THE PERFORMANCE OF THE DC MOTOR BY THE PID CONTROLLING PWM DC-DC BOOST CONVERTER
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1 ISSN (Prnt), ISSN (Onlne) ID: TG Orgnal scentc paper THE PERFORMANCE OF THE DC MOTOR BY THE PID CONTROING PWM DC-DC BOOST CONVERTER Erol CAN, Hasan Hüseyn SAYAN Abstract: Ths paper presents the PID controllng rect current (DC) to the rect current boost converter eds DC motor whch has a 3.68 kw and 4 V o DC voltage nput on ts characterstcs. What s rst ormed s the boost converter mathematcal model at the desgn stage. Secondly, a mathematcal model o the DC motor s created so that the boost converter wth the machne can be establshed and modeled at the Matlab Smulnk. The PID controller s consdered or arrangng a pulse wh modulaton or a boost converter swtch because the needed voltage s provded or a DC motor. Ater that, the PID controllng rect current (DC) to a rect current boost converter runnng the DC motor s mplemented at the Matlab Smulnk. In adton to that, the only constant source runnng the DC motor s smulated at the Matlab Smulnk. The DC motor operated by the PID controllng converter that has a low nput voltage s compared to the DC motor operated by the hgh constant DC voltage. A low voltage nput converter controllng the DC motor has a hgh perormance accorng to the hgh constant DC source runnng the DC motor. Keywords: DC-DC converter; DC motor; PID control; step-snus pulse wh modulaton INTRODUCTION Many researchers deal wth the speed control o the DC machne snce DC motors are controlled over a wde range wth stable and lnear characterstcs. DC motors are preerred at the ndustral workng areas because o the stable speed and stable load perormance [ 3]. In adton to that, sometmes dc energy on systems may be nadequate although rect voltage sources are needed or the operaton o DC motors. The DC-DC converters are consdered good selecton or supplyng the load when the rect current sources are not sucent. So, the DC-DC converters are very mportant at the DC energy regulaton, generaton systems and power applcatons. Some control technques have to be used or the ncrease perormance o the power crcut usng DC sources [4 8].The PID control technques have been appled or the controllng o some power systems [9 ]. In the study, the PID control usng the step snus pulse wh modulaton (SSPWM) DC-DC boost converter s unlke the smlar stues [ 3]. The DC-DC boost converter o the mathematcal model or the system rst part s desgned so that the DC-DC boost converter can ncrease a low-level DC voltage (5 V) to a hgh-level value (5 V). Ater that, a mathematcal model o the DC motor or the system second part s created to perorm at the Matlab Smulnk. For the regulaton o the low DC voltage, the PID control s appled rom the output speed o the DC motor to the swtch o DC-DC converter ater the converter s connected to the DC motor as n Fg.. The DC motor wth the DC-DC boost converter, the DC motor wth the constant DC source are modeled at the Matlab Smulnk or the observaton and the comparson o output perormances, whch are toques, rotor speeds, and currents. The DC-DC boost converter drves DC motor wth 5 V on a closedloop wth the PID control, whle the constant DC source runs the DC motor by 4 V on an open-loop whch s uncontrolled. The runnng DC motor wth a DC-DC converter on a closed-loop control has the demanded results such as hgh settlement current and torques, even though the runnng DC motor wth the constant DC source has hgh voltage on an open-loop control. Fgure PID controllng the DC-DC boost converter runnng the DC motor BOOST CONVERTER Fg. shows the power converter whch operates to rase a rect voltage. Frstly, the power crcut o the mathematcal model s obtaned by the relaton between the nput and output voltage equatons when the MOSFET swtch that s an actve component s operatng the passve components such as nductor, resstance and capactor. In the equatons, V g s the value o nput voltage, V s the value o nductance voltage, and s the value o nductance current, R s the resstve load, C s the capactor or converter output voltage, and D s the duty tme or the swtches. 8 TECHNICA JOURNA, 4(7), 8-87
2 A = DAon ( D) A o () B = DBon ( D) B o (3) Eqs. (4) and (5) show the matrxes on the nal orm: Fgure Boost converter crcut model For the equaton o state space, the orm o equatons and the relatons between the current o nductance and the voltage o output have to be ormed to a x = A x Bu orm. For S = ON V g = V () = Vg () Vg = (3) I V = z C (4) The varables obtaned n the above shown equatons are shown n the matrx orm as ollows. D I Vg V = V D I (5) z DA on C DB on For S = OFF A = ( D ) C RC (4) D B = C (5) 3 DESIGN OF THE PUSE WIDTH MODUATION The pulse wh modulaton technque s wdely consdered or the motors drve and erent loads drve at the some stues [5 ]. The paper deals wth the modulaton technque. The technque s that the step-snus pulse wh modulaton (SSPWM) showed n Fg. 3 controls the swtch o the DC-DC converter. SSPWM s ormed when two erent trangles compare to the step snus sgnals. The swtchng tmes can be are determned wth trangular smlarty, because the steps o snus sgnal ncrease the b unt lengths on the vertcal and erent the k unt lengths on the horzontal, as shown n Fg. 3. The creatng voltage on loads s calculated as analytc because the nteractons o steps wth the trangles orm smlar trangles. Every ormed trangle has a erent sze n all ormed trangles. Pulse whs are produced because the smlar trangle rules are shaped n the hal perod (T/). Pulse whs are shown n Fg. 4 as smlar trangles. D s the rst pulse wh, D a s the average pulse wh, and n s the pulse number. V = V (6) g V c = Vg Vc (7) Vg V c = (8) Vg V = c (9) V V = I I R z C () I V V = I C RC z C () A and B matrx are calculated to orm the state space whch has the requred varables or the boost converter. A as the gven Eq. (), and B as gven Eq. (3). Fgure 3 (a) Steps compared wth the trangles, (b) ormed trangles TEHNIČKI GASNIK, 4(7),
3 Fgure 7 A lnear ncreases o the angular PWM sgnals s created n comparson o the results The wh changes or the SSPWMs are (a, a, 3a, 4a, 5a) n the perod o T/ as shown n Fg. 8. Fgure 4 Formed trangles The PWM swtchng voltages producng current sgnals are shown or nductve loads () n the PWMs n Fg. 5. Fgure 8 A lnear ncreases o the angular PWM sgnals (a) (b) Fgure 5 (a) PWM producng current n between T/ and T, (b) PWM producng current n between and T/ The sze changes o the SSPWMs are a, a, 3a, 4a, 5a n the perod o T/ as shown n Fg. 6. Fgure 6 A lnear ncreases o the PWM sgnals s created n the comparson o the results Whle controllng swtch, the step snus pulse wh modulaton provdes the total current or the nductve load () n Fg. 6 as n the Eq. (6). = n k = k = k n n n n = (6) I two trangles are used to produce SSPWM or every step n the horzontal sze o the steps whch are ncreased or b, two same SSPWMs are created on every step as n Fg. 7. The angular step snus pulse wh modulaton produces the total current o the equaton n Fg. 6 as n the Eq. (7) or nductve loads. = n k = 4 k = k n n n n = (7) The swtchng tmes create a total alternatng voltage accorng to the step snus pulse wh modulaton on a perod o T/. The swtch tmes ncrease rom D to D a. The ncreases are lnear because o the smlar trangle rules because comparson o steps and trangles are arranged or creatng trangular smlarty as n Fg. 4. There are n pulses n a perod o T/. Thereore, the pulses are added as Eq. (8). D D a n 4 DC MOTOR DESIGN (8) The DC motor s mathematcal model mplements a separately created DC machne. The model has certan parameters. The resstance o armature s R a n ohms and the nductance o armature s a n henres. The resstance o eld s R n ohms and the nductance o eld s n henres. The eld armature s mutual nductance s a n henres. The total nerta o the DC machne s J n kg m². The total rcton coecent o the DC machne s B m n N m s. The total Coulomb rcton torque constant o the DC 84 TECHNICA JOURNA, 4(7), 8-87
4 machne s T n N m. KE s the voltage constant and w s the machne speed n rad/s. The armature current s a n ampere. The eld current s n ampere, the electrcal torque s T e n Nm. The eld termnal exsts between (F, F ) wth the nductance a and resstance R a n the seres. The armature crcut s constructed between the A and A whch contan the nductance a and the resstance R a n the seres wth a counter-electromotve orce E calculated as the Eq. (9). E = K w (9) E E s proportonal to the eld current İ n a separately created DC machne model and K E s calculated as the Eq. () E = a I () The mechancal part s descrbed as the Eq. (). dw J = Te B w m () The state space equaton s ormed or the machne speed w as the Eq. (3). J B m dw w = Te m () Te w = (3) Js B The DC machne model o the Matlab Smulnk s shown n Fg. 9 accorng to the created mathematcal equatons. controller s n the Eq. (5). K p s the proportonal gan. K s the ntegral gan. K d s the dervatonal gan. de u( t) = K pe( t) K e( t) Kd (4) K p K K s p Kd s = s K s K s p (5) I the proportonal gan, ntegral gan and dervatonal gan are appled to the DC motor equaton, the Eq. (6) and Eq. (7) are ormed as ollows: K T e w = K p Kd s (6) s Js Bm K p ( Js Bms) K ( Js Bm ) Kd s ( Te ) w = (7) Js Bms 5 EXPERIMENTA RESUTS The applcatons o the PID controllng DC motor on the closed-loop control and the constant DC source eeng the DC motor on an open-loop control are perormed n the Matlab Smulnk. The armature o the DC motor wth the constant DC source s worked wth 5 V whle the armature o the DC motor wth DC-DC converter s perormed wth 5 V at the closed-loop control as shown n Fg PWM sgnal Converter output voltage Volt 4 5 Converter nput voltage Volt Fgure PID controllng the DC-DC converter o nput, output voltages and the PWM sgnal Fgure 9 DC machne model o the Matlab Smulnk The DC machne model o the Matlab Smulnk s gven n Fg. 9 accorng to the created mathematcal models. The PID control s consdered to obtan a better result whle runnng the system. The erental orm o the PID controller s n the Eq. (4). The aplace orm o the PID The speed o the DC motor whch has.9 N m o load can reach 5 rad/s ( rpm), whle 4 V o the constant rect voltage source runs the DC motor as uncontrolled, whch s an open-loop control as shown n Fg.. The speed o the DC motor whch has.9 N m o load reaches 45 rad/s (385 rpm) on a closed- loop control, whle 5 V o rect voltage eeng the converter runs the DC motor as TEHNIČKI GASNIK, 4(7),
5 shown n Fg.. The PID controllng o the DC-DC converter acheves a hgh perormance on the speed o the DC motor although the converter has low voltage accorng to the constant DC source. 5 Te(rad/s) PID controllng torque Uncontrolled torque Speed (rad/s) 5 PID cntrollng speed Uncontrolled speed.5.5 Fgure 3 PID controllng DC-DC boost converter and a constant DC source runnng the torques o the DC motors.5.5 Fgure PID controllng the DC-DC boost converter and the constant DC source runnng the speed o the DC motors Currents(A) PIDcontrollng current Uncontrolled current.5.5 Fgure PID controllng the DC-DC boost converter and the constant DC source runnng the currents o the DC motors Ater 4 V o the constant rect voltage runnng the DC motor as n an open loop control n Fg., a settlng current value o the DC motor can reach 6 A on.3 s whle a startng current o the DC motor obtans a peak current value such as 4 A on.5 s. 5 V o the rect voltage eeng the power converter wth, the DC motor runs on a closed-loop wth a PID control. A settlng current o the DC motor can reach 7 A on. s whle the DC motor reaches 4 A o the peak current value on.5 s as n Fg.. Although the converter has a lower nput voltage whch s 5 V as opposed to the constant DC source o 4 V, the DC motor wth the DC-DC converter acheves a hgh perormance on a settlng current o the DC motor n a closed-loop control. Ater 4 V o the constant rect voltage source runs the DC motor on open-loop control n Fg. 3, a settlng torque o the DC motor can reman such as 5 Nm on.5 s whle the maxmum startng torque reachng 7 N m on.3 s. When the 5 V o rect voltage eeng the DC-DC boost converter runs the DC motor wth the PID controllng as n Fg. 3, a settlng torque o the DC motor can reach 43 N m on. s ater 45 N m o the maxmum startng torque. The PID controllng DC-DC converter acheves hgh perormance on the settlng torque o the DC motor even though the nput o the converter has a low nput voltage accorng to the constant DC source whch s 4 V. The values o the used parameters are shown n Tab. or the system constructed. Table Values o the used parameters Parameter Values Parameter Values a.8 H Converter nput V dc 5 V a. H. mh R a.6 Ω C. mf R 4 Ω K p. H K. B m. N m s K d. J.5 km² T.9 N m T s. s Converter output V dc 55 V 6 CONCUSION The DC motor and the DC-DC boost converter mathematcal model were ormed so that the PID controllng converter connectng the DC motor could be constructed at the Matlab Smulnk. The PID controllng DC-DC boost converter drvng the DC motor and a constant DC source drvng the DC motor are smulated n the Matlab Smulnk or the comparson o output perormances ater the ormed mathematcal model. The results are analyzed n ths study ater the system s perormed. or the current and torque and speed o the DC motor, the DC motor whch has a PID controllng DC-DC boost converter does a better perormance on a closed-loop than a constant DC source 86 TECHNICA JOURNA, 4(7), 8-87
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