IDENTIFICATION OF THE PARAMETERS OF MULTI-MASS DIRECT DRIVE SYSTEM

Transcription

1 Prace Naukowe Intytutu Mazyn, Napędów Pomarów Elektrycznych Nr 66 Poltechnk Wrocławkej Nr 66 Studa Materały Nr Domnk ŁUCZAK* dentfcaton of the mechancal reonance frequence, pectral analy, Fourer tranform, chrp gnal, ne gnal IDENTIFICATION OF THE PARAMETERS OF MULTI-MASS DIRECT DRIVE SYSTEM Th paper preent method for the dentfcaton of mechancal reonance of mult-ma drect drve ytem. Method have been appled n the feld of dgtal gnal proceng. Wa ued pectral analy to dentfy the mechancal reonance frequence of drect drve wth elatc connecton. Dcued method of dentfcaton have been verfed by mulaton and real ytem. Two dfferent nput gnal wa preented: ne and chrp wave. Both nput gnal gave good reult for determne mechancal reonance frequence, however ne wave wth varable frequency determned only for the number of frequency correpondng to the nput gnal frequency gave better reult for determne mechancal antyreonance frequence.. INTRODUCTION The drve multple mechanm uch a drve, robot arm, feedng mechanm of machne tool and drve contructon crane have elatc connecton between the electrc motor and the drven devce. An nteretng oluton the drect drve allow for ncreaed precon potonng. Unfortunately, due to lack of tranmon where entve to the mperfecton of the drven mechanm. In th cae, n the control ytem nclude non-tff connecton between the motor and mechancal ytem []. Mechancal reonance common problem whch degner mut reolve [6]. If the mechancal load tatonary hould be properly determne the value of the mechancal reonance frequence. Degnated parameter allow to tune flte whch am wa to uppre of mechancal reonance [2]. The work wa devoted to dcu and ue dgtal gnal proceng method whch allow to extracton of nformaton about the mechancal reonance frequence and mechancal antreonance frequence from velocty gnal. * Inttute of Control and Informaton Engneerng, Poznań Unverty of Technology, Potrowo 3A, Poznań, Poland, Domnk.Luczak@put.poznan.pl

2 63 2. DIRECT DRIVE WITH ELASTIC CONNECTION 2.. MATHEMATICAL MODEL The ngle mechancal reonance block decrbed by the contnuou tranfer functon: G ξ a ωa + ωa ω = () ξ ω + ω ωa where ω = 2π f and ωa = 2π fa are the reonance and ant-reonance angular frequency for -th block, ξ and ξ a are the reonance and ant-reonance dampng coeffcent. The tranfer functon from electromechancal torque Tem to motor velocty ω m : ωm T em = J d where J d the total moment of nerta and R the number of the reonance block. Smulaton were performed ung the parameter from the Table. = G (2) Table. Parameter of the mulated model J d fa ξar, f ξ (kg m 2 ) (Hz) *0 4 (Hz) * EXPERIMENTAL SYSTEM The ytem cont of three man part: the motor wth load contructon, a PWM (pule-wdth modulaton) converter and the control algorthm mplemented n DSP (Dgtal Sgnal Proceor). A et of metal plate fxed to the arm mounted on the motor haft enable to vary the moment of nerta. The amplng tme of the floatng pont DSP et to τ = 00 μ. An ncremental optcal encoder wth N enc = mpule/rev tet the rotor poton. The peed calculated by dfferentaton of rotor poton wth repect to tme. The peed reoluton uch cae : Δ ω = 0.02 rev/ N τ (3) enc

3 64 Feld-orented control of current n the d and q axe performed by applyng PI control algorthm. The cloed current control loop for ax q decrbed by equaton (4), wth τ cur = 0.3 m τ am = 0.2 m. q = + τ cur e τ am ref q Identfcaton wa made n open loop a hown n Fg.. (4) Fg.. The tructure of dentfcaton 3. SPECTRAL ANALYSIS AS METHOD OF MECHANICAL RESONANCE FREQUENCIES IDENTIFICATION 3.. SPECTRAL ANALYSIS AND INPUT SIGNALS Dcrete Fourer tranform of gnal y(n) of length N defned a: j2π / N N N n= 0 ( k) = y( n) kn W N Y (5) where W N = e, k = 0,, 2,..., N. The nput gnal wa generated a a ne wave wth varable frequency f: x f k) = n(2 π f k τ ) (6) ( Identfcaton wa conducted for dfferent frequence of the nput gnal. The frequency f wa changed n the range 500 Hz n tep of Hz. Were performed 500 dfferent nput gnal wth a duraton of. Spectral reoluton Hz after takng nto account the gnal amplng perod. The pectrum wa determned (5) only for the k number of frequency correpondng to the nput gnal frequency f. The pectrum wa determned n DSP ytem ung the Goertzel algorthm [3, 4]. Second nput gnal wa generated a a lnear up-chrp wave whch ncreang lnearly frequency of ne from frequency f 0 equal to Hz to f equal to 500 Hz n tme t : f f0 x( k) = n 2 π f0 + k τ k τ t (7)

4 65 Input gnal duraton wa et to. The pectrum of the output gnal ha been determned n Matlab RESULTS OF IDENTIFICATION The reult of the mulaton of open-loop ytem for the parameter n Table for the nput gnal (6) wa hown n Fg. 2 and for the nput gnal (7) wa hown n Fg. 3. The reult of real object for the nput gnal (6) wa hown n Fg. 4 and for the nput gnal (7) wa hown n Fg. 5. Both nput gnal allow to fnd the mechancal reonance frequence, however the frt method allow to fnd the mechancal antreonance frequence. In the cae of mulaton found frequence correpond to the mulaton parameter. In the cae of real object found the mechancal reonance frequence where the ame for both method. Fg. 2. Frequency analy of mulated object (6) wa ued a nput gnal Fg. 3. Frequency analy of mulated object (7) wa ued a nput gnal Fg. 4. Frequency analy of real object (6) wa ued a nput gnal

5 66 Fg. 5. Frequency analy of real object (7) wa ued a nput gnal 4. CONCLUSIONS Th paper preent two method to determne the mechancal reonance and antreonance frequence of real object n open-loop. Method were ued to dentfy the mulated object and expermental object. The frt method gve better reult but take longer. The econd method allow to extract nformaton about the mechancal reonance frequence, however the nformaton about antreonance wa unreadable. Degnated pectrum can be analyed to fnd mportant frequence a preented n [5]. Determned parameter wll be ued to tune the flter to reduce vbraton n a cloed loop control ytem. Thoe method are the ntalzaton phae wth a pecfc nput gnal. In the next tage of reearch wll be ntended ue of the velocty gnal to adapt flter durng normal ytem operaton n cloed-loop ytem. The ue of pectral analy allow the dentfcaton of the mechancal reonance frequence and mechancal antreonance frequence. Th work wa realzed wthn the project Prece control of varable mult-ma drect drve, agreement no. 466/B/T02/200/38. REFERENCES [] BENTLEY J.M., LORENZ R.D., VALENZUELA M.A., VILLABLANCA A., Dynamc compenaton of toronal ocllaton n paper machne ecton, IEEE Tranacton on Indutry Applcaton, 2005, Vol. 4, No. 6, [2] BROCK S., LUCZAK D., Speed control n drect drve wth non-tff load, Proc. of 20th IEEE Int. Sympoum on Indutral Electronc, Poland, Gdank, 20, [3] GOERTZEL G., An algorthm for the evaluaton of fnte trgonometrc ere, Amercan Mathematc Monthly, 958, Vol. 65, [4] LUCZAK D., DSP mplementaton of elected algorthm of pectral analy, Proc. of XVII Int. Scentfc Conference Computer Applcaton n Electrcal Engneerng, Poland, Poznan, 202, 6. [5] LUCZAK D., Frequency analy of mechancal reonance n drect drve, Proc. of 2th IEEE Int. Workhop on Advanced Moton Control, Bona and Herzegovna, Sarajevo, 202, 5. [6] ORLOWSKA-KOWALSKA T., SZABAT K., Vbraton Suppreon n a Two-Ma Drve Sytem Ung PI Speed Controller and Addtonal Feedback Comparatve Study, IEEE Tranacton on Indutral Electronc, 2007, Vol. 54, No. 2,