J-DSP-CONTROL: A CONTROL SYSTEMS SIMULATION ENVIRONMENT +

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J-DSP-CONTROL: A CONTROL SYSTEMS SIMULATION ENVIRONMENT + T. Thrasyvoulou, K. Tsakals and A. Spanas MIDL Department of Electrcal Engneerng Arzona State Unversty, Tempe, AZ 85287-7206 thrassos@asu.

1 J-DSP-CONTROL: A CONTROL SYSTEMS SIMULATION ENVIRONMENT + T. Thrasyvoulou, K. Tsakals and A. Spanas MIDL Department of Electrcal Engneerng Arzona State Unversty, Tempe, AZ thrassos@asu.edu, tsakals@asu.edu, spanas@asu.edu ABSTRACT J-DSP-C s a java-based object-orented programmng envronment that was developed at Arzona State Unversty for use n control systems educaton. Ths envronment enables the smulaton of dynamcal systems on-lne from any computer system equpped wth an Internet browser. The J-DSP-C features are prmarly amed to provde an on-lne laboratory experence to dstance learnng students. Combned wth a report submsson and scorng faclty, J-DSP-C ntegrates nteractve examples nto web content for educaton and demonstraton purposes. KEYWORDS Smulaton, Educaton, Control Systems. control systems extenson J-DSP-C wll soon be tested for use n undergraduate control classes. Smlar to ts precursor, J-DSP-C s an objectorented smulaton envronment that enables students to establsh and execute control systems smulatons from any computer equpped wth an Internet browser. All functons n J-DSP-C appear as graphcal blocks that are accessed through pull-down menus and are grouped accordng to ther functonalty. The J-DSP-C edtor allows the user to graphcally setup and smulate systems wth arbtrary nterconnecton topology. An example of the J-DSP-C graphcal user nterface (GUI) s llustrated n Fgure 1. The followng sectons provde an overvew of the J-DSP prototype, the J-DSP-C enhancements and lmtatons, ts current functonalty, and examples of use. 1. INTRODUCTION Ths paper presents a prototype laboratory software tool, called Java-Dgtal Sgnal Processng - Control (J-DSP-C). J-DSP-C can be used to smulate control systems on-lne, takng advantage of recent developments n Internet technology. The man motvaton behnd ts development stems from the recent ncrease of the percentage of dstance-learnng students at Arzona State Unversty (ASU) and other major metropoltan unverstes. Dstance learnng s a trend n today s educaton, and J-DSP-C flls a gap by provdng a smple yet powerful tool for on-lne control systems smulatons. The software s freely dstrbuted and s desgned to enhance dstance-learnng and contnung educaton wth an on-lne laboratory experence. Its precursor s J-DSP that was developed n the ASU Multdscplnary Intatve on Dstance Learnng (MIDL) laboratory. J-DSP was successfully tested n ASU s undergraduate dgtal sgnal processng class. Based on ths experence, further enhancements of ths tool are currently under development n MIDL, for use n controls, communcatons, and mage processng educaton. The Buttons to select blocks Blocks Fgure 1: J-DSP-C user nterface Work space Detals on J-DSP and J-DSP-C are gven n [1] and n the on-lne documentaton at [3]. Fundng for the development of J-DSP and J-DSP-C was provded by the NSF CCLI program and ncludes + Supported n part by NSF CCLI grant DUE J-DSP concept by A. Spanas. For more nformaton on J-DSP and ts dssemnaton please contact spanas@asu.edu..

software development and dssemnaton along wth a seres of on-lne laboratory exercses. 2. J-DSP OVERVIEW The J-DSP edtor s the bass on whch J-DSP-C was developed.

Its underlyng phlosophy was dctated by ts sutablty for operaton over the Internet.

2 software development and dssemnaton along wth a seres of on-lne laboratory exercses. 2. J-DSP OVERVIEW The J-DSP edtor s the bass on whch J-DSP-C was developed. J-DSP was orgnally developed as a platform to smulate the typcal systems and operatons encountered n dgtal sgnal processng. Its underlyng phlosophy was dctated by ts sutablty for operaton over the Internet. Usng object-orented programmng prncples, J-DSP proved to be a successful tool to address the typcal computatonal and vsualzaton needs of DSP courses. The exstng functonalty ncludes basc flter desgn, fast Fourer transforms (FFT), upsamplng, downsamplng, sgnal generaton and plottng. More advanced functons nclude autocorrelaton, varous types of perodograms and correlograms and AR tme-seres. (See [1,3] for detals.) To address the needs of other DSP-related problems, the J-DSP edtor s currently beng expanded to offer new specalzed functonalty. Several new functons are beng developed wthn ths framework to support experments on speech analyss-synthess, tme frequency representatons, mage processng, and communcatons systems [2]. On the other hand, enablng the support of experments n feedback systems requred more substantal modfcatons. A key characterstc of J-DSP was ts sequental processng of nformaton. Once a block s ntroduced n the edtor, ts output s mmedately computed based on the nput t receves. Although ths s an attractve feature, especally for educatonal examples, t cannot accommodate general nterconnecton topologes, such as feedback systems. Addressng ths ssue, J-DSP-C represents a sgnfcant enhancement of the basc J-DSP engne, whle t preserves the same fundamental object-orented structure and most of the already developed nfrastructure. 3. THE J-DSP-C ENVIRONMENT The handlng of feedback and, n general, arbtrary nterconnectons of blocks requred some major changes n the J-DSP edtor nfrastructure. Our objectve durng ths development was to preserve the orgnal structure as much as possble together wth ts underlyng concept. That s, the J-DSP-C development adheres to the same smplcty, compactness, and object-orented phlosophy of ts precursor. Ths resulted n some compromses n terms of generalty and computatonal effcency. However, n ts prmary msson as an educatonal tool, the J-DSP-C lmtatons are not too severe and can usually be crcumvented by a careful plannng of the smulaton experments. The modfcatons of the basc edtor can be dvded nto two categores. One s the enhancement of the GUI nterface, together wth the assocated changes n the object classes. The other s the modfcaton of the executon procedure to enable the smulaton of feedback loops. In the orgnal J-DSP, blocks were rectangular and had two ports, the left one desgnated as an nput port and the rght one as output. Two addtonal ports top/bottom were avalable for exchange of parameters. Ths confguraton was adequate to represent the usual DSP operatons but too nflexble for feedback systems. In order to acheve consstency wth the standard notaton and appearance of feedback control systems, the J-DSP-C GUI and the edtor can now handle blocks wth multple nput/output ports that are not lmted to rectangular shapes. For example, a summaton node can now appear as a crcle wth several nput ports, whle a gan block s shown as a trangle. The new envronment also allows blocks to be rotated and flpped and the connectons to be edted or modfed. Ths capablty s qute essental n mantanng a clean vsual appearance of more complcated system nterconnectons. The dfferences between the GUI capabltes of the J-DSP and J-DSP-C edtors are llustrated n Fgures 2 and 3. Fgure 2: J-DSP user nterface Fgure 3: J-DSP-C user nterface

3 A more extensve modfcaton of the orgnal J- DSP engne was necessary to enable the smulaton of feedback systems. The class of control blocks was expanded to nclude state-space descrptons of dynamcal systems. All blocks now have a state attrbute (trval for memoryless blocks) to enable the recursve computaton of the system response. For smplcty, dscrete-tme approxmatons are used nternally to compute the response of contnuous-tme systems. Ths converson s transparent to the user, but care should be exercsed n the selecton of the samplng tme so that the dscretzaton s reasonably accurate. (A warnng s ssued when the samplng tme seems too large.) In ths settng, the computaton of the response of the system nterconnecton s computed recursvely n tme and teratvely wth respect to the varous blocks. The recursve porton of the soluton s made possble by usng state-space descrptons. At each tme nstant, the soluton can be advanced by one tme step and only the state vector needs to be stored n memory. The teratve porton of the soluton s requred to ensure that the correct nputs are computed for all blocks. That s, at each tme nstant, the nput/output computatons are terated untl they converge, before updatng the states. Ths smplfed approach s compatble wth the objectorented defnton of the varous blocks. However, a subtle pont and a key lmtaton s that convergence s not necessarly guaranteed for any system nterconnecton. It can be shown that: When a feedback loop has no algebrac part (at least one of the systems has no drect throughput) then the teraton convergence n fnte steps, proportonal to the number of blocks n the loop. When a feedback loop has an algebrac part then the teraton converges exponentally as (1-ρ) k, where ρ s the loop drect throughput, provded that ρ < 1. Otherwse, the teraton dverges. In practce, ths lmtaton s not very restrctve but t should be obeyed when defnng the feedback nterconnectons. (Agan, a warnng s ssued when the local teraton fals to converge n a prescrbed number of steps.) Fnally, to avod repeated unnecessary computatons whle edtng the system nterconnectons, a smulaton button has been ntroduced to dsable J-DSP s automatc block executon. Instead the smulaton computatons are performed on-demand by pressng ths button. 4. J-DSP-C FUNCTIONALITY A fundamental set of functons has been developed n order to accommodate the need for control systems smulatons. The currently avalable blocks are brefly descrbed below, grouped n terms of ther fundamental propertes Sgnal generators Sgnal generators are an essental part of every smulaton. The J-DSP edtor has been ftted wth two sgnal generators, provdng a varety of sgnals. The frst sgnal generator supples a smple step sgnal that s encountered most frequently n control systems smulatons. It s smple to use and wthn easy reach. The second sgnal generator has been desgned to offer a more elaborate selecton of sgnals. Among others, ths block provdes dscrete mpulses, snusods, snc functons, random sgnals wth ether unform, Gaussan, or Raylegh dstrbutons and exponental sgnals. Where applcable, sgnals can be chosen to repeat perodcally Memoryless Systems and Arthmetc operatons These nclude summaton nodes, gans and varous other blocks performng arthmetc operatons. For example, the user can multply two sgnals, compute ther exponental or ther natural logarthm Dynamcal Systems Currently ths class contans lnear dynamcal systems that can be specfed n terms of ther transfer functon or ther state-space descrpton. The transfer functon block s used to enter a ratonal transfer functon descrbng a system. More precsely, ths block smulates a system gven a transfer functon n the form H ( s) = n = 0 n = 0 b s a s The numerator and denomnator coeffcents b and a are entered n the block s dalog box, shown n Fgure 4. An alternatve and more general way to specfy a lnear system s wth ts state-space descrpton. Ths block mplements the equaton x& = Ax + Bu y = Cx+ Du where, A R, B R, C R, D R nxn nxm pxn pxm, and x R n, u R m, y R p. x s the state vector, u s the system nput and y s the system s output response. Currently, the maxmum number of states s lmted to 10. The dalog wndow for ths block s shown n Fgure 5, along wth a wndow for enterng a matrx. Notce that the user can select to enter matrces n canoncal or other

common forms, where many of the entres have fxed values that are automatcally ntalzed. 4.5.

Addtonal blocks wll perform matrx manpulatons and leastsquares approxmaton, enablng the mplementaton of adaptve systems.

Notce that the ablty to change the block shape and number of nput/output ports has been ntroduced wth ths goal n mnd. Fgure 4: Ratonal transfer functon dalog wndow Fgure 6: Bode plot 5.

4 common forms, where many of the entres have fxed values that are automatcally ntalzed Blocks Under Development Future enhancements of the J-DSP-C edtor wll nclude addtonal components to facltate the modelng and smulaton of nonlnear systems (e.g., nverted pendulum and other mechancal systems). Addtonal blocks wll perform matrx manpulatons and leastsquares approxmaton, enablng the mplementaton of adaptve systems. Other enhancements nclude the support of systems wth multple nputs and outputs, and the ablty to group several blocks nto a composte one. Notce that the ablty to change the block shape and number of nput/output ports has been ntroduced wth ths goal n mnd. Fgure 4: Ratonal transfer functon dalog wndow Fgure 6: Bode plot 5. EXAMPLES In ths secton, two llustratve examples of J- DSP-C smulatons are presented. The frst example smulates a smple unty feedback system wth Fgure 5: State Space system s dalog wndow 4.4. Plottng and Vsualzaton Blocks The results of a smulaton can be examned usng the graphcal output capabltes of the Plot block. Ths block smply plots ts nput n a lnear or logarthmc scale. It has zoomng capabltes and can provde statstcal propertes of the dsplayed sgnal. In the same famly, the Bode and Nyqust plot blocks can be used to vsualze system propertes and ad the desgn of control systems. The Bode plot dsplays the magntude and phase of the system transfer functon (see Fgure 6), whle the Nyqust block plots real versus magnary parts. H() 2 s + 4s s s s The block dagram and the plot of the smulaton result for a step reference nput are shown n Fgure 7. In the second example, the feedback system contans two transfer functons, one n the forward path and the other n the feedback path. Here, s + 2 H1() s + 3s + 13s +2 2 s + 4s+ 5 H2() s + 6s + 3s + 10 For ths case, the block dagram and the plot of the smulaton result for a step reference nput are shown n Fgure 8.

exercses found n control systems educaton. Its prmary use s envsoned as a dstance learnng tool because of ts ablty to run over the Internet through a smple web browser.

5 feedback system s defned through a GUI edtor by connectng blocks together, mantanng a classcal textbook appearance. Although t lacks the power, effcency, and generalty of manstream commercal software lke MATLAB/Smulnk, J-DSP-C s easy to use and can provde a platform wth suffcent flexblty to smulate the typcal exercses found n control systems educaton. Its prmary use s envsoned as a dstance learnng tool because of ts ablty to run over the Internet through a smple web browser. Furthermore, wth ts open archtecture, J-DSP-C s contnuously mproved wth respect to the collecton of blocks avalable for use n smulatons. Combned wth a report submsson and scorng faclty, J-DSP-C ntegrates nteractve examples nto web content to mprove the qualty and effectveness of control systems educaton. Fgure 7: Block dagram and smulaton results for example REFERENCES [1] A. Spanas et al, Development and Evaluaton of a Web- Based Sgnal and Speech Processng Laboratory for Dstance Learnng, Proc. IEEE ICASSP-2000, Istanbul, Vol. 6, pp , June [2] A. Spanas et al, On-lne laboratores for speech and mage processng and for communcaton systems usng J-DSP, to appear at 2 nd DSP-Educaton workshop, Pne Mountan GA, Oct 13-16, [3] J-DSP on-lne help, Fgure 8: Block dagram and smulaton results for example CONCLUSIONS Ths paper presented the varous enhancements and modfcatons of the J-DSP software tool for use n control systems educaton. Ths new verson, J-DSP-C, s an object-orented programmng envronment, that enables the smulaton of feedback systems n a straghtforward and easy to comprehend manner. The

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