical Engineering Veermata Jijabai Technological Institute Mumbai, India Abstract— This paper deals with the design of PI controllers 휓푟 Space phasor of rotor flux linkages to meet the desired torque and speed response of Induction motor 휓푑푟 Direct axis rotor flux linkages drive. Vector control oriented technique controls the speed and 휓 Quadrature axis flux linkages torque of induction motor separately. This algorithm is executed 푞푟 in two control loops, the current loop is fast innermost and outer 푇푟 Rotor time constant speed loop is slow compared to inner loop. Fast control loop 퐽 Motor Inertia executes two independent current control loop, are direct and quadrature axis current PI controllers. Direct axis current is used to control rotor magnetizing flux and quadrature axis II. INTRODUCTION current is to control motor torque. If the acceleration or HIGH-SPEED capability machines are needed in numerous deceleration rate is high and the flux variation is fast, then the applications for example, pumps, ac servo, traction and shaft flux of the induction machine is controlled instantaneously. For drive. In Induction Motor this can be easily achieved by means this the flux regulator is incorporated in the control loop of the of vector Control/field orientation control methodology [6]. induction machine. For small flux and rapid variation of speed it And hence Field orientation control of an Induction Motor is is difficult to obtained maximum torque. And for the high flux widely used control strategy in the industry due to its high regulation of current is difficult because of voltage deficiency. A reliability [1]-[3]. In Field Orientation Control or Vector proportional and integral (PI) regulator solves these problems. For the reasonable performance of the flux regulation the control, which is a variable frequency drive, a resultant vector bandwidth of the current regulator is high compared to that of of magnetic flux and torque realizes stator current and voltages. the flux regulator. PI regulator, the transfer function of the Using Vector control we can achieve the independent control closed-loop system is set to the first-order low-pass filter. The over flux and torque [4] Different control methodologies have current PI controller’s outputs are the corresponding d and q been studied and implemented along with field orientation axis components of the decoupled stator voltage. The fast control control in last few decades for controlling the induction motor loop executes independent control of stator current components like open loop v/f control, v/f control with slip compensation. and slow control loop executes speed controller. The PI speed V/F control is least preferred control strategy because at low regulator output sets a reference for the torque producing speed, resistive term dominates flux linkage which leads to quadrature axis component of the stator current (풊풔풒) and the PI sudden drop in magnetizing flux up to zero levels. To flourish flux regulator sets a reference for flux producing direct axis the performance of Induction motor at low speed, method used component of the stator current (풊풔풅). is popularly known as voltage boost. It allows torque speed curve to become independent of electrical frequency [5]. Keywords—Internal Model Control(IMC); Vector Control; According to current industry trend, PID controllers are most Induction Motor; Speed regulator; Current regulator preferred controllers in industry. In this paper the Indirect Vector Control method is used for IM control over a wide I. NOMENCLATURE range. The method consists of 3-PI controllers. Tuning a 휔푟 Rotor angular speed multiple PID’s is a tedious job as algorithm presented in [6] for 휔푠 Synchronous speed achieving the maximum torque is rather complex, requiring the 푇퐿 Load Torque tuning of several PI regulators (two PI regulators are used for the current regulation, another one for the speed regulation). 푅푠, 푅푟 Resistance of stator and rotor windings While tuning multi-loop PID’s, Inner loop must be faster as 퐿푠, 퐿푟 Self-inductance of stator and rotor windings compared to outer loop. Most of the time for PID tuning trial 퐿푚 Mutual inductance 푃 Number of pole pairs and error method is used. But its very time consuming. This 푝 makes difficult to obtain an optimal controller gains to get 푉푑푠 Direct-axis stator voltage component excellent control over wide speed and torque range. In this 푉푞푠 Quadrature axis voltage component paper the formula for PID gain calculation is derived. The 푖푠 Space phasor of stator current PID’s are tuned and model is simulated on Real Time simulator 푖푟 Space phasor of rotor current OPAL-RT (OP4500). The field-oriented control utilizes the 푖푑푠 Direct axis stator current component stator current components as control variables. The d- 푖푞푠 Quadrature axis rotor current component component of the stator current acts on the rotor flux, whereas the q-component is proportional to the motor torque as the IJERTV4IS060906 www.ijert.org 817 (This work is licensed under a Creative Commons Attribution 4.0 International License.) International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 control of the motor flux is obtained indirectly by controlling Adjusting the slip angular frequency indirectly controls the the motor currents. position of the rotor flux. Using this process, the stator current is decomposed to the torque and flux component. III. INDUCTION MOTOR MODELLING Induction motor is modelled in a d-q Stationary reference IV. INDIRECT VECTOR CONTROL frame given by the equations of the fluxes and voltages as Induction machines have been utilized for over a hundred 푑 푉 = 푅 푖 + 휓 − 휔 휓 (1) years. Because of their simplicity, ruggedness, reliability, 푑푠 푠 푑푠 푑푡 푑푠 푠 푞푠 푑 efficiency, low cost, compactness, economical and volume 푉 = 푅 푖 + 휓 − 휔 휓 (2) 푞푠 푠 푞푠 푑푡 푞푠 푠 푑푠 manufacturing advantages. Induction machines with a squirrel 푑 0 = 푅 푖 + 휓 − (휔 − 휔 )휓 (3) cage rotor are the most widely used machines at fixed speed. 푟 푑푟 푑푡 푑푟 푠 푟 푞푟 푑 The dynamic model of an induction machine can be expressed 0 = 푅 푖 + 휓 − (휔 − 휔 )휓 (4) 푟 푞푠 푑푡 푞푟 푠 푟 푑푟 by sixth-order state space matrix. Which consists of stator voltage and frequency as inputs and the outputs can be rotor The rotor flux linkages in the reference frame fixed to the speed, rotor position, electromagnetic torque, stator-rotor flux rotor (휓훼푟 휓훽푟) are related to the rotor flux-linkages linkages, magnetic flux linkages, stator-rotor currents and components expressed in the stationary reference frame (휓푑푟 magnetizing current or a combination of these. Induction 푗휃푟 휓푞푟) by the transformation 푒 . Thus the following equation machine can have different rotor windings viz. a wound rotor holds, (slip ring machine) or a squirrel cage windings. The vector control of an induction machine is possible in both types of ⃗휓⃗⃗⃗ = 휓 + 푗휓 (5) windings. The fundamental part in vector control is to get a 푟 푑푟 푞푟 correct space angle, which is the imperative work. The space angle between field winding and stator direct axis as well as ⃗⃗⃗⃗ 푗휃푟 푗휃푟 휓푟푒 = (휓훼푟 + 푗휓훽푟)푒 (6) magnetic flux and stator direct axis can be directly measured in case of an electrically exited synchronous machine and In matrix form:- permanent magnet synchronous machine but not in case of an Induction machine. Furthermore in case of the converter-fed 휓 푐표푠휃 −푠푖푛휃 휓 [ 푑푟] = [ 푟 푟] [ 훼푟] (7) induction machine as there is no external excitation both 휓푞푟 푠푖푛휃푟 푐표푠휃푟 휓훽푟 reactive (excitation) and active (torque producing) currents must simultaneously exist in the stator winding. It has been 휓푑푠 = 퐿푠푖푑푠 + 퐿푚푖푑푟 proved that in special reference frame fixed to magnetizing 휓푞푠 = 퐿푠푖푞푠 + 퐿푚푖푞푟 and stator or rotor flux linkages space phasor, the expression 휓푑푟 = 퐿푟푖푑푟 + 퐿푚푖푑푠 for the electromagnetic torque of the smooth air gap machine 휓푞푟 = 퐿푟푖푞푟 + 퐿푚푖푞푠 is similar to that of separately excited D.C. machine. This recommends that torque and speed control of an induction Based on rotor flux linkages and stator current, the torque is machine can achieve by decoupled control of flux and torque expressed as: producing component of stator currents, which is similar to the field and armature currents in separately excited D.C. 퐿푚 machine. The stator currents can be separated into flux and 푇푒 = 푃푝 (푖푞푠휓푑푟 − 푖푑푠휓푞푟) (8) 퐿푟 torque producing component by utilizing transformations In case of an induction machine rotor flux oriented control is From the field orientation condition i. e. 휓푞푟 = 0 torque usually employed, the modulus and space angle of the rotor equation is written as: flux linkages space phasor are obtained by utilizing the measured stator currents and the rotor speed [8]. As shown in 퐿푚 푇푒 = 푃푝 (푖푞푠휓푑푟) (9) Fig 1 number of PI’s are involved in precise control of an 퐿푟 induction motor. In such case trial and error method of PI The slip angular frequency is represented in terms of rotor tuning is not useful in addition to this tuning by Ziegler flux linkage and q-axis current as: Nichols method is also not useful as the to get the transfer function of such interconnected PI system is not that simple. 푅푟푖푞푟 푅푟 퐿푚 In next section the more useful and easier method of PI tuning 휔푠 − 휔푟 = 휔푠푙 = − = 푖푞푠 (10) 휓푑푟 휓푑푟 퐿푟 is discussed. Under the condition of the constant rotor flux linkages, instantaneous torque of the induction machine is directly proportional to the q-axis stator current.
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