CHAPTER 4 FUZZY BASED DYNAMIC PWM CONTROL


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1 47 CHAPTER 4 FUZZY BASED DYNAMIC PWM CONTROL 4.1 INTRODUCTION Passive filters are used to minimize the harmonic components present in the stator voltage and current of the BLDC motor. Based on the design, the performances of these filters are limited to a narrow range load of operation for any specific speed of the motor. The amount of reduction of harmonics and ripple torque is also limited. There is a necessity for an active filter topology to enhance the performance both in harmonics and torque ripple for a wide range of load and speed of operation. The control characteristics of the BLDC motor are highly nonlinear in nature. Due to the imprecise control characteristics of this motor, Fuzzy logic is found to be an ideal technique to address these issues. + DC Input _ Drive System Two Level Inverter BLDCM G G6 Gate Signals Decoder/ Gate Drive System Fuzzy bases dynamic PWM Controller (FPGA) Hall Signals Figure 4.1 Control block diagram for the Fuzzy based dynamic PWM control for BLDC motor drive system
2 48 The control block diagram for the fuzzy based dynamic PWM control is presented in Figure 4.1. Fuzzy logic has been applied to a large number of control applications such as system control, domestic appliances and traffic control. The control action in fuzzy logic controllers (FLC) can be easily expressed by means of linguistic variables describing simply human friendly ifthen rules. In conventional methods, the hardware implementation of the FLC is based on microcontrollers, as control systems requires high processing and I/O handling speeds microcontrollers have often difficulty with these control applications. Singh & Kuldip (2003) suggested that the use of FPGA results in faster implementation and quick hardware verification. Moreover FPGA based systems are flexible and can be reprogrammed unlimited number of times. Monmasson et al (2007) described that BLDC motor is well suited for digital control methods, thus FPGA based controllers are ideal for controlling this motor. The commutation torque ripple affects the performance of the motor running at combinations of different speed and load conditions. Commutation torque ripple occurs in every 60 electrical degrees changing over of the stator current from one phase to another. Bharatkar et al (2008) stated that the torque ripple increases at lower speeds due to increase in commutation time. This chapter focuses on reconfigurable controller using fuzzy logic technique for variable frequency and variable duty ratio Pulse Width Modulation (PWM) operation to minimize the harmonics and the commutation torque ripple. The frequency and the Duty ratio are dynamically adjusted by the fuzzy controller for any steady speed of the motor. This technique is experimented using Virtex II Pro Field Programmable Gate Array (FPGA). The experimental results confirm the effectiveness of this technique in minimizing harmonics and torque ripple.
3 MOTOR DRIVE SYSTEM The functional elements of the fuzzy logic controlled dynamic PWM based BLDC motor drive system for experimenting the harmonics and torque ripple minimization is presented in Figure 4.2. The DC Chopper is used for varying the voltage for achieving the speed control of the motor. The stator reference current, speed and the hall sensor positional inputs are fed to the FPGA. The FPGA gives six switching pulses to the three phase inverter. The speed of the motor is controlled by varying voltage provided by the chopper. The PWM pulse frequency and duty ratio of the three phase inverter is dynamically varied without affecting the speed of the motor. The change in the input voltage fed from chopper will be controlled by the switching pulses supplied by the FPGA. (Variable voltage) +  Dc chopper Three Phase Inverter BLDC Current ADC PWM Signal for variable voltage FPGA ADC Hall input (A, B,C) Speed Figure 4.2 Fuzzy controlled dynamic PWM based BLDC motor drive system The back EMF induced per phase of the motor winding is constant for 120 electrical of the complete cycle. In order to get constant output power and constant output torque, the current is driven through a motor winding during the flat portion of the back emf waveform.
4 50 From the mathematical modeling of the motor drive system, the ( Vdc 4 Em ) commutation torque ripple is derived as Te _ ripple 2K e t in equation 3L (1.13). Chen et al (2005) and Shi et al (2010) stated that the slopes of stator phase currents during commutation depend on the inductance (L) of the stator coil, peak value of the back emf (E m ) and the DC input voltage to the stator (V dc ). When the frequency of the PWM is high at the instant of commutation and the PWM time period is much smaller than the electrical time constant L R, the effect of R can be ignored. The torque ripple can be minimized to zero while V 4E 0 or V 4E dc m dc m. When the switching frequency of PWM dia increases, the voltage drop due to inductive reactance L increases in dt addition to the back emf E m. The net voltage of the stator winding is made equal to 4E m during the instance of commutation, so that the torque ripple will be minimized to zero. Kim et al (2006) presented that the input and output voltage of the inverter is related by the equation 4.1 V inv D Vin (4.1) 1 D Where D is the duty ratio of PWM, V in, V inv are the input voltage and the output voltage of the inverter respectively. The duty ratio estimated at the instant of commutation to minimize the commutation torque ripple is given in equation 4.2. D 4Ke V 4 K r in e r (4.2) The fuzzy controller is designed to adjust the frequency and duty ratio of the PWM signal in such a way that the ripple torque will be minimal
5 51 for any specific speed and load condition. This control strategy states that at the instant of commutation the frequency of the PWM is made higher so that the sudden transition of stator current can be avoided. This is done by increasing the PWM frequency at the instant of commutation and balancing the voltage by adjusting the duty cycle of the PWM. The slope of the stator current is related to the speed and the stator current of the motor. Due to the nonlinear nature of the system, Fuzzy logic is the ideal technique for performing the control action. The stator current and the speed of the motor are considered as the inputs for the fuzzy system and the variable frequency PWM is the output of the controller. The motor specification for the experimentation is given in Table 4.1 Table 4.1 Motor specification Parameter Stator voltage Stator Current (rated) Speed Range 200 Volts 7.2 Amps 2000 rpm Number of Poles SIMULATION MODEL The Simulation diagram of a BLDC motor Drive system using MATLAB/Simulink is shown in Figure 4.3. The stator current and the speed of the motor are considered as inputs for the fuzzy controller. The output of the fuzzy controller is designed to get the variation in the PWM signal. However the speed of the motor is controlled by the external speed control loop with proportional integral (PI) controller.
6 52 Figure 4.3 MATLAB Simulation diagram of Fuzzy logic controlled BLDC motor Drive system 4.4 FUZZY LOGIC CONTROLLER FOR DYNAMIC PWM A Fuzzy logic control theory is an alternative to the classical control theory. In fuzzy logic, a fuzzy set is a generalization of the classical set with a membership value in the range 0 to 1. Fuzzification is the first step in the FLC which converts real input data into a set of membership values in the interval zero to one in the corresponding fuzzy sets. The entire ranges of inputs are normalized to the integer value 0 to 64. The range of fuzzy set values is considered in the powers of 2 for making it compatible for the FPGA.
7 53 Figure 4.4 Membership Function for speed with range of fuzzy sets The membership function for speed is shown in the Figure 4.4. It consists of fuzzy logic ranges that can be defined using the linguistic terms as Low1, Low2, Med1, Med2 and High1. The ranges are used for demonstrating the fuzzification process in VHDL. Similarly the membership function for current is shown in the Figure 4.5. The fuzzy logic ranges defined using the linguistic terms as Low, Med and High. These two inputs are further processed using the inference engine. The ranges are taken in the powers of two since the programming language can accept only values that are in powers of two. Figure 4.5 Membership Functions for stator current with range of fuzzy sets
8 54 Inference engine consists of two subblocks, fuzzy rule base and fuzzy implication. The inputs, which are now fuzzified, are fed to the inference engine and the rule base is then applied. The output fuzzy sets are then identified using fuzzy implication method. Table 4.2 shows the fuzzy associative memory for speed and current. The ifthen rule fuzzy rule base is followed for evaluating the output conditions. The input to the fuzzy logic controller is speed and current which are fed from analog to digital converter (8bit). The fuzzy rule base is followed and the output constraint is obtained from fuzzy associative memory. The defuzzified output from the fuzzy is 4 bit singleton data which corresponds to the 15 different PWM signals. Table 4.3 shows the fuzzy sets for the output and the corresponding 4bit data of the PWM signal. Table 4.2 Fuzzy Associative Memory Speed/Current High Medium Low Low1 Low1 Low2 low3 Low2 Low4 Low5 Med1 Med1 Med2 Med3 Med4 Med2 Med5 Large1 Large2 High1 Large3 Vlarge1 Vlarge2
9 55 Table 4.3 Fuzzy singleton output and equivalent defuzzified 4 bit data Fuzzy singleton output 4 bit data assigned Low Low Low Low Low Med Med Med Med Med Large Large Large Vlarge Vlarge FPGA IMPLEMENTATION VirtexII Pro FPGA (XC2VP30FF896) is used for the realization of the controller. Figure 4.6 shows the block diagram of software implementation of fuzzy based reconfigurable controller. The block diagram contains three modules. The inputs speed and current of the motor are given to the Fuzzy controller. The controller generates a 4 bit defuzzified output and given to the PWM generation unit which determines the frequency and duty ratio proportional for the FLC output. Based on the Hall sensor input, the Commutation logic block generates the gate signal for the inverter whose switches have to be turned on in sequence so that the stator is excited for continuous rotation.
10 56 From Hall Sensors Commutation Logic To Inverter To DC Chopper PWM Current 8bit Speed 8bit Fuzzy Controller Figure 4.6 FPGA implementation of Fuzzy PWM controller for BLDC motor The FPGA controller is supplied with two inputs speed and current through ADC. The input ranges are normalized to the range of 0 to 64. The membership value ranges in the 0 to 1 is normalized to 0 to 100. The output of the fuzzy controller is designed for four bit singleton output. Further the 4 bit value has the maximum of 15 combinations of PWM output. This 4 bit value selects the switching frequency of inverter and the corresponding duty ratio. The minimum frequency generated is 4 khz and the duty ratio is 6.25%. The maximum frequency generated is 20 khz and the duty ratio is 93.75%. In between this minimum and maximum region the frequency and also the duty ratio will be varied.
11 57 Figure 4.7 RTL schematics of the Fuzzy based PWM controller The RTL schematic of reconfigurable controller is shown in Figure 4.7. The 8 bit data for the speed and the current are fed as the control inputs. The FPGA clock frequency of 100 MHz is taken as the clock input to the control process. Hall sensor inputs A, B, C are applied as the one bit input to the controller for deciding the commutation sequence of the stator windings. The 6 gate signals to the three phase inverter and the PWM for the chopper are taken as the outputs from the controller. 4.6 RESULTS AND DISCUSSIONS The functionality of the PWM controller implemented in FPGA is verified using the simulated response using ModelSim 9.1.
12 58 Figure 4.8 Simulation results for the speed ( ) and current ( ) The simulation results shown in Figure 4.8 confirm the functionality of the controller. Switches S1, S3, S5 are the high side switches for phase A, B, C and S4, S6, S2 are the low side switches for phase A, B, C respectively. The input to the fuzzy controller is fed from motor through ADC. At any instant for input values of speed ( ) and the current ( ) and the hall sensor output A=1, B=0, C=1, the corresponding inverter switches to be closed will be B high and C low. The frequency and the duty ratio of the PWM is 4 khz, 6.25% respectively. The digital storage oscilloscope output shown in Figure 4.10 shows the PWM output of the fuzzy logic based FPGA controller for BLDC motor. The experimental results are shown in Figure 4.10a is for the input speed ( ), current ( ). The frequency and the duty ratio are khz and 25% respectively. Figure 4.10b is for the input of speed ( )
13 59 and current ( ). The frequency and the duty ratio are khz and 75% respectively. The variable frequency, variable duty ratio operation of the Fuzzy logic controller designed for any specific steady speed operation. Here the frequency and the duty ratio are self compensated for steady speed of operation. (a) (b) Figure 4.9 PWM signall for (a) speed is , Current is (b) speed is , current is
14 Harmonics The simulated stator voltage, current profiles with corresponding harmonics spectrum are presented in Figure It is observed that the voltage harmonics are reduced to 5.49 %THD and the current harmonic are reduced to 5.34%THD. (a) (b) Figure 4.10 Simulation response a) stator voltage profile and harmonic spectrum b) Stator current and harmonic spectrum
15 61 An experimental prototype is developed in laboratory to test the performance of the fuzzy based dynamic pulse width modulation for the brushless DC motor. Motor Specifications for the experimentation is presented in Table 4.4 Table 4.4 Design parameters Motor parameter Rating Stator voltage (rated) 300V Speed (rated) 2000 rpm Stator Current (rated) 7.2 A Number of Poles 4 The experimented stator voltage and current profile with the conventional two level inverter are compared with the fuzzy logic controlled dynamic PWM applied to twolevel inverter for investigating the effectiveness of this methodology in harmonics and torque ripple minimization. Figure 4.11 shows the voltage profile and the corresponding harmonics spectrum of the stator voltage with conventional PWM in twolevel inverter. It is observed that the stator voltage profile is mere trapezoidal in nature. The harmonics present in the stator voltage is 51.96%THD. Figure 4.12 shows the stator voltage profile and the harmonic spectrum with Fuzzy based dynamic PWM. It is observed that the voltage profile turned to be a smooth profile with less harmonics. The harmonics present in the stator voltage reduced to 12.11%THD.
16 V (a) Waveform V Vrms, %THD (b) Figure 4.11 (a) Voltage profile with conventional PWM in two level inverter (b) Harmonics spectrum V (a) Waveform V Vrms, %THD (b) Figure 4.12 (a) Voltage profile with Fuzzy based dynamic PWM (b) Harmonics spectrum
17 63 Figure 4.13 shows the profile of stator current and the harmonics spectrum for the conventional PWM with twolevel inverter. The harmonics present in the stator current is shown in Figure 4.13b. It is observed 36.96%THD present in the stator current. Figure 4.14a presents the stator current profile using fuzzy based dynamic PWM. The current ratio is selected as 100 for accurate prediction of the current waveform. For every 60 electrical, transition occurs in the current profile due to the electronic commutation. When applying the dynamic PWM, the profile of the stator current is improved towards a smooth profile. There are small amount of spikes observed and shall be rectified by proper tuning of the fuzzy system. It is observed that the profile has transformed towards a smooth profile. The transitions in the stator current are very much reduced and the harmonics reduced to 13.83%THD. Since the Harmonics is observed for the percentage of the fundamental quantity, the current ratio will not changing the %THD value A (a) Waveform I Arms, %THD (b) Figure 4.13 (a) Stator current profile with conventional PWM in two level inverter (Current Ratio 1:1) (b) Harmonics spectrum
18 64 A (a) Waveform I Arms, %THD (b) Figure 4.14 (a) Stator current profile with Fuzzy based dynamic PWM (Current Ratio 1: 100) (b) Harmonics spectrum The current and voltage harmonic comparison bar graph of conventional method and the fuzzy based dynamic PWM technique applied for the BLDC motor drive system are presented in Figure 4.15.
19 65 Two level inverter %THD (I) Simulated %THD (I) Experimented Two level inverter with dynamic PWM (a) Two level inverter Two level inverter with dynamic PWM %THD (V) Simulated %THD (V) Experimented (b) Figure 4.15 Harmonic comparison bar graph a) stator current b) stator voltage
20 Speed and Torque The simulated speed and torque profile of the BLDC motor are presented in Figure 4.16a and 4.16b. The speed controller controls the speed at 2000 rpm. The load is applied at 0.5 s simulation time and it is observed that there is a sudden drop in speed. This drop in speed adjusts to steady speed immediately without any overshoot. Figure 4.16b shows the torque profile corresponding to the speed profile while applying the conventional PWM to the twolevel inverter. It is observed that at stable load, the width of the ripple torque is 2.3Nm. Figure 4..16c shows the torque profile for the fuzzy based dynamic PWM applied to the twolevel inverter. It is observed that the ripple torque for the same load conditions is reduced to 1.2Nm. The ripple torque is reduced to almost half the value of the conventional PWM technique. Compared to the torque profiles for the conventional PWM and the fuzzy based dynamic PWM technique, it is observed that there is an overshoot of torque profile in the conventional PWM technique and smooth transition of torque profile in the fuzzy based dynamic PWM method. (a) Figure 4.16 (Continued)
21 67 (b) (c) Figure 4.16 (a) Speed profile for 2000rpm (b) Torque profile with conventionall PWM (c) Torque profile with dynamic PWM Comparing similar works, Sathyan et al (2009) suggested only two duty ratios of PWM (D low ) and (D high ) for reducing the speed ripples of the BLDC motor. This method discusses 15 different PWM frequencies at different duty ratios for effective minimization of speed ripple. This in turn reduces the torque ripple and provides smooth rotation of the rotor. Also the profiles of the stator current and voltage are near sinusoidal in nature, which leads to reduction harmonics.
22 68 Ripple Torque (Nm) Two level inverter Two level inverter with filter Two level inverter with dynamic PWM Load (kg) Figure 4.17 Torque ripple comparison The commutation torque ripple comparison between conventional two level inverter, the two level inverter with passive filter and the two level inverter with Fuzzy based dynamic PWM are presented in Figure 4.17 for comparing the torque ripple minimization. Using the conventional twolevel inverter, the ripple torque increases as the load increases. The effect of passive filter is better for a small range of load. While adopting the fuzzy logic based dynamic pulse width modulation, the torque ripple is further reduced linearly for the wide range of load. With reference to the conventional twolevel inverter, the ripple quantity is reduced to almost half the quantity when using the Fuzzy based dynamic PWM. The experimental setup for the fuzzy logic based dynamic pulse width modulation technique implemented with FPGA is shown in Figure 4.18.
23 69 Figure 4.18 Experimental Setup 4.7 CONCLUSION A reconfigurable digital fuzzy logic based dynamic PWM controller for reducing the harmonics and torque ripple of the BLDC motor is presented in this chapter. The frequency and the duty ratio of the PWM signal for the twolevel inverter are dynamically adjusted based on the load current and the speed of the motor. This methodology effectively minimizes the harmonics present in the stator voltage and current. The commutation torque ripple is considerably reduced using the fuzzy based dynamic pulse width modulation. The stator current waveform experiences spikes at the instant the commutation takes place due to overcompensation of the fuzzy system. Further the current wave forms have to be transformed into smooth profile so
24 70 that the harmonics and the torque ripple are further reduced. Shunt active filters are effective in improving the current profile of the system which can further reduce the current harmonics and in turn it reduces the torque ripple of the motor. The shunt active filter with multilevel inverter shall provide more stages of control action in order to achieve a smooth current profile for the stator current. Since the system is highly nonlinear in nature, non linear control strategy is preferred for effective minimization of the harmonics and torque ripple of the motor. The next chapter discusses the fuzzy controlled threelevel shunt active filter for reducing the harmonics and torque ripple for the BLDC motor.
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