Applied measurement of the motor speed controller for washing machine with random loads, part II

Received Sep 7, 2019 Revised Nov 2, 2019 Accepted Nov 28, 2019 This research presents a very important industrial issue of controlling the production target, despite changing loads. Engines of various types, whether synchronous or synchronous, operate on single and three phase AC, DC motors or special motors such as stepper and servo. In all these motors, the speed control of the torque and speed of the above motors has gained considerable importance. There are three main ways reviewed in the current search, the second that completes the previous research referred to in the references. The three methods are PID method, LQR method and feeding – forward control methods. A real DC motor was used in electrical engineering machine laboratory at University of Diyala, Iraq. Where the actual parameters of the DC motor were actually calculated. The practical parameters were then integrated into the three control method Matlab codes for the purpose of comparing the results and representing the motor performance in the indicated control methods.


INTRODUCTION
The There are many types of control units which are used in the control field of electrical and mechanical equipment's. Most of electrical machines such as single or three-phase AC induction motors, AC Synchronous motors and DC motors depend mainly on the control feedback units to achieve optimum performances [1]. The feedback control units which are used with the motors are composed of different types of sensitive electronic devices: sensors, transmitters, comparator, and servo-controller [2]. A controller unit is very significant to get the steady state in shorter time and to reduce the rise time, overshooting and settling time [3]. This paper presents two main developments concern the mechanism of the washing machine: applying armature control which allows to control the speed of separately excited dc motor using PID controller, modelling the system of the DC motor and using MATLAB for representing the performance and analyzing the whole control system.

GENERAL SETUP OF WASHING MACHINE
The washing machine is an apparatus which is capable of operating in constant changing load and can be found using either AC or DC motor. The motor speed increases or decreases depending on the load. Varying of motor speed with varying the load causes decrease the efficiency of the motor and then decrease the speed the machine agitator [4]. So, it is very necessary to get a good performance of the machine we have to get the speed and torque constants whenever the load is changed. When the power that is supplied to the four-pole motor, the rated speed reaches slightly around 1500 rpm at no-load condition. This rated speed is high and is very difficult to run with a loaded agitator in the washing machine. Therefore, the speed of the agitator should be reduced to suitable and safe load speed. The safe load speed can be achieved using two different diameters of the motor and agitator pulleys. The choice of the diameters is based on the speed ratio between the motor and safe speed of the agitator. The second important matter is how to keep the speed of the agitator is invariant with the variable load. To get a constant speed of the agitator and its motor whatever the load is changed represents the main work of this project. Figure 1 depicts a washing machine which contains the electrical motor, pulleys and agitator.

Separely excited DC motor
As per Figure. 2, the equivalent circuit of the DC motor is attached with the external variable load on the armature shaft of the DC motor. The equivalent circuit is composed of two parts: the first is the stator field windings or may be permanent magnets and the second pat is the rotary armature circuit [5][6][7][8]. The DC motor used in this paper is manufactured by KI Company (Taiwan) with its ratings shown in Figure 2. Where Ia, is the armature current, Ra represents the armature resistance, the armature inductance represents by La. Tm represents the motor torque in newton-meter (N.m). The measurement for rotating inertia of motor bearing is represented by J and damping coefficient is expressed by B [9-13].

PID controller
Generally, the schematic diagram of the PID controller is consisted of three main parts as shown in Figure 3. The real PID used is manufactured by Telefunken Company (Germany) which is available in the electric machine laboratory, COE, Diyala University as sown in Figure 4. The transfer function (TF) of the PID controller can be represented by (2). Where the PID parameters are Proportional gain (Kp), Integral gain (KI) and the derivative gain (Kd) [14][15][16][17][18].  The mathematical relations among the three parameters Kp, KI and Kd of the PID controller and their effects on the response parameters: rise time, overshoot, settling time and steady state error [19][20][21][22] are shown in Table 1. The tachometer used in this experiment is manufactured by Telefunken, Germany. It will be used as an instrument to measure the rotating speed of the used electrical machine. The voltage generated by the tachometer Etac is given by: .
(3) Where the symbols Ktac is a proportional constant and Ntac is the angular velocity of the tachometer. The transfer function of the DC motor is clarified in Figure 5.
In the DC motor, armature inductor La can be neglected due to its small value in practice, so, the TF (s) can be simplified through (5) and (6).
denominator of the (6) can be expressed into (7) the motor gain Km involves four parameters: Ra, B, Kb and KT as shown in (8).
. (8) the time constant of the DC motor τ is given as: (9) The transfer function of the completed DC motor electric control circuit applied in the proposed electric washing machine is clarified in Figure 6.

Feed forward controller
It is a set of methods and procedures used by the designer to identify and discover any factors that may limit the success of the process in determining the target early so it is called Pre-censorship, thus for avoiding any problems and monitoring any changes. At the operational level, prior control requires the designer to focus his efforts towards selecting inputs, outputs and procedures with complete care to minimize potential problems. In the strategic level, pre-censorship is designed to alert and warn the designer of any practical changes that will affect long-term objectives [23,24].

Linear quadratic controller
The goal of this theory is to control the ideal performance of the system at the lowest economic cost. The system is described by a set of differential linear equations. The cost is described by a quadratic function called LQ. One of the most important results of the theory is to obtain a feedback system with the LQR system, which is part of the LQG solution.
The mathematical algorithm that controls the cost reduction process at the same time controls the reduction of deviations from the main goal, such as voltages or speed. The results will be compared with the reference objectives of the required design, which are considered as standard objectives. The process of control is an iterative process, and in the end the parameters are adjusted to produce the best values for the system goal.
The frontal feed system in this method is to adjust the control of the target variable not based on error as in the PID method. It is based on practical knowledge of the measure of disturbance in the signal based on a mathematical model [25][26][27][28]. Figure 7 shows the name plate of the DC motor used in the test which is available in Electric Machine Laboratory, COE, University of Diyala.

EXPEREMENTAL RESULTS AND DISCUSSION
In Based on Table 2, the motor will be tested under 1500 rpm with random loads. K parameter or called torque/ampere is the relation between the torque of the DC motor shaft and the input armature current. Practically, the ratio can be determined by applying a variable torque to the shaft and measuring the drawn armature current of motor. The b parameter or called volt/speed parameter is the relation between the input voltage of the DC motor and the shaft speed. Moment of inertia is determined mathematically depending on the summation of inertias rotor and load masses and its diameter. Armature resistance R, is measured using an Ohmmeter directly. Inductance of the armature, is determined practically by applying a low AC voltage on the two terminals of the armature and measuring the passing current. Calculating the impedance of the armature requires information of R which is found to be L = 2.75µH. The experimental values of K, b, J and R are mentioned in Table 2. There are three case studies which are implemented using MATLAB coding. Each study explains the differences between two output responses due to two inputs: ideal step and disturbance step. The output response are steady state error, overshoot, settling time and rise time. Figure 8 explains the angular velocity response to due to a step change in voltage.  Figure 8. The angular velocity response to a step change in voltage.

Feedforward control design
The Root locus of the system with using integrator K/s is shown in Figure 9. The roots of the DC motor system used explains that the system is stable. These roots depends on the entire system specifications. Figure 9. Root locus of the system with using integrator K/s.

LQR control design
To further improve performance, try designing a linear quadratic regulator (LQR) for the feedback structure shown below in Figure 10. Comparison of the three designs in Figure 11, the input signal takes the zero value for five seconds and then subtracts the torque value to -0.1 for 5 seconds. This disturbance in the output signal on the lip will be examined and tested in three cases: the output response in the case of using feed forward system is as shown in blue color line behaves as a pulse according to the torque input signal Td. If the same input signal Td is used to change the input torque with the feed back root locus, the output response in the green color will need more time to reach the stability state, ie, the transient period is greater than the first.
In the case of feeding LQR, the change in output response (red line) with change in input torque Td is better between the two previous cases feedforward and feeback. In spite of the disturbance in the input signal Td, the external response is good and stable. The transint period does not exceed one and a half seconds, and the change in the amount of external signal does not exceed 0.2. Figure 11. Setpoint tracking and disturbance rejection

CONCLUSION
This paper presents study of three methods of control to modify and correct the dropping in the speed of the electrical motor of a washing machine due to sudden or pre-starting loads. The feedback controller consists of comparators such as PID, LQR and feed forward to make improvement and minimizing to the difference between the actual and setting speed of the motor under variable loads. The actual/real motor is measured and the parameters are implemented into MATLAB coding to emulate in reality the optimized performance of the motor in required case study. It is observed from the experiment that in the case of a step responses change in the DC motor, it is preferable to use a LOR control rather than PID, and PID is better than feedforward while the cost of feedforward is the best of all control methods PHD and LQR.