Robust Control of a Brushless Servo Motor Using Sliding Mode

Transcription

1 Buletin Teknik Elektro an Inormatika (Bulletin o Electrical Engineering an Inormatics) Vol.1, No.4, December 2012, pp. 295~304 ISSN: Robust Control o a Brushless Servo Motor Using Sliing Moe Raita.Arinya Universitas Satyagama JI. Kamal Raya No. 2A Cengkareng, Jakarta Barat raitatech@yahoo.com Abstract The application o sliing moe techniues the position control o a brushless servo motor is iscusse. Such control laws are well suite or electric power inverter. However, high reuency commutations are avoie ue to the mechanical systems. Various recent schemes are stuie an operate to erive control solutions which are technically easible. In spite o straightorwar applications the resulting systems show robust perormances to parametric variations an isturbances. Robustness stuie with respect to rotor lux uncertainties an to stator resistance which varies with the temperature o the motor. Keywors: non linier control, brushless servo motor, sliing moe, robust control 1. Introuction This journal is written through system o technical controls non linear with sliing moe. Sliing control theory moe constitutes one o classic control technical or non linear system. With metho controls sliing moe, trajectory is situation is restraine that ollows trajectory basis (reerence) one that is establishe. This metho is ivie two phases which is trajectory is pulle making or an area has alreay is eine previous an surace name sliing (sliing surace) an trajectory moves by glie(sliing) at previous upper surace. Severally sliing control than metho this moe is: Can be utilize or system syntheses non tall orer linear. Can be utilize or MIMO'S system (Multi Input, Multi Output). Resulting control system robust to parameter an perturbation variation (trouble). Can be utilize or system what oes have uncertainty so can solve inaccurate problem ace to ace. Result o sliing' metho this moe will be applie on one system which is Brushless c's motor. Brushless motor are three phase synchronous motor that utilize electronic commutation to processes switching current among phase or utilizes silicone rectiier as component o static commutation synchronous starting motor permanent magnet has iiosyncrasy as ollows: Rotor construction brushless just consisting o magnet just so not reuires care. 1. Very tall approachable top spee. 2. Moment o inertia o bottommost rotor or angular spee motor or or torsi motor. 3. Motor construction without brush utterly being close to water an airproo. On scientiic journal writing this, will o operation result analysis to motor spee, irect current( i ), voltage uaratic (V ), voltage irect (V ) an robustness to lux ace value change rotor( Ф ) an stator prisoner( R s ) 2. Brushless Motor DC State Space o state rom - transorms with moel assuming taken rom by rotor eault moel. Division gap lux airs that resulting by iel circumerence asymmetrically lies aroun iel pole iameter. this pole is wicke name route or irect pole. pole o armature wave lies 90 egrees o iel pole is name uaratic pole. Written numeric s ata as ollows Receive August 7, 2012; Revise October 25, 2012; Accepte October 27, 2012

2 296 ISSN: V = irect Voltage (Volt) V = uaratic Voltage (Volt) Φ = Direct Flux Φ = Quaratiue Flux = Stator Inuctance ( H) = Rotor Inuctance ( H) R s = Stator Resistance (0.6Ω) J = moment o inertia (expenses an motor) (11 x 10-4 kg m 2 ) P = poles (4) F v = viscous amping coeicient (1.4 x 10-3 kg m 2 s -1 ) Ω = Rotor spee (ra /sec) Φ = Rotor lux (constant) ( Wb) C = Torsi expenses (constant) (Nm) Moel euation s consisting o electrical euation an mechanical euation. Relationship among voltage an lux is V = R S.i - pωφ (1) V = R S.i - pωφ (2) With : φ =.i + φ, φ =.i (3) An electrical torsi: C m = p[ ( ) i + φ ] i (4) Mechanic Euations: θ = φ (5) J Ω = C m + C - v Ω (6) Servo motor ynamic euations: φ 0 0 θ P C v φ (7) [( ) i + ] i Ω J X = = R s + Ω i i p i i φ p Ω p Ωi Ω 0 J J 1 + Rs 0 i 0 V 0 V 1 3. Sliing's Moe control or Brushless servo motor The system has two inputs which is V an V. torsi count (4) point out that inuctances ierence ( - ) play one role on system i current i zero unlike. Strategy that enables to control brushless servo's position or spee motor via sliing's metho moe is make i as zero. Besies this strategy current rule pock phase. I an i restraine separately. Current i an i etermine lies loop's outboar so sliing is moe happens on switching's surace s i = 0. On generally i etermine at the price zero, since i not result motor torsi, thereore motor on't epen i. [5] Two surace sliing we can etermine while two intent ots get concurrently been reache. That thing is sai apropos while two sel supporting entry is gotten which is V an V. That looking at x etermine part o system, V etermine one o part o V or V an S (x) are surace sliing. Sliing control moe can be reache i available law controls with conition sś < 0. V = V e + V n (8) While Ve are solution o Ś (x, ν) = 0. V e will can control while S(x) = 0 an so-calle euivalent control in stanar terms. Design o V e on euation (8) rather octrinaire: more ten to exact linearization rom output S(x) with one pole place (pole placement) to provenance. V n esigne or meeting situation conition trajectory to pull to surace S(x) = 0. Controls problem Buletin TEI Vol. 1, No. 4, December 2012 :

3 Buletin TEI ISSN: in common be ivie into two subs about problems which is solve wholly inepenently. It becomes maybe while i mae as zero an will make a aboe little in many situation. Sliing moe successul control i. 4. Direct Current Metho (i ) Sliing Surace: S i = i,re - i = - i (9) S = i i Substitute (7) an (10) (10) S i = R s i pω i V (11) To calculate Ve, we solve euation S i = 0 V = R. i pω i, e s (12) With V = V,e + V,n sliing moe conition S < 0 i S i Then V n Si 0 V = V + K sign( S ) (14), e i (13) Where k i is real positive constant. K taken accoring to point V,e an or point what o it or motor tension entry. 5. Spee Control Metho re constituting constant reerence o spee rotation. S v = Ω re - Ω wie o the mark or sliing's surace einition while input is not explicit ala lay in S. Deine back S v = K v e v + e with e v = Ω re - Ω an with k v positive regular reality results S = k Ω + In conseuence v v t Ω p v + J [( ) i + φ ] (15) J C i J J V, e = K Ω+ pωφ + pω i + R i p v s [( ) i + φ ] J V = V,e + V,n conition o S < 0 eclare V, np i S i [( ) i + φ ] J < 0 (16) (17) Robust Control o A Brushless Servo Motor Using Sliing Moe (Raita.Arinya)

4 298 ISSN: an V = V,e + K sign (S v ) (18) K is real constant positive. 6. Sliing's Moe application Surace on Sliing moe is prescribe by appreciative ε. Meanwhile e pointing out actor's eviation spee (velocity error). Spees bias actor can be set own o euation: e = Ώre Ώ (19) Working out on euation 4.1 can be igure on asa's area (ė,e) while methos to conuct euivalent is applie on bounary layer ( ε < S< ε ). Bounary layer sliing's explanation this moe is pointe out.on sliing surace, spee eviation is gotten o euation: ė = K v x e (20) Spee actor eviation can orm asymptote that approach zero i K v > 0 an system will wen ot o asa's area as on Figure no2. Price K v causing spee as convergent. Coeicient K etermine as K v. On simulation by use o Mathlab is etermine score or K v = 1000, K = 24, K = 500 an ε = 0. Robustness analysis o controller is still was taken into account since not yet available point change to rotor lux (Ф ) an Stator prisoner (R s ). signum( s i ) 1 S i -1 Figure 1. signum (s i ) unction s ė ε e Euivalent Control area Figure 2. Sliing Moes: Bounary ayer Buletin TEI Vol. 1, No. 4, December 2012 :

5 Buletin TEI ISSN: Figure 3. Sliing Moes: Spee response to time Figure 4. Sliing Moes: i response to time Figure 5. Sliing Moes: V t response to time Figure 6. Sliing Moes: V response to time Robust Control o A Brushless Servo Motor Using Sliing Moe (Raita.Arinya)

6 300 ISSN: Simulation result appears that marks sense unction signum on controller will cause eect chattering on response V an V. To avoi phenomenon chattering this, unction signum can be substitute by one ala one unction continue approximate. 7 Smooth Sliing Moes Signum s unction as upon can evoke eect chattering, which is a phenomenon where happens changing control with reuency that very tall while trajectory available surace aroun sliing an while sign's price oten arbitrary. To avoi this chattering phenomenon, unction signum can be substitute by one ala one unction continue approximate. Metho conucts this was gotten by replaces unction sign (s i ) with unction sign 2 one that constitute sat's unction sat(s i ). On asa's area (ė,e ), bounary layer becomes like on Figure 8. sat( S / ε ) ε 2 ε1 0 ε 1 ε 2 S Figure 7. Smooth sliing moe with sat (s i / ε) unction Figure 8. Smooth Sliing Moes: Bounary layer Figure 9. Smooth Sliing Moes: Spee response to time Buletin TEI Vol. 1, No. 4, December 2012 :

7 Buletin TEI ISSN: Figure 10. Smooth Sliing Moes: i response to time Figure 11. Smooth Sliing Moes: V response to time Figure 12: Smooth Sliing Moes: V response to time On sign's simulation 2, price or unchange parameter rom sign1 which is: Ώ re = 100 ra secons, i re = 0 ampere, K v = 1000 an K = 24. Score o ε 1, ε 2, ε1 an ε 2 etermine to reuce phenomenon chattering. Appreciative elect or ε 1 = 1, ε2 = 10, ε1 = 10 3, ε 2 = 10 4 show that eect chattering on graph V an V can be reuce. Graph to respon spee unchange to respons rom irst metho (sign1). 8. Robustness Test Stuy robustness is aresse to measure in as much as which tech sturiness conucts that is use to parameter or perturbation change. Ater gets metho to conuct or nominal situation, applie by that metho to system alreay being given by variation. Robust Control o A Brushless Servo Motor Using Sliing Moe (Raita.Arinya)

8 302 ISSN: Teste i by gives variation to lux appreciative change rotor (Ф) an stator prisoner (Rs). Robustness o controller is analyze by use o s ign 2, since that controller response gets minimize eect chattering. On robustness's examination change assesses rotor lux (Ф) an stator prisoner (Rs) are as ollows; changing point s rotor lux (Ф ) as ±10% rom point nominal (Ф = Wb ) Changing stator prisoner point (Rs) as big as 50% o ace value (Rs=0. 6 Ώ ). Face value ascension R s because o ascension temperature motor Determine by parameter Ώre, i re, K v, K, K, ε 1 = 1, ε2 = 10, ε 1 = 10 3 an ε 2 = Shown that response o lux point change rotor is as ollows: For rotor lux change (Ф ) as big as + 10% will be shown that controller will hasten motor spee response. Constant controller robust while is ace value R s raise as big as 50% For rotor lux change (Ф ) as big as 10% will be shown that controller will slow motor spee response. Constant controller robust while is ace value R s raise as big as 50%. Figure 13. Spee robustness stuy with rotor lux change as big as +10% Figure 14. Spee robustness - with rotor lux change as big as 10% Figure 15. V response to time with change rotor lux +10% Buletin TEI Vol. 1, No. 4, December 2012 :

9 Buletin TEI ISSN: Figure 16. V response to time with change rotor lux -10% Figure 17. V to time with change rotor lux +10% Figure 18. V response to time with change rotor lux -10% 9. Conclusion Strategy to control position or spee motor servo without brush via tech sliing moe is make i eual to zero. Current or i etermine at the price zero, since i oesn't result torsi motor, so motor not epens i. 1. Simulation result appears that prescribe spee accors at the price reerence which be etermine in the perio o less than 0.04 secon. There is eect even chattering on sliing moe can be reuce by replaces unction sign (s i ) with unction sat (s i ) or unction sat (s i /ε). 2. sliing controller moe can be utilize or system multivariable which is by restrains V an V separately 3. Resulting control systems have robust character to parameter an perturbation variation (trouble), which is change to rotor lux an stator prisoner. Flux ace value ascension rotor will hasten spee response an lux ace value ecrease rotor will slow spee response.. Robust Control o A Brushless Servo Motor Using Sliing Moe (Raita.Arinya)

10 304 ISSN: Reerences 1. Hasimoto, H., Yamamoto, H., Yanagisawa, S., an Harasima, F., 1988, Brushless servo motor control using variable structure approach, IEEE Transaction on Inustrial Applications, 24, anier, C., Commane par moes glissants une machine synchrone. University o Nantes, Ecole Centrale e Nantes, DEA Report. 3. Muhamma H.Rashi., Power Electronics: Circuit, Device, an Applications, Prentice Hall Internasional, Pragasen pillay & Ramu Krishnan, Moeling, Simulation, an Analysis o Permanent Magnet Motor Drives, Part I: The Brushless DC Motor Drive, IEEE Transaction on Inustry Applications, Vol 25, No 2 March/April Sabanovich, A., an Izosimov, D.B., 1991, Applications o sliing moe to inuction motor control, IEEE Transaction on inustrial Applications, Slotine, J-J. E., i, W., Applie Nonlinier Control, Englewoo Clis, USA: Prentice Hall International,1991 Buletin TEI Vol. 1, No. 4, December 2012 :