Closed-Loop Speed Control of PM-BLDC Motor Fed by Six Step Inverter and Effects of Inertia Changes for Desktop CNC Machine

The brushless DC motors with permanent magnets (PM-BLDC) are widely used in a miscellaneous of industrial applications. Usually, these applications are characterized by relatively high torque ripples. In this study, closed-loop speed control of PM-BLDC motor fed by six step inverter for desktop CNC machine investigated. Motor has 3 phases, 0.0089 kg/m /0.00091 kg/m changes inertia moment, 0.005 viscous damping, 3000 rpm reference speed, 4 poles and trapezoidal back EMF wave form. Inverter has 3 bridge arms, snubber resistance 5000 ohms, snubber capacitance 1 uF. Developed speed control PM-BLDC motor use in desktop CNC machine. Also simulated on MATLAB and results are presented in the study.


I. INTRODUCTION
Nowadays, brushless DC motors with permanent magnets (PM-BLDC) are widely used in a miscellaneous of industrial applications. The permanent magnet brushless dc (BLDC) motor is gaining popularity being used in military, aerospace, computer, automotive, industrial and household products because of its high torque, compactness, and high efficiency [1], [2]. Furthermore, brush maintenance is no longer required, and many problems resulting from mechanical wear of brushes and commutators are improved by changing the position of rotor and stator in DC motor. To alternate the function of brushes and commutator, the BLDC motor requires an inverter and a position sensor that detects rotor position for proper commutation of current [3]- [5]. To improve the performance of BLDC motors, different control methods have been developed by many researchers. Those are such as the field weakening control method, overlapping method, PWM chopping method [6]- [11]. Usually, these applications are characterized by relatively high torque ripples. In this study, closed-loop speed control of PM-BLDC motor fed by six step inverter for desktop CNC machine investigated. Motor has 3 phases, 0.0089 kg/m 2 /0.00091 kg/m 2 changes inertia moment, 0.005 viscous damping, 3000 rpm reference speed, 4 poles and trapezoidal Manuscript received March 7, 2012; accepted May 12, 2012. back EMF wave form. Inverter has 3 bridge arms with IGBTs, snubber resistance 5000 ohms and snubber capacitance 1 microF. Developed speed control PM-BLDC motor use in desktop CNC machine. Developed system simulated using matlab also used in real industrial system. PM-BLDC motor which has closed-loop speed control algorithm used in CNC machine for mechatronic laboratory experiment.

II. ANALYSIS OF PM-BLDC MOTOR
The stator of a brushless DC motor is equipped with a polyphase winding. The phases are connected to the DC bus through a switching circuit. The switching sequence is controlled so that it is synchronized with the position of the rotor. As a result, the stator produces a rotating magnetic field. The rotor is equipped with permanent magnets, creating a structure with the same number of poles at the stator. The stator switches act like a commutator in a classic DC motor. In brushless permanent-magnet DC (PM-BLDC) motors, the armature currents are commutated exactly according to rotor position. The signal of rotor position may be obtained from a position sensor, or from induced voltages for sensor-less control system [6], [7]. The performance of BLDC motors is analyzed via a time-domain simulation. The voltage equation in the time domain is shown in Equation (1): where R 1 , L d , L q , and L 0 are armature resistance, d-axis synchronous inductance, q-axis synchronous inductance, and 0-axis inductance, respectively. , where (2), (3) and (4) are terminal voltages, induced voltages, and winding currents, respectively. The transformation matrices for two phases, three phases, and four phases system, noted as C 2 , C 3 , and C 4 , are as follows: where (5), (6) and (7) (8) where in equation (8), T load is load torque, J moment of inertia and B viscous damping, m ω radial speed of motor.
We assumed; all power electronics equipments are ideal, motor is not saturated and motor has no power loss. The effectiveness of proposed system has been validated by comparative studies and simulation results. The proposed system has been simulated by MATLAB software, and a comparative study among the proposed and conventional methods has been done to validate the advantages of proposed method. PI controller is used as a speed controller for recovering the actual motor speed to the reference. The reference and the measured speed are the input signals to the PI controller. In the Fig. 1, K P and K I values of the controller are determined by error method for each set speed.
Since the model equations are of non-linear, they are solved by ode4 numerical technique simulated using MATLAB. Table I and Table II are true table of switches and hall sensor, respectively.
These two tables are used for switching the IGBTs.

III. SIMULATION RESULTS OF PM-BLDC
Closed-loop speed control strategy of PM-BLDC motor consist of IGBT based six step inverter, a speed regulator, and hall sensors, respectively.
Control strategy of PM-BLDC is shown in Fig. 2. this is general view of closed-loop speed control block in Matlab.
Current values changes with the moment of inertia but back-emf closed values. Two different inertia of moment selected the simulated machine and results presented in Fig.  3. The moment of inertia value taken for this case is 0.0089 kg/m 2 and it reaches steady state speed at time 0.25 seconds. When the moment of inertia decreased 0.00091 kg/m 2 , it reaches steady state speed suddenly at time 0.1 seconds. Low moment of inertia means low steady state time for speed and torque, evidence of this is shown in Fig. 3 (a-f). When the moment of inertia decreased 0.00091 kg/m 2 , it reaches steady state speed suddenly at time 0.1 seconds in Fig. 4 (b). The moment of inertia value taken for this case is 0.0089 kg/m 2 and it reaches steady state torque at time 0.25 seconds in Fig. 5 (a). When the moment of inertia decreased 0.00091 kg/m 2 , it reaches steady state torque suddenly at time 0.1 seconds in Fig. 5 (b). The simulated motor parameters are shown in Table III.

IV. CONCLUSIONS
Closed-loop speed control of PM-BLDC motor has been investigated for desktop CNC machine. Also effect of inertia of moment investigated influence on reaching steady state time. Two different inertia moments selected for simulation. These are 0.0089 kg/m 2 /0.00091 kg/m 2 . When the inertia of moment 0.0089 kg/m 2 selected, it reaches steady state speed at time 0.25 seconds. When the moment of inertia decreased 0.00091 kg/m 2 , it reaches steady state speed suddenly at time 0.1 seconds. Low moment of inertia means low steady state time for speed and torque. PI controller is used as a speed controller for recovering the actual motor speed to the reference. K P and K I values of the controller are determined by error method for each set speed.