COMPARATIVE STUDY OF CLOSED LOOP MODEL OF BLDC MOTOR WITH DIFFERENT CLASSICAL CONTROLLER
Year: 2021

A Brushless DC Motor (known as BLDC) is a Permanent Magnet Synchronous Electric motor which is driven by direct current (DC) electricity and it accomplishes electronically controlled commutation system instead of a mechanically commutation system. In this paper, Closed Loop Control system of BLDC motor drives using different combination of classical controller is presented. MATLAB Simulation is done for various combination of classical controller and their performances are compared to find out the best combination. Moreover, Frequency Analysis using Fast Fourier Transform is also done to know the controller behavior and to calculate the current THD (Total Harmonic Distortion) to confirm the best combination for the system. The main objective of this study is to confirm the best combination of classical controllers.  BLDC motor, Closed loop, Classical Controller, Frequency Analysis, Simulation.  Brushless DC motors (BLDC) has many applications in industries due to their high power density and ease of control. Since BLDC motor does not have brush, it has longer life, higher efficiency, higher speed and maintenance free. Therefore, BLDC Motors become very popular in modern drive technology. They gain popularity rapidly in the fields of Consumer Appliances, Automotive Industry, Industrial Automation, Chemical and Medical, Aerospace and Instrumentation and the range is increasing day by day. The ratio of Torque delivered to the size of the motor is higher, making it useful in applications where space and weight are critical factors [1 15] Stator and Rotor are the main part of the BLDC motors like Brush DC motor. Hall sensor may be considered as one part of BLDC motor since most of them are sensor by Hall Effect signal. Hall sensors work on the hall effect principle that when a current carrying conductor is exposed to the magnetic field, charge carriers experience a force based on the voltage developed across the two sides of the conductor. If the direction of the magnetic field is reversed, the voltage developed will reverse as well. For Halleffect sensors used in BLDC motors, whenever rotor magnetic poles (N or S) pass near the hall sensor, they generate a HIGH or LOW level signal, which can be used to determine the position of the shaft. There are single phase, 2 phase and 3 phase configurations, Out of these, 3 phase motors are the most popular and widely used. The stator of a BLDC motor consists of stacked steel laminations with windings placed in the slots that are axially cut along the inner periphery. The rotor is made of permanent magnet and can vary from two to eight pole pairs with alternate North (N) and South (S) poles. Based on the required magnetic field density in the rotor, the proper magnetic material is chosen to make the rotor [1, 6, 10, 11, 12] The brushless motors are generally controlled using a three phase power semiconductor bridge. The motor requires a rotor position sensor for starting and for providing proper commutation sequence to turn on the power devices in the inverter bridge. Based on the rotor position, the power devices are commutated sequentially every 60 degrees. Instead of commutating the armature current using brushes, electronic commutation is used that is why it is called as an electronic motor. For Each commutation sequence, one winding is energized to positive, the other winding is energized negative and the next is in a non energized condition. Torque is produced due to the interaction between the two magnetic fields generated by the stator coils and the permanent magnets. Ideally, the peak torque is observed when these two fields are in quadrature to each other. In order to keep the motor running, the magnetic field generated by the windings should shift their position, as the rotor moves to catch up with the moving stator field [1, 2, 10] In case of Closed loop control, feedback is given from the output to get the desired speed. The main advantages of this method are the system stability; minimal disturbances compared to open loop control and reduced sensitivity for dynamic load variations. Normally, there are two loops for feedback; the outer loop is use for speed or voltage control and the inner loop is use for torque or current control. Desire speed or Reference Speed is given as the input which is compare with the output speed, if there is any difference between the two, it will be treated as an error and it will be minimized by the controller so that the output will be same as the reference speed. So, the output is depending on the reference speed and the controller, it is independent of the applied voltage which is fixed at a particular value. Generally, classical controller such as PID, PI and P controller are used for controller.  The three part of PID controller act as follow: (a) System rise time will be reduced by Kp, it provides faster response in variable load condition. (b) Steady state error will be reduced by K i, hence the motor speed is pushed near to reference speed. (c) Settling time and oveshoot will be reduced by Kd, hence provide faster response. The continuous control signal u(t) of the PID controller is presented in the following equation [11] u(t) Kp* e(t) Ki e t 0 (t) dt Kd e(t) (i) PI CONTROLLER: PI controller is an accurate and provides good system stability i.e. less steady state error response. But the integral factor in controller takes more iteration to reduce error to zero. This controller is fundamentally used to limit the steady (c) 2021 JETIR July 2021, Volume 8, Issue 7 www.jetir.org (ISSN 2349 5162)  www.jetir.org a288 state error coming about because of P controller hence it is important to blend the proportional and integral to increase the speed of response. The PI controller can be used to control speed as well as torque or current of BLDC motor. The Effects of PI parameters are: (a) Improve Damping. (b) Zero offset (c) Decrease/ No steady state error. The speed/position encoder is utilize to obtain running speed of brushless DC motor and compare it with the reference value and the resulting difference is examined by PI controller which is governed by using the equation below [11] u(t) Kp e (t) Ki e t 0 (t) dt (ii) P CONTROLLER: A proportional or P Only controller is the simplest algorithm in the PID family. Proportional Controller is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value (set point, SP) and the measured value (process variable, PV).The gain Kp is used in P controller and output produced that is inversely relative to steady state error so the system becomes unstable if the gain Kp is high. P controller is directly proportional to incoming error; hence a little change in error can cause system instability. The following equation used to govern Proportional (P) controller [11] u(t) =Kp e (t) (iii) Where u(t) signal of actuating e (t) signal of error Kp: constant of proportional gain PID parameters Proportional gain Kp, Integral Gain Ki, and Derivative Gain Kd affects system's overall performance. Hence choosing right parameters for a system is a difficult process and can be done by using several tuning methods which includes manual tuning, Ziegler Nicholas, Particle Swarm, Ant Colonization, Genetic Algorithm and Cohen coon tuning. The advantage of Classical controller is its feasibility and stability, simple and easy to be implemented and adjusted. The PID gains can be designed based upon the system parameters if they can be achieved or estimated precisely. Without creating mathematical model of the system, it can still be used by tuning it with trial and error. They are not heavy on hardware; therefore it can be implemented on cheap hardware also. If once designed, then its further tuning does not require skilled personnel. Moreover, the PID gain can be designed just based on the system tracking error and treats the system to be "black box" if the system parameters are unknown.  The block diagram of Closed Loop Control is shown in Fig. 1. It has five main blocks such as Voltage Source, Inverter, Motor, Speed Controller and Torque Controller.  Block Diagram of Closed Loop Control of BLDC motor II: MATHEMATICAL MODELLING In modeling a BLDC motor a, b, c, phase variable model is preferred as the mutual inductance between stator and rotor is nonsinusoidal. Before formulating the equations following assumptions are made in modeling the BLDC motor. The motor is not saturated. Resistances of all the stator windings are equal, self and mutual inductances are constant. The power semiconductor devices are ideal. There are two possible methods to model a BLDC motor, one is a, b, c phase variable model and the other is d q axis model. BLDC motor has the permanent magnet with trapezoidal back EMF whereas synchronous motor has sinusoidal back EMF. So transforming to d q axis does not provide any added benefit, thus a, b, c phase variable model is chosen. The equivalent diagram of the BLDC motor is as shown in the fig.2 [3, 5, 8, 12] (c) 2021 JETIR July 2021, Volume 8, Issue 7 www.jetir.org (ISSN 2349 5162)  www.jetir.org a289 Fig.2: Three phase BLDC motor equivalent circuit. The voltage equations of BLDC motor are: V a R a i a L a d dt i a e a (1) V b R b i b L b d dt i b e b (2) V c R c i c L c d dt i c e c (3) where, L a L b L c L, are the self inductance [H] V a, V