22 CHAPTER 2 POSITION SERVO DRIVE OF BLDC MOTOR FOR SINGLE LINK ROBOTIC ARM 2.1 INTRODUCTION An industrial autoation involves robotic to handle aterials in different environents with different pay loads in all directions. Based on linear and rotational otion of ar oveent, robots are ajorly classified into cartesian, polar and cylindrical. Moveent of ar creates certain issues based on gravitational force related into position and orientation of displaceent. Electric otor driven robotic ars are being developed in recent years for sooth operations so that the electric drives can be subjected to bidirectional speed control with regenerative braking capability. The otor drive should be able to adopt for closed loop position, speed and current control in order to obtain perfect trajectory tracking point. This chapter presents a clear theory about the issues related to gravitational force when single link ar rotation and detailed construction with control of Brush Less DC (BLDC) otor in closed loop position servo drive. 2.2 ROBOTIC ARM MOVEMENTS The word robot originated fro Czech language, robota eans copulsory service. Robot is a achine that autoatically loads and unloads, cuts, welds, or casts which are used by industry in order to obtain accuracy, safety, econoy and productivity. Prograable coputers integrated with
23 achines that often substitute for huan labour in specific repeated task are called as odern robot. Such devices even have anthropooric echaniss, including what we ight recognize as echanical ars, wrist, and hands. A robot anipulator is ade up of several links connected usually in series by the joints to for an ar. A link is a revolute or prisatic depending upon the type of otion caused by the actuator attached to its joint. When the actuator of joint causes rotational otion, the link is called revolute and when the actuator produces translational otion, the link is called prisatic. A gripper, which is referred to as a hand or an end-effector, is attached to the ar by eans of wrist joints. The function of the wrist is to orient the end effector properly. Waist rotation Shoulder rotation Elbow rotation Wrist Figure 2.1 Six axis PUMA industrial robot A general industrial PUMA (Prograable Universal Manipulator for Assebly) robot is shown in Figure 2.1 for a revolute anipulator. The
24 otion of a anipulator and end-effector are caused by oveents of the actuators, which drive the joints. The joint actuators are electric otor or hydraulic otor or pneuatically driven devices. The positions of the joint deterine the configuration of the ar, which places the end-effector at a specific location in the environent. The otion of the joint produced by the actuators deterines the position and orientation of the end-effector at any tie. Transducers such as encoder and tacho generators can be used to provide inforation for deterining the position and orientation of the endeffector and to control the anipulator otion. The set of all points that can be reached by the end-effector of a anipulator ar fors the workspace of the anipulator. A particular position of the end-effector is specified by three independent coordinates, which represent the three Degree-Of-Freedo (DOF). Siilarly, a specific orientation of the end-effector is deterined by three independent variables. Thus, six independent variables are needed to describe the position and orientation of end-effector. However, robots with less than six joints, designed for specific task, are also available. The objective of providing position control for a robot anipulator is to design an appropriate controller for the robot otors so that the position and the orientation of the end-effector follow the desired trajectory with no errors even in the presence of disturbance. A ulti-link anipulator is a highly coplex syste-each link of the robot ar has varying inertia and exerts varying torques on all the other links as the configuration of robot ar changes. Shown PUMA robot has six DOF, first link of waist joint rotates horizontally in and around 360 echanical. Second and third link of joints, which are shoulder and elbow respectively, rotate vertically in and around 360 echanical. The wrist rotation includes horizontal and vertical rotation based on previous link rotations. A load torque is varied depending upon horizontal or vertical rotation, for the siplicity, a single link ar is considered to describe this enoenon.
25 2.2.1 Horizontal Motion Consider a single link ar rotating in and around 360 horizontally as shown in Figure 2.2 for waist otion. A directly coupled otor or with gear arrangeent rotates the ar link horizontally with carrying soe of pay load in their gripper. Ignoring the windage and friction losses, the load torque required to drive the otor with respect to ar position shows linear. Joint horizontal axis rotation Ar Link Gripper Motor +TL Clockwise rotation o o o -360-270 -180 o -90 0 o o o o o 90 180 270 360 Counter clockwise rotation -TL Figure 2.2 Single link horizontal rotating ar and torque The load is acting in the centre of the ar at a constant agnitude depending upon the object carrying fro the gripper. The agnitude of load torque does not vary with respect to angular position displaceent in degree. For clockwise rotation, otor torque and load torque are in positive sign and
26 equal opposite agnitude up to full 360 rotation. For the sae load, during counter clockwise direction of horizontal otion, both otor torque and load torque are in negative sign and equal opposite agnitude up to full 360. Hence the otor drives are required to operate only in forward otoring and reverse otoring quadrants. Braking quadrant is not applicable in this horizontal otion and load torque reains constant and hence drive is siple to operate like other load (water pup, air copressor, cooling fan, etc...) driving syste. 2.2.2 Vertical Motion Consider a vertical rotating single link ar in and around 360 echanical as shown in Figure 2.3 for shoulder and elbow rotation. The load torque aplitude is varied depending upon ar position and orientation due to gravitational force acting on the ar in centric load. Vertically rotating single link ar is directly coupled with payload or with gear arrangeent. For vertical rotation, the speed reducing and self locking gear arrangeents like war and war wheel or ball screw arrangeent is required to keep the ar at desired position after the otor speed goes to zero. Pay load Joint vertical rotating ar theta Load torque Motor Figure 2.3 Single link vertical rotating ar
27 Ignoring the gear arrangeent, windage and friction losses a vertically rotating ar load torque with respect to ar position is shown in Figure 2.4. When the ar rotates 0 to 180 in clockwise direction, the otor rotates in forward direction. While the payload is oving upward direction, the load torque varies depending upon ar position. Payload torque tries to down the ar in counter clockwise downward direction due to gravitational force and the load torque (T L ) is considered in this region is positive. o 180 FM RM o 90 o 270 RB FB ARM o o 0 or 360 Anticlockwise Rotation +T Clockwise Rotation Reverse Motoring Forward Braking -360 o -270o -180o -90o 0o 90o 180 o 270o 360o Reverse Forward Braking Motoring -T Figure 2.4 Vertical rotating ar load torque with effect of gravity The electroagnetic torque (T e ), generated by the otor gives equal and opposite load torque (T L ) to lift the ar in upward direction to reach the destination. Motor speed ( ) and load torque are in sae positive sign to drive the otor in forward otoring ode. Load torque increases proportionally with increasing position upto 90 and it is required axiu
28 torque when the ar reaches 90. Hence the speed of otor reduces while increasing load torque and hence requires ore tie for the ar to reach desired position of 180. Load torque is reduced when ar oves fro 90 to 180 and reaches zero torque when ar reaches 180 and hence load torque curve through this period shows like a half sine wave. This enoenon is due to the gravitational force and the load torque agnitude is continuously varying through 0 to 180. Whatever the load torque is varied, the drive is required to operate at constant speed to ensure the ar to reach desired destination within the prescribed tie. When the ar rotates through 180 to 360 in clockwise direction, the otor rotates in forward direction. During the downward otion of ar, pay load torque pulls down the ar in clockwise direction due to gravitational force. The load torque T L is considered in this region as negative. Still the otor speed ( ) is in positive region due to ar rotates clockwise direction to drive the otor in forward braking ode. During this region the load torque curve shows siilar like a half sine wave as like forward otoring ode but in negative direction. Due to gravitational force, the ar pulls down faster than in the speed of upward otion and there is a possible to drop the pay load and or dash to floor causes daage to ar and or payload. Also in soe circustances it ay create accident to huan those who are working near. Hence the speed of the otor is aintained constant to reach ar destination position within prescribed tie by applying braking. Whatever load torque, speed and quadrant changes, the drive is required to aintain unifor reaching tie of ar. Siilar enoenon exists in reverse rotation of ar. When the ar rotates through 0 to -180 (360 to 180) in counter clockwise upward direction, the otor rotates in negative direction to lift the pay load and gives
29 negative torque. Load torque due to gravity force tries to pulls down the ar in clockwise downward direction (torque is considered in this region is negative) and the speed will be in counter clockwise direction, akes the drive to operate in reverse otoring ode. The load torque also varies depending upon ar position and the curve looks like as sae in forward otoring ode but in negative direction. Variation of load torque delays the reaching tie of ar into desired destination. Hence the drive is required to aintain the unifor reaching tie as like other odes without ore delay in order to increase the productivity of the industry. When the ar rotates through -180 to -360 (180 to 0) in counter clockwise downward direction, siilar enoenon of forward braking will exist. But the load torque lays in positive direction and speed of the otor is in negative direction, hence drive operates in reveres braking quadrant ode. Also during this ode drive is required to aintain unifor reaching tie as like all other quadrants. The curve connecting various positions of the ar and load torque resebles as sine wavefor in both directions as shown in Figure 2.4. Hence the load torque applied to the otor shaft (T ) is defined as trigonoetric sin function of actual position in echanical degree ultiplied with a pay load torque T L as shown in Equation (2.1). T sin (2.1) T L where T T L - Mechanical shaft torque given to otor in N - Pay load torque added with ar in N - Ar position in degree
30 The load torque (T L ) depends upon the ar length, ass and gravity constant as shown in Equation (2.2). TL lg (2.2) where l - Mass of pay load in gra - Length of ar in eter g - Gravity constant 9.81 /s 2 A constant length ar is connected with a constant weight (w=*g) pay load for vertical rotating single link is considered for analysis of this research. 2.2.3 Four Quadrant Analysis Four odes of operating quadrants when the ar rotates in and around 360 in both the directions are shown in Figure 2.5. When the ar oves upward direction in both clockwise and counter clockwise directions, the speed and load torque sign are sae but oppose each other. When the ar oves upward in clockwise direction, speed and torque are in positive sign hence the otor operates in first quadrant of forward otoring ode. When it oves in upward counter clockwise direction, speed and torque are in negative sign hence the otor operates in third quadrant of reverse otoring ode.
31 +W 180 TL W TL 180 W 270 90 360 0 Forward Braking II I Forward Motoring -TL Reverse Motoring III IV Reverse Braking +TL TL TL W -180 W -180-90 -270 0-360 -W Figure 2.5 Four quadrant odes When the ar rotates downward direction in both clockwise and counter clockwise directions, the speed and load torque sign are opposite to each other but the forces are added together and hence the otor is ade to work on braking ode. Subsequently, when the ar oves downward in clockwise direction, the speed is in positive sign but torque is in negative sign and hence the otor works in second quadrant of reverse braking ode. Likewise when the ar oves downward in counter clockwise direction, the speed is in negative sign but the torque is in positive sign and hence the otor works in fourth quadrant of reverse braking ode. The ain objective of this research is to aintain the unifor speed of otor irrespective of quadrants and pay load torque variation of vertical rotating single link ar with respect to angular position displaceent to reach the desired destination within unifor settling tie. Hence the design of feedback controller plays a vital role in this operation.
32 2.2.4 Selection of Motor After the echanical structure of a robotic anipulator is deterined, a suitable schee for producing otion ust be developed. This will include the specification of echanical couplers and drivers as well actuators and control syste. If the electric otor is chosen for actuating robot ar, then the selection of otor is an iportant role to obtain perfect otion of the robot. The selection of otor for robot ar includes several paraeters and they are listed in below. Torque and power requireent of robot ar Operating voltage availability Size and weight restriction Working environental teperature Speed of otor Continuous or discrete, linear or rotational otion requireent Precision and accuracy Encoder requireent for position and speed easureent Static and dynaic characteristics (starting and braking) Cost Based on the above criterions for the selection of otor for the application in robot ar, a Brush Less Direct Current (BLDC) otor is wide suitable due to their construction, working characteristics and advantages explained in next.
33 2.3 OVERVIEW OF BLDC MOTOR In electrically actuated robots, brush failures in the DC servootors used on the joints account for a ajor source of downtie. The wearing of these devices cause the effective terinal resistance of the arature to increase significantly, thereby reduce the efficiency of the servo. Hence the increased heating and torque reduction are two of the ajor consequences. In addition, as the otor turns, arcing between the brushes and coutator segents occurs due to the sudden interruption of current in the particular coil being coutated. Besides contributing to echanical deterioration of the brushes theselves, which can liit their use in clean roo applications, this situation also prevent robots so actuated fro being used in explosive environents. Finally, the Electro Magnetic Interference (EMI) produced by the electrical spark can also create reliability probles for other electronic devices working in the vicinity of the robot. In recent years, DC otor has been developed which avoid any of the difficulties attributable to the brushes of a standard servootor. When the function of coutator and brushes are ipleented by solid state switches, aintenance free otors can be realized. These otors are known as Brush Less Direct Current (BLDC) otors. The function of agnets is the sae as in both brushless otor and in the brushed coutator otor. The ost obvious advantage of brushless configuration is the reoval of brushes. Brush aintenance is no longer required and hence any probles associated with the brushes are reoved. An advantage of the brushless configuration in which the rotor is inside the stator is that ore cross sectional area is available for the power or arature windings. At the sae tie conduction of heat through the frae is iproved generally also an increase in the electrical loading is possible, providing greater specific torque. The efficiency is likely to be higher that of a coutator otor of equal size and the absence of brush friction help further in this regard.
34 2.3.1 Construction The stator of the BLDC otor is ade up of silicon steel stapings with slots in its interior surface. These slots accoodate the stator windings, usually concentrated approach, which produces a square wavefor distribution of flux density around the air gap. Usually three ase star connected stator windings are displaced by 120 electrical and each ase windings spans 60 electrical on each side. These windings are to be wound for a specified nuber of poles. These windings are suitably connected to a Direct Current (DC) supply through a power electronic switches circuitry. A typical BLDC otor with 12 stator slots and 4 nubers of poles on the rotor is shown in Figure 2.6. Peranent Magnet Concentrated windings N S S N Stator iron core Rotor Figure 2.6 BLDC otor construction Rotor is ade up of forged steel. Rotor accoodates 180 electrically pole arc peranent agnet. Nuber of poles of the rotor should be an even nuber. The rotor shaft carries a rotor position sensor usually in Hall Effect sensors. This position sensor provides inforation about the
35 position of the rotor at any instant to the controller which sends suitable signals to the electronic coutator. 2.3.2 Electronic Coutation In view of the fact that the absence of echanical coutator, three ase windings are required to excite DC supply through power seiconductor switches with respect to rotor position inforation. This schee of control is known as self controlled ode. An inverter fed trapezoidal Peranent Magnet Alternating Current (PMAC) otor drive operating in self controlled ode of operation is known as brushless DC drive. Vs D1 D3 C Q1 D1 Q3 D3 Q5 D5 a b c D2 D4 Q2 D2 Q4 D4 Q6 D6 BLDC Motor Q1 Q2 Q3 Q4 Q5 Q6 Hall sensor signals Coutation Logic Figure 2.7 BLDC otor control syste Figure 2.7 shows such arrangeent of BLDC otor control syste. If the available is AC supply, then the required DC supply can be ade through rectifier. The six self coutated switches IGBT of three ase inverter are used to supply the DC to three ase windings. The gate pulses of these switches are generated fro coutation logic controller unit with respect to rotor position inforation easured fro Hall Effect sensor ounted on rotor shaft so as the drive is operating in self controlled ode.
36 240 o o 300 S N o 180 N S o 120 o 60 Hall effect bipolar sensor + Vin - Hall sensor Vo Flux flow -B Output voltage +Vo Flux density +B -Vo 0o Figure 2.8 Hall sensor Three ase Hall Effect sensors are placed 120 electrically ase displaced with each other to sense rotor position inforation and thus enabling the appropriate three ase stator coil to be excited. Figure 2.8 shows the placeent of hall sensors and their working with its characteristics. For a four nuber of pole rotor, three hall sensors are placed 60 echanically displaced each other as per Equation (2.3). p (2.3) e 2 where e - Electrical degree p - Nuber of poles - Mechanical degree When the hall sensor is placed near peranent agnet rotor and a separate DC source is supplied, then the flow of flux direction deterines the flow of current. A signal conditioning circuit integrated within the hall sensor provides a TTL copatible pulse with sharp edges. The output of a hall
37 sensor is HIGH (logical 1) when the south pole is in close proxiately to it. The output is LOW (logical 0) if the agnets of north pole is passing by. Table 2.1 Coutation table for clockwise rotation Rotor position (electrical in degree) Hall sensor status Switch status Phase current agnitude H a H b H c Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 I a I b I c 0-60 1 0 1 1 0 0 1 0 0 + - 0 60-120 1 0 0 1 0 0 0 0 1 + 0-120-180 1 1 0 0 0 1 0 0 1 0 + - 180-240 0 1 0 0 1 1 0 0 0 - + 0 240-300 0 1 1 0 1 0 0 1 0-0 + 300-360 0 0 1 0 0 0 1 1 0 0 - + Based on the hall sensors inforation, the triggering pulses of the six switches are generated in specific coutation. Table 2.1 shows the coutation table for clockwise rotation with respect to ascending increent of rotor position in 60 electrical. Table shows 1 for ON (logic HIGH) and 0 for OFF (logic LOW). Six possible sectors are required to coplete one full electrical revolution (half echanical revolution). Upto 180 electrical, the hall signal generates HIGH (logic 1) and for the reaining 180 electrical it will be LOW (logic 0) or vice versa. Three hall sensors are placed 120 electrical with each other and hence the generated hall signals H a, H b and H c are ase displaced 120 electrically with each other.
38 Ha Hb Hc Q1 Q2 Q3 Q4 Q5 Q6 Ia Ib Ic Ea Eb Ec 0 o 60 o 120 o 180 o 240 o 300 o 360 o 420 o 480 o 540 o Rotor position (electrical degree) Figure 2.9 BLDC otor wavefors in clockwise rotation Q1 Ha Hb Q3 Hb Hc Q Hc Ha 5 Q2 Ha Hb Q Hb Hc 4 Q6 Hc Ha (2.4) For clockwise rotation, three ase currents are ust excited in positive sequence. For 120 conduction ode, I a is in positive sign upto first two sectors (120 electrical) then rest condition for 60 electrical (one sector) and after 180 to 300 electrical I a should be in negative. During the corresponding inverter ase switch is triggered to obtain positive I a, the switch Q 1 is ON fro 0 to 120 electrical. The switch Q 2 is ON fro 180 to 300 electrical to obtain I a negative. Reaining sectors for both switches are in OFF (logic 0) condition. This logic is obtained fro the hall position inforation by using cobinational logic circuit as per coutation logic table. The Boolean logic for is shown in Equation (2.4), obtained fro Karnaugh ap.
39 Likewise for other ases I b and I c, the ase currents are 120 electrically ase displaced in positive sequence and hence the otor rotates in clockwise direction. For clockwise rotation with respect to rotor position in electrical degree corresponding to hall position, gate pulse, ase current and generated back electro otive force (ef) wavefors are shown in Figure 2.9. The wavefor is obtained fro the coutation Table 2.1, fro the observation of wavefors, the back ef shows the trapezoidal wave shape in nature. The reverse rotation of a otor is analysed by changing reverse order of rotor position in descending decreent of every 60 electrical interval. Table 2.2 shows the coutation table for counter clockwise direction. Likewise for clockwise rotation, six possible sectors are separated and corresponding hall position statuses are noted in descending order. The hall sensor status H a, H b and H c are sae as clockwise coutation table by looking botto to top. Q1 Ha Hb Q3 Hb Hc Q5 Hc Ha Q 2 Ha Hb Q4 Hb Hc Q6 Hc Ha (2.5) Table 2.2 Coutation table for counter clockwise rotation Rotor position (electrical in degree) Hall sensor status Switch status Phase current agnitude H a H b H c Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 I a I b I c 360-300 0 0 1 0 0 1 0 0 1 0 + - 300-240 0 1 1 1 0 0 0 0 1 + 0-240-180 0 1 0 1 0 0 1 0 0 + - 0 180-120 1 1 0 0 0 0 1 1 0 0 - + 120-60 1 0 0 0 1 0 0 1 0-0 + 60-0 1 0 1 0 1 1 0 0 0 - + 0
40 Ha Hb Hc Q1 Q2 Q3 Q4 Q5 Q6 Ia Ib Ic Ea Eb Ec 360 o 300 o 240 o 180 o 120 o 60 o 0 o -60 o -120 o -180 o Rotor position (electrical degree) Figure 2.10 BLDC otor wavefors in counter clockwise rotation For counter clockwise direction of rotation, ase current agnitudes are ultiplied with negative sign. Hence positive signs are changed into negative and negative signs becoe positive. Now by observing the ase current agnitude fro the Table 2.2, the ase currents are ase displaced by 120 electrical each other. Phase current I c lags 120 electrical after I a instead of I b. Hence the negative ase sequence changes the direction of otor in counter clockwise rotation. Corresponding gate pulse signals Q 1 to Q 6 are generated to obtain negative sequencing excited current with respect to hall signals. Boolean logic corresponding to counter clockwise direction is shown in Equation (2.5) and it is just logic inversion of Equation (2.4). For
41 counter clockwise rotation with respect to rotor position in electrical degree hall signals, gate triggering pulses, ase current and generated back ef are shown in Figure 2.10. Fro the observation of gra, ase current and back efs are in negative sequence. Hence the otor rotates in counter clockwise direction. 2.3.3 Speed Torque Characteristics Speed torque characteristics of a BLDC otor can be realized fro the ef and voltage equations of otor. The ef equation of BLDC otor is quite siple and reseble to the conventional DC otor. Induced ef in a single coil can be expressed in Equation (2.6). e 2B rlt (2.6) g where e - Ef generated per ase in Volt B g - Flux density of air gap in wb/ 2 r l - Radius of air gap in - Length of arature in T - Nuber of coil turns per ase - Angular velocity in echanical rad/sec Considering another coil connected with slot angle gives equal agnitude. Hence the resultant induced back ef per ase is shown in Equation (2.7). e 4B rlt (2.7) g
By considering the back ef constant K 4B rlt back ef becoes as shown in Equation (2.8). g 42, the generated e (2.8) K per Equation (2.9). Voltage equation of BLDC is siilar to conventional DC otor as V 2e 2IR 2V (2.9) dd where V - Supply voltage in Volt I - Arature current in Ap R - Arature resistance per ase in Oh V dd - Voltage drop of the device in Volt Usually voltage drop is neglected, then arature current can be expressed by Equation (2.10). V 2e 2IR 2IR V 2 e I V 2e (2.10) 2R Substitute Equation (2.8) in to Equation (2.10), I V K 2R (2.11)
43 Fro the Equation (2.11), the speed of otor can be expressed as shown in Equation (2.12). I 2 R V K K V 2IR V 2IR (2.12) K Fro the Equation (2.12), the speed of otor can be derived. Torque can be derived fro the power equations. Power input to the otor is given by VI as per Equation (2.13). P VI 2e 2IR V I (2.13) in 2 dd VI 2Ie 2I R 2 2 V dd I where VI - Electrical power input in Watts 2Ie - Power converted as echanical (P ) in Watts 2I 2 R - Resistive loss of arature winding in Watts 2V dd I - Power loss of device in Watts Hence the echanical power developed in the otor becoes as shown in Equation (2.14).
44 P 2Ie P 2I 2B rlt g P 4B rlt I (2.14) g Torque developed in the otor is given by in the Equation (2.15). T P (2.15) where T - Torque developed fro the otor in N P - Power developed fro the otor in Watts - Speed of otor in rad/sec Substituting Equation (2.14) into Equation (2.15), the finally developed torque is derived and is shown in Equation (2.16). T 4B g rlt I T 4B g rlt I By considering the torque constant K 4B rlt torque of the otor becoes, g, the developed T K I (2.16)
45 Fro this observation, the back ef constant and torque constant of BLDC otor are sae as K. Hence the working of BLDC is siilar like a conventional DC otor. The speed torque characteristic of a BLDC as shown in Figure 2.11 and it is drawn fro the derived equations. Peak torque Tp Torque Rated torque Tr Interittent torque zone Continuous torque zone Speed Rated speed Maxiu speed Figure 2.11 Speed torque characteristics There are two paraeters used to define a BLDC otor, peak torque (T p ) and rated torque (T r ). During continuous operation, the otor can be loaded up to the rated torque. Torque reains constant for a speed range up to the rated speed. The otor can be ade to run upto the axiu speed, which can be of 150% the rated speed, but the torque starts dropping. Applications, which are having frequent start, stop and reversals of rotation with load on the otor for robot ar deand ore torque than the rated torque. This requireent coes for a brief period, especially when the otor starts fro a standstill and during acceleration. During this period, extra torque is required to overcoe the inertia of the load and the rotor itself. The otor can deliver a high torque, axiu up to peak torque, as long as it follows the speed torque curve.
46 2.3.4 Advantages Since a special kind of BLDC otor with brush less arrangeent is required with additional electronics coutation unit and hence the cost is increased. The power rating also restricted due to peranent agnet rotor and otor field cannot be control and require special arrangeent of rotor position sensors. But nowadays in uch industrial autoation for autootive, textile, residential, coputers and robotic ars, the BLDC otors with advanced drivers are used due to their advantages listed below. There is no field winding so that field copper loss is neglected. There is no echanical coutator, hence spark free operation. Size becoes very sall. Less weight, hence less oent of inertia. Better ventilation because of arature accoodated in stator. Regenerative braking is possible. Speed can be easily controllable. Better power factor. Motor can be designed for high voltage. It is possible to have very high speed. Motor can be operated in hazardous atoseric condition. It is a self starting otor. Efficiency is better.
47 2.4 POSITION SERVO DRIVE Once the otor running perforance is verified, the otor is designed to perfor particular task to follow coand input through servo drive. The word servo defines following (service) the coand input. The electric drive control unit should control the otor to perfor a specified task. The task ay be adjustable current control or speed control or position control. The drive ay be operated in siple open loop control without considering actual control paraeter. In order to obtain precision and accuracy, the particular control paraeter actual inforation is observed through specific sensor to perfor closed loop control. Below explained the design of BLDC servo drive for robot ar position control through open loop and closed loop in step by step. 2.4.1 Open Loop Control Position control can be achieved without position sensor by predictable oveent over tie in siple open loop control schee. Figure 2.12 shows a open loop of BLDC drive. A three ase inverter fed BLDC otor is self controlled through hall position inforation. The hall signals are decoded through decoder to obtain six driving gate pulses. The decoding should be designed as per theoretical or in cause vendor specified as per different anufacture of the otor. The direction changing logic is perfored inside of decoder by ultiplying negative sign of direction changing logic signal. The speed of the otor can be controlled through the changing of voltage by Pulse Width Modulation (PWM) of inverter gate pulses. For a trapezoidal BLDC drive in 120 conduction ode of operation, the two switches are in closed positions at any instant over tie, one fro upper ar
48 of the inverter and another fro the lower ar of the inverter. Hence controlling the gate pulse width of any upper ar or lower ar switches is sufficient to control the voltage of otor in order to reduce switching voltage stress. Figure 2.12 shows the upper ar switches Q 1, Q 3 and Q 5 are chopped through PWM control unit and lower ar switches Q 2, Q 4 and Q 6 are just ON and OFF as per gate pulse signals coing fro hall decoder. Rectifier Inverter Vs D1 D2 D3 D4 Q1 D1 Q3 D3 Q5 D5 C a b c Q2 D2 Q4 D4 Q6 D6 BLDC Motor Hall signals Q1 Q2 Q3 Q4 Q5 Q6 Hall decoder PWM Reference signal + - 0 0 + - 0 + High Frequency Saw tooth Carrier oscillator 0 0 - + Direction changing Logic 0 - Figure 2.12 BLDC open loop control Variable duty pulse width is achieved by odulation unit. A high frequency saw tooth carrier wave is generated fro separate oscillator and copared with reference signal fro coand potentioeter to perfor odulation through coparator. Coparator produces square wave pulse with variable ON duration (pulse width) with respect to reference signal. Frequency of square wave is sae as carrier frequency but the duty cycle alone is varied to get variable output voltage as per Equation (2.17).
49 T Vo T on V s T T on T off 1 f T on T V V (2.17) o s where V o - Output voltage in Volt T on - ON duration in Seconds T off - OFF duration in Seconds T f V s - Total duration in Seconds - Frequency in Hertz - Duty cycle - Input supply voltage in Volt The generated upper ar gate PWM pulses are coputed with logic AND. Hence the controlling of duty cycle will change the output voltage of inverter for control the speed of BLDC otor. For position control, the otor should be allowed to rotate over the prescribed tie and then the otor is ade to run in the zero speed to settle nearest position. This requires a separate huan operator to verify the actual position and to change the coand speed to obtain the desired position. Hence in order to reduce these coplexities, the actual position is easured through encoder and is perfored in closed loop autoatic control in further.
50 2.4.2 Position Measureent Position easureent is often required to obtain closed loop position servo drive, in which a special position sensor is placed in robot joints and it ay be potentioeter, resolver or optical encoder. Apart fro the other techniques, optical increental encoder is used because of their ability to sense up to the end of travel without any proble associated with echanical switches. Figure 2.13 shows the scheatic of optical encoder disk arrangeent. A revolving slotted disk attached with shaft will interrupt the light falling to oto sensors fro Light Eitting Diode (LED). Two oto sensors (oto transistor) are placed in 90 electrically to produce enhanced Quadrature Encoder Pulse (QEP). Figure 2.13 Optical encoder disk Integrated chip attached with encoder produces logic 1 if light falling into sensor else 0 light is interrupted. The generated square pulses of QEP signals Q a and Q b are 90 electrically ase displaced with each other. If the disk rotates in clockwise direction, Q b lags Q a after 90 electrical. If the disk rotates in counter clockwise direction, Q b leads Q a before 90 electrical. A special arrangeent, called quadrature pulse decoder, can perfor
51 easureent of position, direction and speed of rotating disk fro this QEP signals. A single track of slot patterns in the periery of an increental encoder creates rising and falling square pulse pairs equal to the nuber of slots per revolution. Every slot creates one rising and one falling edge of square pulse and hence counting the nuber of pulse per revolution (ppr) over one full rotation of disk shows the actual position equivalent pulse counts. The precession can be increased by increasing nuber of slots in the disk and quadruple addition of two encoding pulses Q a and Q b. Figure 2.14 shows the quadrature encoder pulse decoding operation. As stated above, whenever disk rotates clockwise direction, Q b lags Q a after 90 electrical and hence QEP decoder starts up counting of both rising and falling edges. Whenever disk rotates counter clockwise direction, Q b leads Q a before 90 electrical and hence QEP decoder starts down counting of both rising and falling edges. QA QB 5 6 4 4 3 3 2 Pulse 2 Counts 1 1 0 0 Clockwise rotation 5 Anti-Clockwise rotation Figure 2.14 Quadrature encoder pulse (QEP)
52 Fro these the nuber of edges per revolution (pulse counts (PC)) can be found as per Equation 2.18 and thus the resolution of the drive can be increased. Actual position of rotating ar is found fro the pulse counts as per Equation (2.19). PC Q a sin Q Q Q (2.18) ri g a falling brising b falling 360 PC (2.19) ppr 4 where - Actual echanical position in degree ppr - Pulse per revolution of encoder PC - Nuber of pulse counts + - Indicates up counting - - Indicates down counting The sae encoder signals are also used to easure the speed of revolving ar. The tie duration of the generated QEP signals Q a and Q b square wave depends upon the speed of disk rotation. Hence the frequency of QEP can be easured as per Equation (2.20) and the speed of rotation can be calculated as per Equation (2.21). nt PCn PC 1 T f QEP (2.20) T N 60 f QEP (2.21) ppr
53 where f QEP - Frequency of QEP signal in Hertz PC(nT) - Present saple pulse count value PC((n-1)T) - Previous saple pulse count value T - Sapling tie in Seconds N - Speed in RPM A special arrangeent fro quadrature pulse decoder is used to identify the ase angle difference between Q a and Q b signals and the direction of rotation is identified as per Equation (2.22). If is lagging 0 electrical then direction logic signal = +1 If is leading 0 electrical then direction logic signal = -1 (2.22) where - Phase angle difference between Q a and Q b + - Indicates clockwise rotation - - Indicates counter clockwise rotation 2.4.3 Closed Loop Control Actual position of otor shaft is easured through increental encoder to perfor closed loop position servo drive. Coplete functional block diagra of a conventional closed loop position servo drive is shown in Figure 2.15. This block diagra includes three closed loop cascaded control, the first in outer loop which consists of position servo control, the second in iddle loop which includes speed control and the third in the inner loop which consists of current control.
54 AC Supply Rectifier Inverter BLDC Motor QEP Set Liiter Liiter Liiter Position PID Hall Decoder + N* PID Iabc* PID _ Position + _ Speed + _ Current & Controller Controller Controller delta Gate Driver Act N Position Iabc Speed Calculator Quadrature pulse Decoder Qa,Qb Habc Figure 2.15 Conventional closed loop position servo drive The actual position is easured fro encoder signals Q a and Q b through quadrature pulse decoder. Set and actual position inforation are copared to obtain position error and then fed into conventional PID (Proportional + Integral + Derivative) controller to obtain position servo control. The output of the position controller generates the reference speed within the liited axiu speed of otor through liiter. The actual speed is easured through sae quadrature signal Q a and or Q b. The actual speed and set speed are copared to obtain the speed error to feed the conventional PID controller to control the speed servo. The output of speed controller generates reference ase current agnitude within the liited axiu current of otor through liiter to protect the otor. The actual three ase current of the otor is easured through separate Current Transforers (CT) and they are copared with reference ase current agnitude to generate current error. Obtained current error is fed into conventional PID controller which is used to current control loop. The output of current controller generates the duty cycle for pulse width odulation. BLDC otor is self controlled through hall signals inforation through hall decoder which generates six gate pulses for MOSFET or IGBT based three ase inverter. Required driving DC power is obtained by conversion of available AC through rectifier. The conventional position servo drive syste includes three closed loop cascaded control and hence the
55 coplexity in controller design is increased. Moreover actual current of BLDC otor is easured through three CTs and hence increases the cost of servo drive. The proposed closed loop robot ar position servo drive as shown in Figure 2.16 reduces the coplexities of conventional control drive syste. Proposed drive includes only two control loops, outer loop of position control and inner loop of current control. Hence the design of control syste is siple and the proposed drive introduces fuzzy based PID controller to iprove the perforance. Also the proposed drive uses DC link current instead of three ase currents to reduce the ipleentation cost. AC Supply Rectifier Inverter BLDC Motor QEP Set Position + _ Act Position Conv PID or Fuzzy PID Position Controller Quadrature pulse Decoder Liiter Qa,Qb Idc* Idc _ + Conv PID or Fuzzy PID Current Controller Hall Decoder & Gate Driver Habc Robotic Ar Figure 2.16 Proposed closed loop ar position servo drive A vertically rotating single link ar is siply coupled directly with otor shaft without any speed reducer and self locking gear like war and war wheel arrangeent in order to reduce the cost of laboratory setup ipleentation. Such arrangeents are andatorily required for real tie industrial developents. Actual position of robot ar is easured fro encoder signals Q a and Q b through quadrature pulse decoder. Set and actual position inforation (0 to 360) are copared to obtain position error and fed into position controller of conventional PID or fuzzy based PID. The output of position controller generates reference DC link current I dc * agnitude within the safe liit of -6A to +6A peak through liiter. The sign
56 of reference DC link current I dc * indicates the direction of otor to run. Positive sign indicates the clockwise direction and negative sign indicates the counter clockwise direction. Actual DC link current I dc easured fro hall current sensor does not go on negative sign and hence absolute value of reference DC link current I dc * is copared with actual I dc to obtain current error. The current error is fed into inner loop conventional PID or fuzzy based PID current controller. The output of current controller generates the duty cycle of odulating signal in the liited range of 0 to 1 for pulse width odulation. Motor is self controlled through hall position inforation fro which the hall decoder then generates six gate pulses to feed three ase MOSFET or IGBT based inverter through gate driver. The required 310V DC supply is obtained fro available AC source through uncontrolled diode rectifier. User can change the conventional PID of fuzzy based PID controllers for verification of dynaic behaviours of vertical rotating single link ar. 2.5 SUMMARY In this chapter, the horizontal and vertical otions of robotic ar with their related issues in four quadrants are analyzed. The detailed construction and electronics coutation process are tabulated in Table 2.1 and Table 2.2 for clockwise and counter clockwise respectively of BLDC otor are discussed over their advantages. Position easureent schee through quadrature encoder is explained in detail. The open loop control of BLDC otor and closed loop conventional position-speed-current control with conventional PID control systes are explained. A siplified positioncurrent loop servo drive with fuzzy based PID controller is proposed for vertically rotating single link ar and the functional block diagra is explained. The forthcoing chapter provides the detailed discussion of conventional and fuzzy based PID controller design, siulation and hardware ipleentation with their results of vertical rotating single link robotic ar.