CHAPTER 6 CURRENT REGULATED PWM SCHEME BASED FOUR- SWITCH THREE-PHASE BRUSHLESS DC MOTOR DRIVE

Transcription

1 125 CHAPTER 6 CURRENT REGULATED PWM SCHEME BASED FOUR- SWITCH THREE-PHASE BRUSHLESS DC MOTOR DRIVE 6.1 INTRODUCTION Permanent magnet motors with trapezoidal back EMF and sinusoidal back EMF have several advantages over other motor types (Hanselman et al 1994). Most notably, (compared to dc motors) they are lower maintenance due to the elimination of the mechanical commutator and they have a high-power density which makes them ideal for high-torque-to weight ratio applications (Miller 1989). The permanent magnet brushless dc (PMBLDC) motor is gaining popularity being used in computer, aerospace, military, automotive, industrial and household products because of its high torque, compactness, and high efficiency (Pillay et al 1989). A conventional BLDC motor drive is generally implemented via a six-switch, three-phase inverter and three Hall-effect position sensors that provide six commutation points for each electrical cycle (Krishnan 1985). Cost minimization is the key factor in an especially fractional horse-power BLDC motor drive for home applications. Cost reduction of BLDC motor drive is accomplished by two approaches: the topological approach and the control approach. In topology approach, minimum number of switches and eliminating the mechanical sensors are the options while the control approach has choices in terms of complexity in control (Dhaouadi et al 1991), nature of the control, implementation platform etc. In the control approach, using high performance processors, algorithms are designed and implemented in

2 126 conjunction with a reduced component inverter to produce the desired torque characteristics (Krishnan et al 2001). Therefore, effective algorithms should be designed for the desired performance. Recently, a four-switch, three-phase inverter (FSTPI) topology has been developed and used for a three-phase BLDC motor drive (De Rossiter Correa et al 2006). Reduction in the number of power switches, dc power supplies, switching driver circuits, losses and total price are the main features of this topology (Lee et al 2003). It results in the possibility of the four-switch configuration instead of the six switches. Compared with the four-switch converter for the induction motor, it is identical for the topology point of view. However, in the four-switch converter, the generation conducting current profiles is inherently difficult due of 120 to its limited voltage vectors. This problem is well known as asymmetric voltage PWM. It means that conventional PWM schemes for the four-switch induction motor drive cannot be directly used for the BLDC motor drive. Therefore, in order to use the four-switch converter topology for the three-phase BLDC motor drive, a modified control scheme should be developed. A complete model of the PMBLDC motor drive with its performance in closed loop has been presented (Varatharaju et al 2011). The discussions have been a readable text on the operation, modeling, and control of BLDC motor for graduate students studying electric drives and control as well as practicing engineers in industries. The solutions can be obtained from a modification of the conventional voltage controlled PWM strategies, such as the space vector PWM. However, it naturally requires lots of equations for the transformation of voltage and current vectors, and a b c frames. As a result, the current control such as block becomes much more complicated. Moreover, in order to

3 127 handle the complicated calculations in one sampling period, a high-speed digital processor is also necessary, which increases the manufacturing cost. Therefore, for the low cost BLDC motor applications, voltage vector PWM schemes cannot be regarded as a good solution for cost effective purpose. Modeling and simulation of electromechanical systems with BLDC drives are essential steps at the design stage of such systems. The fundamental operation of FSTP inverter fed BLDC motor drive has been analyzed by simulation. The developed the nonlinear simulation model of the BLDC motors drive system is used for proportional-integral (PI) control. The simulated results in terms of electromagnetic torque and rotor speed are given. 6.2 DESCRIPTION OF PMBLDCM DRIVE Figure 6.1 describes the basic building blocks of the PMBLDC motor drive. The drive consists of speed controller, reference current generator, pulse width modulation (PWM) current controller, position sensor, the motor and a IGBT based voltage source inverter (VSI). The speed of the motor is compared with its reference value and the speed error is processed in PI speed controller. The output of this controller is considered as the reference torque. A limit is put on the speed controller output depending on permissible maximum winding currents. The reference current generator block generates the three phase reference currents (i a, i b, ic ) using the limited peak current (Qiang Han et al 2007).

4 128 ref e Speed controller Limiter * T Reference Current Generator * I a * I b PWM Current Controller I a I b r r Position V dc Four switch Three Phase VSI Actual Speed Sensors PM BLDC Motor Figure 6.1 PI-Speed Controller The PI controller is widely used in industry due to its ease in design and simple structure. The rotor speed r (n) is compared with the reference speed r (n) and the resulting error is estimated at the n th sampling instant as: e(n) r (n) * r(n) (6.1) The new value of torque reference is given by T(n) T(n 1) K Pe (n) e (n 1) K 1 e(n) (6.2) Where, e (n 1) is the speed error of previous interval, and e (n) is the speed error of the working interval. K P and K I are the gains of proportional and integral controllers respectively. By using Ziegler Nichols method the K P and K I values are determined.

5 Reference Current Generator Unlike a brushed DC motor, the commutation of a BLDC motor is controlled electronically (Sebastian 1989). To rotate the BLDC motor, the stator windings should be energized in a sequence. Most of BLDC motors have three Hall sensors embedded into the stator on the non-driving end of the motor. Rotor position is sensed by Hall Effect sensors embedded into the stator which gives the sequence of phases. Whenever the rotor magnetic poles pass near the Hall sensors, they give a high/low signal, indicating the N or S pole is passing near the sensors. Based on the combination of these three Hall sensor signals, the exact sequence of commutation can be determined (Rubai et al 1992). The magnitude of the reference current (I ) is determined by using reference torque (T ) and the back emf constant (K b ); I * * T. K b Depending on the rotor position, the reference current generator block generates three-phase reference currents (i a, i b, i c ) considering the value of reference current magnitude as I, I and zero. The reference current generation is shown in Figure 6.2 and Table 6.1 (Luk et al 1994). Table 6.1.Rotor position signal Vs reference current Rotor Position Signal r Reference Currents (i a, i b, i c ) to I I I I I 0 I I I I I I 0 I

6 130 Figure 6.2 Back EMF, current profile, modes, conducting switches in the four-switch converter for three-phase BLDC motor drives Figure 6.3 shows the FSTP BLDC drive with current regulation. The PMBLDC motor is modeled in the 3-phase abc frame. The general voltampere equation for the circuit is shown in the Figure.6.4. Terminal voltages of a BLDC motor in the four-switch inverter with respect to the mid-point of the dc bus are as follows: dia Vao Ria L ea Vno (6.3) dt dib Vbo Rib L eb Vno (6.4) dt dic Vco Ric L ec Vno (6.5) dt

7 131 V c1 S 1 S 3 R Ls M e a a c i a i c R Ls M e c b i b R Ls M e b V c2 S 2 S 4 Current Re gulators S S S S 4 ia ib I Ref i a Ref i b Ref Current Re ference Generator H a H b H c Figure 6.3 Four-switch converter topology for three-phase BLDC motor Figure 6.4 Inverter circuit with PMBLDCM drive

8 DIRECT CURRENT CONTROLLED PWM From the motor point of view, even though the BLDC motor is supplied by the four-switch converter, ideal back-emf of three-phase BLDC motor and the desired current profiles can be described as shown in Figure 6.2. From the detailed investigation of the four-switch configuration and back-emf and current profiles, it could be concluded that the existing PWM method for B6 inverter can not perform with FSTP inverter. Under a balanced condition, the three-phase currents always satisfy the following condition: Ia Ib Ic 0 (6.6) Then, (6.6) can be modified as I c (Ia I b) (6.7) In the case of the ac induction motor drive, at any instant there are always three phase currents flowing through the load, such as Ia 0 ; Ib 0 ; Ic 0 (6.8) However, in the case of the BLDC motor drive, (6.8) is not valid anymore. Note that in Figure 6.2 phase A and B currents are only controllable and phase C is uncontrollable. The modes of operation FSTP inverter is depicted in Figure 6.5. Table 6.2 implies that due to the characteristics of the BLDC motor, such as two-phase, only two phases (four switches) needed to be controlled, not three phases. Therefore, based on Table 6.2, one can develop a switching sequence using four switches.

9 133 S 1 S 3 S 1 S 3 c a c a b b S 2 S 4 S 2 S 4 (a) (b) c S 1 a S 3 c S 1 a S 3 b b S 2 S 4 S 2 S 4 (c) (d) S 1 S 3 S 1 S 3 c a c a b b S 2 S 4 S 2 S 4 (e) (f) Figure 6.5 Switching modes of FSTP Inverter with direct controlled PWM (a) Mode I (S4). (b) Mode II (S1 and S4). (c) Mode III (S1). (d) Mode IV (S3). (e) Mode V (S3 and S2). (f) Mode VI (S2).

10 134 Table 6.2 Switching Sequence of Four switch BLDC motor Modes Active Phases Silent Phases Switching Devices Mode 1 Phase B and C Phase A S 4 Mode 2 Phase A and B Phase C S 1 and S 4 Mode 3 Phase A and C Phase B S 1 Mode 4 Phase B and C Phase A S 3 Mode 5 Phase A and B Phase C S 2 and S 3 Mode 6 Phase A and C Phase B S 2 As shown in Table 6.2, the two-phase currents need to be directly controlled using the hysteresis current control method by four switches (Lajoie-Mazen et al 1985). Hence, it is called the direct current controlled PWM scheme Current Regulation Based on the switching sequences in Table 6.2, the current regulation is actually performed by using hysteresis current control. The purpose of regulation is to shape quasi-square waveform with acceptable switching (ripple) band. The detailed waveforms and switching sequences are described in Figure 6.6. The bold line is the current reference value, which is obtained from the torque and speed control loop to achieve the reference torque. The switching frequency and torque ripple are the main considerations for setting the upper and lower limits. It means that a smaller band causes higher switching frequency, but lower torque ripple. Using mode II and mode III, the current regulation can be explained as follows: In mode II, I a and I b currents (I a >0, I b <0) flow and I c =0. Therefore, mode II is divided into two cases, such as dia 0 dt, dib dt 0 and

11 135 di a 0 dt, dib 0 dt. In this mode, as shown in Figure 6.6(b), switches S1and S5 are used. Until I a (I b ) reaches the upper (lower) limit, S1 and S4 are turned on for supplying dc-link energy to increase the current. When the current reaches to the upper limit, S1and S4 are turned off to decrease the current through the anti-parallel diodes D2 and D3. Upper Limit (UL) I a Reference Lower Limit (UL) I b I c Mode I Mode II Mode III Mode IV Mode V Mode VI Mode I S4 D3 S1 D S1 S 2 D2 1 D2 S1 D2 S 3 D S 4 3 D4 S 2 D S 1 2 D1 S2 D1 S2 S4 D3 S 4 D3 S3 D S 4 3 D4 D1 S4 D3 Figure 6.6 Current regulation and detailed switching sequences At that time, the reverse bias (negative dc-link voltage) is applied to the phases, resulting in decreasing the current. On the other hand, in mode III, only one current (I a ) can be controllable. It means that only switch S1 can be used as shown in Figure 6.5(c). However, the same principle as used for mode

12 136 II is applied to mode III. When I a increases, S1 is turned on and other case S1 is turned off. Special attention should be paid to mode II and mode V. In these modes, phases A and B are conducting the current and phase C is regarded as being unexcited, so that it is expected that there is no current in the phase C. However, the back EMF of phase C can cause an additional and unexpected current, resulting in current distortion in the phases A and B. Therefore, in the direct current controlled PWM, the back-emf compensation problem should be considered. This phenomenon can be explained with the aid of the simplified equivalent circuit in Figure 6.7. As an example of mode II, in the ideal case, only one current (phase A or phase B) needs to be sensed and switching signals of S1 and S4 are identical. In the case of sensing phase A current, the switching signal of S1 is determined independently and S4 depends on the S1 signal, so that phase A current can be regarded as a constant current source. However, in this case, phase B current can be distorted by the phase C current. On the other hand, if phase B is controlled, phase B current can be a constant current source, and then the phase A current can be distorted. The same explanation can be applied to mode V. From the equivalent circuits of Figure 6.8, one can come up with a solution. If phases A and B are regarded as independent current sources, the influence of the back-emf of phase C can be blocked and cannot act as a current source, so that there is no current in phase C. It means that in the direct current controlled PWM, phase A and phase B currents should be sensed and controlled independently and the switching signals of S1 (S3) and S4 (S2) should be created independently, as shown in Figure 6.8.

13 137 a a Phase A Phase A V d c Vcn 0 Winding n V d c ec Winding n V d Phase B Winding V d Phase B Winding b (a) (b) b Figure 6.7 Simplified equivalent circuits of modes II and V (a) Ideal case. (b) Actual case when the back EMF causes current in phase C I a Re f S1signal I bref S 4signal I a I b Current Controller Figure 6.8 PWM strategy for compensating the back-emf problem 6.4 PROBLEM FORMULATION Permanent magnet brushless dc motor (PMBLDCM) drives are continually gaining popularity in motion control applications. This paper investigates the performance of direct current controlled pulse width modulation (DCC-PWM) based control of four-switch three-phase (FSTP) inverter feeding permanent magnet brushless dc (PMBLDC) motor.

14 138 A MATLAB/Simulink model for the FSTP fed PMBLDC motor is developed and tested with direct current controlled PWM method. The triumph of the DCC-PWM in obtaining desired speed-torque characteristics is validated with help of simulation results. The DCC-PWM is also implemented with proportional-integral controller using TMS320LF2407 digital signal processor. The fundamental operation of FSTP inverter fed BLDC motor drive has been analyzed by simulation. The developed the nonlinear simulation model of the BLDC motors drive system is used for proportional-integral (PI) control. The simulated results in terms of electromagnetic torque and rotor speed are given 6.5 SIMULATION RESULTS In this work the drive model with PI speed controller is developed and simulated in order to validate the FSTP inverter control of BLDC motor model and the designed controller and the complete simulink diagram as shown in figure appendix A-5. The set of equations representing the model of the drive system is schematized. For conducting the studies and analysis, this paper considers a typical industrial BLDC motor (Arrow Precision Motor Co., LTD) with importance specifications: Power =180, 300rpm, 8 poles. Figure 6.9 represents the back EMF resulted in the simulation and Figure 6.10 shows the sectors of FSTP inverter while feeding BLDC motor. The phase currents are illustrated in Figure Figure 6.12 shows the torque and the speed variations in starting for the reference speed of 150RPS and load on 6 N-m. The motor speed quickly converges to the reference during the startup.

15 139 Figure 6.9 Back EMF Figure 6.10 Sector Representation of FSTP inverter fed BLDC motor

16 140 Figure 6.11 Stator phase currents. Figure 6.12 Torque and speed responses during startup transients

17 HARDWARE IMPLEMENTATION Based on the statute presented in the previous sections it is possible to derive an algorithm that can control the BLDC drive better. This algorithm is adequate for compensating the back EMF and current distortions. The direct control PWM is implemented in DSP processor TMS320LF2407A. The Texas instruments TMS320LF2407 DSP [103] controller (referred to as LF2407) is a programmable digital controller with a C2XX DSP central processing unit (CPU) as the core processor. The LF2407 contains the DSP core processor and useful peripherals integrated onto a single piece of silicon. It combines the powerful CPU with an on-chip memory and peripherals (Bhim singh et al 2002). The complete setup is shown in Figure Figure.6.15 shows the representative phase current waveform. The effectiveness of the designed PI controller is validated for the step change in dc link voltage and presented in Figure 6.16 and Figure Figure 6.13 Hardware setup

18 142 Figure 6.14 Hardware schematic of the sensor-controlled, four-switch BLDC Motor drive based on TMS320LF2407A DSP Figure 6.15 Representative Phase Current

19 143 Figure 6.16 Speed response for step increase dc-link voltage Figure 6.17 Speed response for step decrease in dc-link voltage

20 144 For Step change reference speed the drive takes negligible steady state error and settling time of 0.01s without any overshoot. The hardware results are very marginal to simulation result which is much lesser, and then the difference occurred during multiple observations in digital storage oscilloscope 6.7 SUMMARY This chapter presents a method to generate PWM signals for control of fourswitch three-phase inverters. The simulation model of the BLDC motors drive system with PI control based four switch three phase inverter on MATLAB/Simulink platform is presented. The system is realized in TMS320LF2407 DSP platform. The main advantages are increased system reliability and cost reduction of the overall system. The performance of the developed algorithm based speed controller of the drive has revealed that the algorithm devises the behavior of the PMBLDC motor drive system work satisfactorily. In comparison with the usual three-phase voltage-source inverter with six switches, the main features of this converter are twofold: the first is the reduction of switches and freewheeling diode count; the second is the reduction of conduction losses. For a step change the reference speed the drive takes negligible settling time of 0.01s without any overshoot.