Op-amp, A/D-D/A converters and Compensator Emulation

Transcription

1 EE35L CONTROL SYSTEMS LABORATORY Purpoe Opamp, A/DD/A converter and Compenator Emulaton The objectve o th eon are To learn the bac ampler crcut or typcal phaelead and phaelag compenator and degn a typcal analog phaelead and phaelag compenator. To nvetgate how gnal are paed through the realtme control hardware/otware ytem ung D/A and A/D converter. To replace the analog compenator wth dgtal compenator that emulate the phycal compenator. Buld the WnCon applcaton, mplement and tet the compenator n the realtme Introducton Operatonal Ampler A typcal control ytem nclude a lter or compenator alo known a controller whoe role to mody or hape the reerence command nput n way that mprove the ytem repone. Analog controller are commonly realzed wth pave crcut element and operatonal ampler. The crcut ymbol or an opamp wth t ve eental termnal and t voltage traner charactertc hown n Fgure 2.. v n v p V CC V CC v o Op amp Symbol V CC v o A V CC V cc A v p v n Vcc A( vp vn) < Vcc V0 = A( vp vn) Vcc A( vp vn) V Vcc A( vp vn ) > Vcc cc Fgure 2. Opamp ymbol and the nput/output charactertc When V V mall the opamp behave a a lnear devce. Outde th lnear range p n the opamp aturate and behave a a nonlnear devce. For operaton n the lnear range the net nput voltage contraned to the voltage Vcc appled to the power termnal. For a typcal opamp operatng on t lnear regon, the voltage derence between the two nput very mall, le than 2 mv,.e., v = v v 0. Alo the nput retance x p n 2.

2 very large, and the output retance neglgbly mall. For example, the common opamp ha A 0, R n 2 0 Ω, and Ro 40Ω. Becaue o the hgh nput retance, neglgbly mall current low nto the two opamp nput, uually on the order o µa. In mot practcal applcaton, the crcut analy can be mpled wth good accuracy by aumng the opamp to be deal,.e., A, o that v = v = n p =, o that = = 0 R n Ro = 0. Phaelead and phaelag compenator n p The mplementaton o a traner uncton mot commonly done ung nvertng opamp crcut. Snce the opamp a very hgh gan devce, eedback mut be added to the ampler n order to tablze t. The eedback crcut connected rom the output termnal to the nvertng nput termnal. Th connecton reult n negatve eedback. An example o a practcal opamp crcut n doman hown n Fgure 2.2. Z () Z () v n n V cc V () v p p V cc V () o Fgure 2.2 General nvertng operatonal Ampler Snce n p 0 and vn v p = 0, KCL wll reult n V() Vo() = 0 Z () Z () or V () () o Z = (2.) V() Z() By proper choce o mpedance we can realze phaelead compenator (Hghpa lter), phae lag compenator (lowpa lter), PI, PD, or PID compenator that wll be ued to mprove the perormance o the control ytem. The traner uncton n (2.) contan a negatve gn. To obtan a potve gnal we can add another nvertng opamp wth two dentcal nput and eedback retor,.e., R2 = R2 Conder the crcut o Fgure 2.3 wth mpedance contng o parallel RC crcut. 2.2

3 C C R R 2 V () R n v n p v p V cc V cc V () 2 R 2 V () o Fgure 2.3 Bac compenator crcut The parallel branch mpedance are R / C R Z () = = R / C RC and R / C R Z () = = R / C R C Thereore, V () ( ) 2() Z R RC = = V () Z () R ( R C ) I another nvertng opamp wth equal orward and eedback retor are ued the gnal would be nverted and the compenator traner uncton become Vo() C ( / RC ) Kc( a) () = = = V () C ( / R C ) ( b) Where C Kc =, a=, and b= C RC R C For a realtc compenator a and b are greater than zero and the pole and zero are located n the let hal plane a hown n Fgure 2.4. (2.2) (2.3) θ b θ a θ a a a b b (a) Phaelead (b) Phaelag Fgure 2.4 Compenator phae angle contrbuton For a gven = σ jω, the traner uncton angle gven by θc = θa θb potve a< ba hown n Fgure 2.4 (a), and the compenator known a the phaelead θ b 2.3

4 controller. On the other hand a > ba hown n Fgure 2.4 (b), the compenator angle θ = θ θ negatve, and the compenator known a the phaelag controller c a b The relaton n (2.3) can be ued to realze the phaelead or phaelag compenator, and nce there are three equaton and our unknown, a utable value or one o the parameter ay R choen and the other element are calculated rom (2.3). I removed Z ( ) = R, and then we have C V2 () Z () R ( RC ) R = = = R C V() Z() R R The compenator traner uncton known a Proportonal Dervatve or PD controller become o() () = V R R C V() = R (2.4) or () = KP KD (2.5) where R KP =, and KD = RC (2.6) R I R removed Z ( ) = / C, and then we have V2 () Z () RC C / R C = = = V() Z() RC C The compenator traner uncton known a Proportonal Integral or PI controller become () / RC () = Vo C V () = C (2.7) or where G K c KI () = KP (2.8) P C = C, and K I = RC (2.9).3 Phaelead and phae lag Frequency Repone The phaelead compenator traner uncton Kc ( a) () =, where a< b ( b) The requency repone traner uncton 2.4

5 Kc( jω a) Kca jω/ ω ( j ) o ω = = ( jω b) b jω/ ω p Where ω o = a, and ω p = b are the two corner requence. Ka c Aumng a dc gan o unty or the compenator, (.e., = ) the traner uncton b jω / ωo ( jω ) =, wth ω0 < ω p jω / ω p The Bode plot a hown n Fgure 2.5. It apparent that the phaelead compenator a hghpa lter. Fgure 2.5 Bode dagram or phaelead compenator For the phaelag compenator ω0 > ω p and the compenator a lowpa lter a hown n Fgure 2.6. The maxmum potve angle n the cae o the phaelead compenator or maxmum negatve angle n the cae o the phaelag compenator occur at geometrc mean value o ω and ω or the requency at maxmum phae lead or phae lag gven by o p ω = ωω (2.0) m o p 2.5

6 Fgure 2.6 Bode dagram or phaelag compenator 2 Prelaboratory Agnment 2. Phaelead compenator realzaton (a) Degn an opamp crcut to realze a phae lead compenator wth the ollowng traner uncton. 8( 20) () = ( 60) For practcal conderaton, ue retor n the range o K Ω to0 M Ω and capactor le that 0 µ F. You may ue a 2 µ Fcapactor or C n (2.3). (b) Fnd the requency repone traner uncton G phae angle o ( jω ) at the requency o = 0 Hz. c ( jω ) and evaluate the magntude and (c) Ue the bode uncton n MATLAB to obtan the requency repone. 2.2 Phaelag compenator realzaton Repeat (a)(c) or a phaelag compenator wth the ollowng traner uncton 0.5( 6) () = ( 2) 2.6

7 2.3 PID Compenator Fgure 2.7 how an arrangement or the PID compenator. / c R / c R 2 V () R n v n p v p V cc V cc V () 2 R 2 V () o Fgure 2.7 A crcut or the PID compenator Show that the compenator traner uncton gven by KI () = KP K D (2.) where R C KP = R C K K I = RC = R C D (2.2) 2.3 Dgtal Emulaton o compenator In many modern ndutral and commercal control ytem analog compenator are replaced wth a dgtal computer that perorm calculaton that emulate the phycal compenator. A dgtal computer n the loop wth ampleandhold unt can replace numerou analog compenator wth a ubequent reducton n cot. Any change or modcaton that are requred n the uture can be mplemented wth mple otware change rather than expenve hardware modcaton. In the realtme control ytem the nput gnal converted rom analog orm to dgtal orm by mean o the analogtodgtal converter. Ater pang the nput through compenator developed n Smulnk, the C code generated automatcally by Matlab RTW, whch then converted to analog orm by the dgtaltoanalog converter. In th lab the phaelead and phaelag compenator ntroduced n ecton 2 wll be emulated n Smulnk and the reultng analog gnal wll be oberved and meaured on the ocllocope. 2.7

8 3 Laboratory Procedure 3. Obervaton o a gnal through A/D and D/A converter Attach a T connector to the 3320A uncton generator, connect a BNC cable to one end o the T connector and connect the other end o the cable va a BNC to RCA adapter to o the analog nput. Connect a BNC cable rom the other end o the T connector to Channel 2 o the ocllocope. Connect a BNC cable wth a BNC to RCA adapter rom analog Output # 0 to Channel o the ocllocope a hown n Fgure 2.7. Analog Output #0 Phono adapter Analog Input # Hz Phono adapter T connector Channel Channel 2 BNC Cable Fgure 2.7 Wrng dagram Turn on the uncton generator and adjut or a ne wave o 0 Hz wth 2 V peaktopeak. I the uncton generator not et to the hgh mpedance mode, a readng o V on the uncton generator repreent an output o 2 V peaktopeak. Turn on the ocllocope and reet t by the equence Save/Recall, Deault SetUp (otkey), Autocale. Set the horzontal channel to 0 mec/dv and both vertcal channel to 500 mv/dv, and et the Center Adjut to zero mv on both channel. Start a Smulnk model. From Quaner Toolbox/Quaner Conultng MQ3 Sere get a Quaner analog nput block and et the Channel to Ue to 0. Get a Quaner analog output and et the Channel to ue to 0. Connect the two block together and attach a dgtal Scope a hown n Fgure 2.8. Quaner Conultng MQ3 ADC Quaner Conultng MQ3 DAC Analog Input Dgtal Scope Fgure 2.8 Implementaton model Analog Output Save the model (ay Lab2A.mdl). Set the Smulaton parameter (elect the Solver tab and et the amplng rate on the compenator to 0.00 econd under Fxed Step Sze. Select ode4 Rung Kutta or ntegraton method). In the Smulaton drop down menu et the model to External. Start the WnCon Server on your laptop and then ue Clent 2.8

9 Connect, n the dalog box type the proper Clent worktaton IP addre. Clck WnCon/Buld, th wll generate the code and download t to the clent. Clck on the Start button on the WnCon Server to run the model. Clck on Plot/New/Scope n WnCon Server and n the Select varable to dplay dalog box, clck on Dgtal Scope (The name you agned to the Smulnk Scope) to elect the varable you want to plot and pre OK. Th open a realtme plot and dplay the gnal a read by A/D. Snce the gnal requency 0 Hz (T=0. ec), n the dgtal Scope menu clck Update/Buer and or the Buer ze type 0.2 (econd) to dplay two cycle. You alo hould have the recovered analog gnal on the ocllocope. Pre Sngle on the Aglent Scope and capture a ngle trace o data. You hould have the Aglent IntuLnk otware or the ocllocope, and the USB port NI488.2 drver ntalled on your laptop. The IntuLnk can be ound by openng Mcroot Excel, and then lookng to ee the "Aglent 54600" toolbar appear jut below the top row o Excel pulldown menu. I t doe not appear, then you need to ntall the otware rom a CDROM (avalable at the MSOE EECS TSC, room S350). Capturng the Ocllocope plot and plottng data Connect the GPIB or the ocllocope to the USB port on your laptop. Start Excel and pre the Get Waveorm Data con to capture the data. Delete the rt row contanng text. Hghlght the data (no text) n the rt three column to the lat data row and copy the data to the clpboard. In MATLAB open a new MFle and pate the data coped to the clpboard. Save the data wth a le name havng extenon dat. (e.g., VnVout.dat). Set the current drectory to where the le VnVout.dat tored and type the ollowng tatement at the MATLB prompt to obtan a MATLAB Fgure plot. >> load VnVout.dat >> plot(vnvout(:, ), VnVout(:, 2), 'r', VnVout(:, ), VnVout(:, 3), 'b' ), grd >> legend('recovered analog gnal', 'Orgnal analog gnal') Clck on the STOP button to top runnng the model. 3.2 Phaelead Compenator emulaton and mplementaton Save your mplementaton model (Lab2A.mdl) under a new name ay (Lab2B.mdl). Get a Traner Fcn block rom the SIMULINK Contnuou lbrary, and nert t n the new model a hown n Fgure 2.9. Note that the gnal goe through the A/D converter va the compenator to the D/A converter. Double clck on the Traner Fcn block to open t dalog box, enter [8 60] and [ 60] or the numerator and denomnator repectvely. Quaner Conultng MQ3 ADC (8 60) ( 60) Quaner Conultng MQ3 DAC Analog Input Phaelead compenator Vout Analog Output 2.9

10 Fgure 2.9 Smulnk mplementaton dagram or phae lead compenator. Turn on the uncton generator and adjut or ne wave o 0 Hz wth 2 V peaktopeak. In the WnCon erver clck Fle/New and ue Clent Connect, n the dalog box type the proper Clent worktaton IP addre. Generate the realtme code correpondng to your dagram by electng the Buld opton o the WnCon menu rom the Smulnk wndow. Clck on the Start button on the WnCon Server to run the model. From the WnCon Server Plot/New/Scope elect Vout to dplay the gnal a read by A/D. In Update/Buer et the Buer ze type 0.2 (econd) to dplay two cycle. Set the horzontal channel to 20 mec/dv and the vertcal channel to utable mv/dv, et the Center Adjut to zero mv on both channel. You hould now ee the output gnal on the ocllocope. Capture the data n Excel, copy the data (no text) to the clpboard pate n a new page n MATLAB edtor and ave a a.dat le (ay PhaeLead.dat). Set the current drectory to where the le PhaeLead.dat tored and type the ollowng tatement at the MATLB prompt to obtan a MATLAB Fgure plot. >> load PhaeLead.dat >> plot(phaelead(:,), PhaeLead(:, 2), 'r', PhaeLead (:, ), PhaeLead(:, 3), 'b' ), grd >> legend('output gnal', 'Input gnal') Change the gnal requency rom Hz to about 50 Hz and jut oberve how the output ampltude and phae angle change and draw a concluon regardng the lter charactertc. Alo note that a the requency ncreae the recovered gnal become le accurate why? Clck on the STOP button to top runnng the model. Fnd the peaktopeak value o the two waveorm and determne the voltage gan. Alo ue the Curor to meaure the compenator phae ht θ c. 3.3 Phaelag Compenator emulaton and mplementaton Save your mplementaton model (Lab2B.mdl) under a new name ay (Lab2C.mdl). Set the traner uncton parameter to the gven value a hown n Fgure 2.0. Quaner Conultng MQ3 ADC (0.5 8) ( 2) Quaner Conultng MQ3 DAC Analog Input Phaelag compenator Vout Analog Output Fgure 2.0 Smulnk mplementaton dagram or phaelag compenator. Turn on the uncton generator and adjut or ne wave o 0 Hz wth 2 V peaktopeak. 2.0

11 In the WnCon erver clck Fle/New and ue Clent Connect, n the dalog box type the proper Clent worktaton IP addre. Buld and run the model. You hould now ee the output gnal on the ocllocope. Capture the data n Excel, copy the data (no text) to the clpboard pate n a new page n MATLAB edtor and ave a a.dat le (ay PhaeLag.dat). Set the current drectory to where the le PhaeLag.dat tored and type the ollowng tatement at the MATLB prompt to obtan a MATLAB Fgure plot. >> load PhaeLag.dat >> plot(phaelag(:, ), PhaeLag(:, 2), 'r', PhaeLag (:, ), PhaeLag(:, 3), 'b' ), grd >> legend('output gnal', 'Input gnal') Change the gnal requency rom Hz to about 50 Hz and jut oberve how the output ampltude and phae angle change and draw a concluon regardng the lter charactertc. Clck on the STOP button to top runnng the model. Fnd the peaktopeak value o the two waveorm and determne the voltage gan. Alo ue the Curer to meaure the compenator phae ht θ c. 2.