MASTER-SLAVES SPEED SYNCHRONIZATION OF TRIPLE 3-PHASE INDUCTION MOTORS USING PI AND PID CONTROL METHODS

This paper presents two methods used for three closed loop speed controller of Variable-Voltage Variable-Frequency (VVVF) triple 3-phase Induction Motors (IMs) master/slaves system. A dynamic d-q model of a 3-phase IM in state space form and its computer simulation in MATLAB/SIMULINK software package are described. The two different methods of speed control which are used to improve the performance of three IMs drive system are named as conventional PI controller and PID controller. For PID speed controller, simulation results clearly show that the response of the system is superior compared to PI speed controller in terms of rise time, settling time, accuracy and steady state error. The design, analysis, and speed responses of the system obtained under both controllers have been simulated, studied and compared using MATLAB/Simulink environment for different operating conditions such as sudden change in reference speed and load torque. The simulation results showed good synchronization between the master and the slave IMs with suitable tracking error.


INTRODUCTION
Induction Motor is became more popular in motion control field for its advantages of low price, ruggedness, simple construction and high dependability. In modern induction motor industrial applications, a challenging problem is that the movement of multiple motors must be controlled in a synchronous manner. Many reasons such as oscillations, incompatible dynamics, and changing of parameters can be damaged the multiple motors system synchronization performance (Dezong Zhao et al. 2009).
Fast and accurate speed responses, quick improvement of speed from load disturbances are some of the important criteria of high performance drive system. The core of algorithm conventional control for induction motor drives were PI/PID control because of the simplicity and stability.
In 2012 Mhaisgawali and Muley presented the simulation result for speed control of one 3phase induction motor using PID controller (Madhavi L. Mhaisgawali et al.2012).
In 2013 the same authors above compared between the traditional PI and PID controllers at full load condition. MATLAB is used to simulate the system in order to investigate the speed control results of one I.M. with PI, PID controllers and without any controller at full load situation (Madhavi L. Mhaisgawali et al. 2013).
At the same year above, Swati Sikarwar and Amol Barve reviewed the implementation of discrete PI and PID control scheme when applied to model of single I.M. MATLAB environment is used to develop both controllers. A comparison is made between the performance of discrete PI and PID controllers with that of classical controllers in terms of steady state error and rise time (Swati Sikarwar et al. 2013).
At the same year, Ahmed A.M .Emam and the others introduced a new design of a master slave control system. This new design was used for synchronization between the different motors.
The principle of the Field Oriented Control (FOC) is explained. PI-FO controllers are designed for two I.Ms. in master slave arrangement (Ahmed A.M .Emam et al. 2013).
In 2014 Vismay Chauhan and Prof. V.P. Patel, proposed several synchronization methods in order for satisfying synchronization speed during deceleration, acceleration and varies in load requires angle and speed synchronization between at least two axes. They are described the Master-Slave, the Relative Coupling Strategy, Bi-axial cross coupled control method and Cross Coupling Technique (Vismay Chauhan et al. 2014).

Suroor M. Dawood
In this work, one of the induction motors has been used as a master and the others as slaves, the speed of the master motor uses as a reference signal for a close loop control system that controls the speed of the slave motor to follow the speed of the master. Scalar control method is used for controlling the induction motor to operate it at the steady state, by changing the magnitude and frequency of the supply voltage. This method gives limited speed precision specially in the poor dynamic torque response and small speed range (Ashok Kusagur et al. 2009).
In this work, 3-phase voltage source inverter (VSI) which is carrier based Sinusoidal Pulse Width Modulation (SPWM) is used. SPWM inverter which powered induction motor drive make it possible to control both amplitude and frequency of the voltage applied to the IM under condition of constant V/f ratio. Consequently, PWM inverter is more variable and offer a wide range better efficiency and higher performance when compared to fixed frequency motor drives.
The sinusoidal PWM is better than other PWM techniques because it offers smooth exchange of V/f and removes harmonics in both open and closed loop applications (C.S. Sharma et al. 2013). V/f drives work well on applications in which the load is predictable and does not change quickly, such as fan and pump loads (Frank D. Petruzella 2010).
Several applications used more than one motor to bear the high load (Ahmed A.M. Emam et al. 2013). This paper is concerned with the design of master/slaves control system of three IMs accountable for synchronization between these motors.
The master-slave synchronization control for IM is an important problem since it is often used in manufacturing and production processes. The synchronization between multi motors directly affects the reliability and control accuracy of the whole system. The traditional PI and PID control methods are used for improvement the system's response.
A comparison between the performance of the multiple IMs system under both controllers is presented by simulation results that verify appropriateness of the approach under various operating situations and provide the fast and robust control.

DYNAMIC D-Q MODEL OF 3-PHASE IM
To check the actions of a high performance IM drive, the d-q model of the IM has been used (Aleck W. Leedy, 2013 andAshish Kamal et al., 2013). The differential equations produced from analysis of the equivalent circuits of the induction motor represented in the rotating reference frame in Fig. 1   Where, d is the direct axis, q is the quadrature axis, Vds is the d-axis stator voltage, Vqs is the q-axis stator voltage, Vdr is d-axis rotor voltage, Vqr is q-axis rotor voltage, ids is the d-axis stator current, iqs is the q-axis stator current, idr is d-axis rotor current, iqr is q-axis rotor current, Rs is the stator resistance, Rr is the rotor resistance, ωe is the angular velocity of the reference frame, ωr is the angular velocity of the rotor, λds , λdr, λqs, and λqr are flux linkages.
The d-q stator and rotor currents can be expressed in terms of flux linkages as follows: (1)  Where P: no. of poles; J= rotor inertia; TL= load torque.
The self inductances can be expressed as: Where Llr is the rotor leakage inductance, and Lls is the stator leakage inductance (Aleck W. Leedy, 2013).
The Simulink model of 3-ph IM can be constructed by creating Simulink subsystems using eqs.

VOLTAGE SOURCE SPWM INVERTER
PMW technology used for reducing the inverter's size and harmonics restricted in the output voltage. To produce the required voltage to feed the IM, Sinusoidal Pulse Width Modulation (SPWM) technique is used. This method is gradually more used for AC drives. In general, the gating signals of SPWM three output legs generated by comparing a constant amplitude and frequency triangular carrier signal, with 3-phase sinusoidal signals called "reference signals", which has variable amplitude and frequency to get the desired output voltage, this comparison leads to generate a sequence of variable width pulses used to gating 3-Ph VSI (C.S. Sharma et al., 2013). Fig. 9. illustrates the principles of SPWM.
The inverter model is represented by the relationship between the control logic signals (Sa, Sb, Sc) and output phase voltages (Va, Vb, Vc) to create the output voltage as the following eqns.
The simulink model of this VSI using eqns. (18) which feeding by SPWM signals is shown in Fig. 10.

SCALAR CONTROL METHOD
The Volt/Hertz control is basically a scalar control technique where only the magnitudes of the control variables are varied simultaneously (in this case, voltage and frequency of stator supply voltage). This technology is the most economical and popular method used in industrial applications as shown in Fig. 11. In variable-speed applications in which a small variation of motor speed with loading is permissible, scalar control scheme can produce satisfactory performance. Scalar control strategy controls shaft speed by changing the voltage and frequency of the signal powering 3-Ph VSI which feed the induction motor. Volts per hertz control in its easiest form takes a speed reference command from an external source and varies the voltage and frequency applied to the motor. The voltage and frequency are changed in the same ratio to keep the air gap flux approximately constant according to eqn. (19).

CLASSICAL MASTER/SLAVES MOTORS SYSTEM
For master-slaves motors synchronization control system, one of induction motors is selected as a master motor, the other motors are selected as slaves motors, the master I.M. output speed will be as the speed reference value for the slave I.M. So it has been concluded that any speed change or load variation added to the master motor will be reflected on the slave motor, but any disturbances from slave motor cannot feedback to the master motor. Multi induction motors synchronization control system is shown in Fig. 13 (Ahmed A.M. Emam et al. 2013).
Where: Nr is the reference speed and Nm is the motor actual speed.
To make the synchronization error as small as possible, the master-slave technique is used by assuming that the slaves motors are tracked the master one immediately. Electronic synchronization is recommended recently, because it provides certain merits in terms of reliability and flexibility (Pratiksha Shingade et al. 2014).

PI SPEED CONTROL OF I.M.
(Proportional Integral) PI controllers are the feedback controller which reduces the system sensitivity to changes in the surrounding environment and small changes in the system. They offer the easiest and yet most efficient solution to many real-world control problem. It is a type of feedback controller whose output, that is a control variable (CV), is generally based on the error e(t), between user reference speed (Nref) and measured actual speed (N) after converting both of them into frequencies. Each element of the PI controller refers to the particular action taken on the error. The PI controller produces an output signal u(t) consisting of two terms one proportional to input signal e(t) and other proportional to the integral of the input signal e(t) according to the following expression (Jeyalakshmi et al. 2010). Where,

KP is a proportional gain
Ki is an integral constant. drive circuit is shown in Fig. 15.

PID SPEED CONTROL OF I.M.
The classical Proportional-Integral-Derivative, PID, controller is widely used in manufacturing control system. PID controller has all the essential dynamics: (P) controller gain is used for removing oscillations, (I) controller gain is used for raising in control signal to lead error towards zero (D) controller gain is used for high-speed response. The output of PID controller

34
Suroor M. Dawood consists of three terms the error signal, the error integral and the error derivative according to the following expression. Fig. 16 shows the simulink model PID controller. A complete PID speed control based 3-ph I.M. drive circuit is shown in Fig.17.

SPEED CONTROLLER OF MASTER/SLAVE INDUCTION MOTORS
The model of the speed controlling system as shown in Fig. 18 consists of two induction motors each driving a different load and feeding from separated 3-ph VSI. One motor is the master and the other motor is the slave. The master motor directly executes the desired trajectories. The encoder of the master motor is also used as the master encoder for the parallel slave motor.
Thus, in essence, the slave motor simply follows the motion of the master motor.

SPEED CONTROLLER OF MULTI THREE-PHASE INDUCTION MOTORS
Three induction motors (first master and others slaves) are shown in Fig. 19. These motors are powered by separate VSIs. The master motor is the reference motor which followed by one or more slave motors.

SIMULATION RESULTS AND DISCUSSIONS
In this work a PI controller then PID controller are used to improve the multi I.Ms speed responses. The nominal parameters of the I.M. are listed in Table 1. second, the electromagnetic speed and torque are plotted against time. It can be seen that when the load is applied the speed drops down its rated value 1500 rpm and cannot builds up again to its rated value.  The speed response is robust to variations in load. When sudden load applied at 4 second of time the speed response have fall then return to its value 1500 rpm and then rise up above its value when the load is removed at 8 sec.
At t=0, the motor is stand still. When the moment supply is given, the motor reaches its nominal speed gradually. The load torque is initially kept zero and then at time t=3sec, the load torque is made 2 Nm. By trial and error method, the PID gains KP, KI and KD selected as (0.08, 3.5 and 1.4) respectively. The operation performance under different reference speed commands; For comparison, the following simulation tests show the speed and torque responses respectively of the system while using PID and PI for various reference speed, applied and removed load.
In Fig. 30, multi reference speeds (700, 1200 and 850 rpm) were used with load applied at time = 3 s and removed at time = 12 s. As noticed in this figure, the actual speed went down after each load applying, while both PI and PID showed a good response to this change. It is clear from the figure that PID showed faster response in both rise time and settling time compared with PI response for multistep speed input. As a result, PID showed better performance compared with PI controller. PID also showed the ability to control speed of the 3-ph IM and provide an accurate and fast response with fairly no overshoot and no steady state error. Fig. 31 shows the IM developed torque under the same conditions above. were used with load applied on master motor at time = 2s and on slave motor at time = 5s. The slave speed recouped its initial speed (master motor speed) in load application. The slave motor followed any change in master motor speed due to load change but not vice versa. Fig. 33 shows the torque profile under the same above conditions.   As noticed in the this figure, the actual speed went down after applying each load, and up after load removing then it's return to the required value so both PI and PID obtained an excellent performance to this change. PID controller provided rapidly reaction in both rise time and settling time compared with PI reaction. So, PID controller has the best response than PI controller because that it's highly improved the speed tracking step response.  sec a 2 Nm load torque step change is applied on master IM, it is clear that the two slaves motor followed the master motor, the same value of load applied at t=6.5 sec on slave1 motor so the second slave followed the first one and TL=2Nm applied on slave2 motor at t=8 sec. It is obvious from Fig. 38 that the sudden load change on master IM reflected on the two IMs slaves, but the sudden load change on the slave motors never affect the master motor.
In Fig. 39, a comparison has been done between the speed response of three IMs operated with conventional PI controller under the following load conditions (TL=2Nm applied on master motor at t=2sec then the same value applied on slave1 at t= 6.5 sec and on slave2 at t=8 sec),

42
Suroor M. Dawood and with PID controller with sudden change in load applied to the master motor from no-load to 2 Nm at 2 sec and the same value applied on both slaves at t=5 sec but removed from slave2 at t=7 sec. As shown in speed graph, controller obtained with PID control reached to the desired reference speed 1500 rpm in a very short time while controller obtained with PI control reached to reference speed after much longer period of time both under load change conditions. So in the above Fig. 39, a comparison is shown between three I.Ms under PI and PID controllers.
From this one can be noted that PID controller is better than PI controller. The speed of induction motor using PID controller settled early than that of PI controller. The comparative results for rated speed (1500 rpm) under both controllers are reported in Table 2 below.  Fig. 40, second comparison between the speed response of multiple IMs operated with PI and PID controllers under different reference speeds (1450, 1250 and 950 rpm) with sudden load of 2Nm applied on both master motors at t= 2 sec ,then under PI controller load torque TL=2 Nm applied on slave1 at t=7 sec and on slave2 at t=2sec, under PID controller, the same value of TL applied on both slave motors at t=12 and 13 sec respectively and removed from slave2 motor at t=14 sec.

CONCLUSION
In this work, the speed control of triple ( motors. The effectiveness of the system is analyzed through the speed and torque response profiles achieved from the simulation. The results shows that the PID controller is more effective than PI controller in controlling multi induction motors speed.
When a single IM model is supplied from 3-phase VSI drive and runs without control, its dynamic response has been made by causing sudden step change in load from 0 to 2 Nm at 5sec. The results show that the motor speed cannot returned to its required value due to sudden change in load because of the absence of controlled.
Two types of controllers have been used to improve the multi IMs speed profile. Each motor speed is the feedback signal after converting it to frequency for determining error in frequency at instant of starting and loading. The output of the controller is then fed to the voltage source inverter.
The implementation of PID controller improves the speed and torque responses as settling time The three motors performance under both PI and PID controllers has been checked and compared for different reference speeds and load conditions. The results show that the motors have very high starting torque and their speed curves pass through small durations of variation and disturbance after sudden load application or removal.
As a future work, the hardware of the project can be implemented and more advanced controller can be used instead of PI and PID controllers 12.