Simulation of Model Based System Design Using Real Time Windows

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1 Simulatin f Mdel Based System Design Using Real Time Windws Engr. Lubna Min, Dr. Shahid Ali, Dr. Vali Uddin Natinal University f Science and Technlgy Pakistan Engineering Cllege, Karachi engr_lubna@yah.cm, shahidali32@yah.cm, v_uddin@htmail.cm Abstract- Real-time systems are lsely defined as the class f cmputer systems that interact with the external wrld in a time frame defined by the external wrld. It is an envirnment where a single cmputer is a hst and a target. After creating a mdel and simulating it with simulink in nrmal mde we can generate executable cdes with real time wrkshp. Here we have used MATLAB as an applicatin tl which prvide us the specialized tl bxes fr specific areas. The real time windw target cmmunicates with the executable prgram acting as a cntrl prgram and interfaces with the hardware device thrugh the I/O prt. Here we tried t analyse a magnetic levitatin system. The cntrl gal is t suspend a steel sphere by means f a magnetic field cunteracting the frce f gravity and t be able t apply a cntrlled disturbance t frce the sphere t fllw a predetermined trajectry. The cntrl t be applied is the vltage, which is cnverted int a current via internal circuitry in the cntrller lcated in the mechanical unit. The current passes thrugh and an electrmagnet which creates a magnetic field in its vicinity. The sphere is placed alng the vertical axis f the electrmagnet after the cntrl system is started in the sftware. In this way a apprach twards real time wrkshp is analysed and applied. Design and fabricatin f a sensr t sense the ball s vertical displacement (height). Design and implementatin f a PID cntrller. Design and fabricatin f an electrmagnet that prvides sufficient magnetic attractin t suspend the metallic ball. Designing and fabricating the actuatr (a vltage cntrlled current surce) t regulate current flwing int the electrmagnet s cil. Simulatin f the cntrller in MATLAB using Simulink. Explring MATLAB s Magnetic Levitatin Mdel. 11. BASIC APPROACH Magnetic Levitatin mdel may be cnsidered as a clsed lp feedback cntrl system, whse basic blck diagram is illustrated in Fig 1. KEY WORDS Magnetic levitatin, PID cntrller, actuatr, sensr, real time MATLAB simulatin 1. INTRODUCTION A. Definitin f Magnetic Levitatin System Magnetic levitatin, maglev, r magnetic suspensin is a methd by which an bject is suspended with n supprt ther than magnetic fields. The electrmagnetic frce is used t cunteract the effects f the gravitatinal frce. Magnetic levitatin may be defined as the prcess f suspending a bdy in free space by cunteracting the frce f gravity acting n it. In simpler wrds it may be termed as the stable suspensin f an bject against gravity.[2] B. Objective f the research The verall bjective f this prject is t levitate a metallic ball by prducing a magnetic field which cunteracts the natural gravitatinal frce. In rder t achieve this gal, the fllwing sub-bjectives need t be accmplished. Fig 1. Blck diagram f Magnetic Ball Levitatin Cntrl System. The plant s utput is the ball s vertical displacement which is sensed by an ptical sensr. Current prduced by the sensr is cnverted t a prprtinal vltage, cmmnly referred t as the sensr vltage, by means f a current t vltage cnverter. The setpint vltage (a knwn reference) is subtracted frm the sensr vltage t generate an errr signal which is acted upn by the PID cntrller. The actuatr is simply a vltage t current cnverter that prduces current prprtinal t the cntrller s utput vltage. Magnitude f this current decides the magnetic field strength and, hence, the upward frce with which the ferrmagnetic ball is attracted. The magnetic levitatin system can be seen t cmprise f the fllwing fundamental elements.[4] A. Plant The electrmagnet alng with the suspended metallic ball may be cllectively termed as the plant.input t the

2 plant is the current flwing in the electrmagnet s cil.the plant s utput is the vertical displacement f the suspended ball. It is wrth mentining that is nt pssible t cntrl the plant while it perates in pen lp. The reasn being its highly unstable nature. B. Sensr The sensr used in this prject is a phtvltaic cell whse shrt circuit current (Isc) varies linearly with light intensity.as the metallic ball is attracted upwards by the electrmagnet it partially cvers the sensr, bringing abut a change in its surface area expsed t the light surce. This actin is depicted by Fig 2. Fig 3. System. Hardware schematic f Magnetic Ball Levitatin. 111 MAGNETIC LEVITATION SYSTEM Fig 2. Diagram illustrating phtvltaic sensr s peratin. The metal ball is under the influence f tw ppsing frces, namely, the dwnward gravitatinal frce and the upward pull f the electrmagnet, as shwn in Fig 1.4. Perfect levitatin is achieved nce these tw frces exactly balance each ther. The ball s vertical displacement is gverned by the fllwing electrmechanical equatin:[3] C. Current t vltage cnvertr The current t vltage cnverter is an peratinal amplifier based circuit that cnverts the phtvltaic cell s shrt circuit current (Isc) t a prprtinal vltage (Vsensr). D. PID Cntrller The PID cntrller acts upn the errr signal generated by subtracting the setpint vltage (Vsetpint) frm the sensr vltage (Vsensr). Prprtinal cntrl ensures that the cntrller utput is prprtinal t the amunt f errr. Integral cntrl takes int accunt the errr signal s time duratin as well as magnitude and cmpletely eliminates steady state ffset. Derivative cntrl ensures that the crrective actin taken by the cntrller is prprtinal t the rate f change f errr. Hence, an early crrective actin is initiated. E Actuatr The actuatr is a vltage t current cnverter that receives an input vltage frm the PID cntrller and cnverts it t a prprtinal current, which excites the electrmagnet.the schematic shwn in Fig3. gives the reader an verview f the hardware details and fundamental cmpnents f the levitatin system. where: m is the ball s mass. g dentes gravity. X is the distance f the ball frm the electrmagnet. I is the current flwing thrugh the electrmagnet. k is a cefficient. FIG4.Mathematical mdel f the Magnetic Levitatin System 1V. PID CONTROLLER A. Intrductin f PID Cntrller

3 A prprtinal-integral-derivative cntrller (PID cntrller) is a generic cntrl lp feedback mechanism widely used in industrial cntrl systems. It attempts t crrect the errr between a measured prcess variable and a desired setpint by calculating and then implementing a crrective actin. The PID cntrller invlves three separate parameters; the Prprtinal, the Integral and Derivative values. The Prprtinal term prduces a respnse that is prprtinal t the errr signal, the Integral term examines the setpint s ffset ver time and crrects it when and if necessary, while the Derivative term prduces an utput that is prprtinal t the rate f change f errr. The sum f these three actins is cllectively termed as PID cntrl.by "tuning" the prprtinal, Integral and Derivative gains, the PID cntrller can be made t prvide cntrl actin in accrdance with specific prcess requirements. The cntrller s behaviur can be described in terms f its respnsiveness t the errr signal, the degree t which the where: Kp is the prprtinal gain Ki is the integral gain Kd is the derivative gain u(n) is the cntrller utput. V. ANALOG IMPLEMENTATION OF THE PID Fig6. PID cntrller s analg implementatin. Fig5. A typical PID cntrl utput vershts the setpint and the degree f system scillatin. B Objective f PID Cntrller in ur research The cntrller s basic functin is t respnd t any variatins in the ball s vertical displacement frm the electrmagnet by taking necessary crrective actins. C Designing f PID Cntrller The PID cntrller reads the errr vltage generated by subtracting a predefined set pint frm the measured variable. Crrective effrt is initiated using this errr vltage in three ways. 1. Prprtinal cntrl ensures that the crrective actin is prprtinal t the amunt f errr. 2. Integral cntrl takes int accunt the time duratin f the errr and cmpletely eliminates steady state ffset. 3. Derivative cntrl ensures that the cntrller utput is prprtinal t the rate f change f errr. The mathematical equatin describing a PID cntrller s behaviur is as fllws: We implemented the cntrller using LM358A IC s instead f the 741 pamp IC. LM358A was the better ptin because it has an advantage f being a dual p amp IC which saves circuit space and the number f ICs required. The PID cntrller was implemented in cascaded frm since all three terms must recieve the errr signal simultaneusly, after which their respnses are summed by means f a summer circuit. V1. TUNING THE CONTROLLER Individual gains f P, I & D were adjusted using ptentimeters t ensure ptimum perfrmance f the cntrller. The prprtinal gain was precisely adjusted t achieve minimum rise time. Hwever, increasing Kp made the transient respnse wrse by intrducing large vershts. Ki was varied t reduce the steady-state errrs and finally Kd was adjusted t imprve unwanted vershts and t decrease the system s settling time.[2] Parameter Rise time Over sht Settling time S.S errr Kp decrease increase Small change decrease Ki Decrease Increase increase eliminate Kd Small change decrease decrease Small change Table 1. Effect f increasing prprtinal, integral and derivative gains

4 cnnected t an A/D cnverter, t sense the steel ball s vertical psitin. The cil is driven by a pwer amplifier interfaced with a D/A cnverter. A pictrial representatin f the mdel itself is given fr further clarity.[2] Fig7.Prprtinal gain Kp n step respnse f cntrller. Fig10. Matlab s Magnetic Levitatin Mdel. Fig8. Effect f variatin f Ki n the step respnse f cntrller V11. SIMULATION OF THE CONTROLLER IN MATLAB USING SIMULINK. The clsed lp cntrl system shwn in Fig belw was simulated in MATLAB and the results clsely analysed. The bjective f this simulatin was t get a better understanding f PID cntrl and the individual effects f prprtinal, integral and derivative terms. Fig 11. Blck Diagram f the Levitatin mdel. There is prvisin t vary the signal s frequency and amplitude as well. Fig 9: Simulink mdel f PID cntrller V111. MATLAB S MAGNETIC LEVITATION MODEL In rder t appreciate magnetic levitatin and t get a thrugh insight int the fundamentals f feedback cntrl, it is wrth explring matlab s Magnetic Levitatin Mdel. This mdel may be accessed by typing vrmaglev n matlab s cmmand windw, as is shwn belw. It may als be accessed frm matlab s virtual reality tlbx. The Magnetic Levitatin Mdel is meant t demnstrate cntrl prblems assciated with nn-linear and unstable systems. It cmprises f a psitin sensr Fig12. Obtained by duble clicking the signal generatr blckset. By duble clicking n the scpe ne can bserve hw the plant s utput tracks the chsen signal. The images that fllw will further clarify this pint.

5 Fig13. The plant s utput trying t track a sinusidal wave. Fig16. Obtained by duble clicking the PID blckset. 1X. REAL TIME WINDOWS TARGET The Real-Time Windws Target brings rapid prttyping and hardware-in-the-lp simulatin.. It is the mst prtable slutin available tday fr rapid prttyping and hardware-in-the-lp simulatin This picture shws the basic cmpnents f the Real-Time Windws Target. Fig 14. The plant s utput trying t track a square wave. Fig17. Real-Time Windws (rtwin) Target Fig 15 The plant s utput trying t track a sawtth wave. By duble clicking n the PID blck, ne can change the cntrller s parameters. These include, KP (prprtinal gain), KD (derivative gain) and KI (Integral gain). Parameter tuning is dne interactively, by simply editing Simulink blcks and changing parameter values. Fr viewing signals, the Real-Time Windws Target uses standard Simulink Scpe blcks, withut any need t alter yur Simulink blck diagram. Signal data can als be lgged t a file r set f files fr later analysis in MATLAB.[3] The Real-Time Windws Target is ften called the "nebx rapid prttyping system," since bth Simulink and the generated cde run n the same PC. A run-time interface enables yu t run generated cde n the same prcessr that runs Windws The generated cde executes in real time, allwing Windws t execute when there are free CPU cycles. The Real-Time Windws Target supprts ver 100 I/O bards, including ISA, PCI, Cmpact PCI, and PCMCIA. Sample rates in excess f 10 t 20 khz can be achieved n Pentium PCs.

6 Fig18. Magnetic Levitatin System Cde Generatin Optimizatins The Simulink cde generatr included with Real-Time Wrkshp is packed with ptimizatins t help create fast and minimal size cde. The ptimizatins are classified either as crss-blck ptimizatins, r blck specific ptimizatins. Crss-blck ptimizatins apply t grups f blcks r the general structure f a mdel. Blck specific ptimizatins are handled lcally by the bject generating cde fr a given blck. Listing each blck specific ptimizatin here is nt practical; suffice it t say that the Target Language Cmpiler technlgy generates very tight and fast cde fr each blck in ur mdel. with the high impedance f the electrmagnet cil and the cnsequent large phase difference between vltage and current. RTWT cmbines the pwerful functinality f MATLAB, Simulink and Real-Time Wrkshp and allws users t implement any kind f cntrl algrithm. REFERENCES [1] On the develpment f a real-time digital cntrl system usingxpc-target and a magnetic levitatin device shiaklas,p.s.;piyabngkarn, D. Decisin and Cntrl, Prceedings f the 40th IEEE Cnference n Vlume 2, Issue, 2001 age(s): vl.2 Digital ObjectI dentifier / [2] Real-time adaptive cntrl using neural gener - alized predictive cntrl Haley, P.;Slway, D.; Gld, B. American Cntrl Cnference, Prceedings f the 1999Vlume 6, Issue, 1999 Page(s) : vl.6 Digital Object Identifier /ACC [3] Develpment f a real-time digital cntrl system with a hardware-in-the-lp magnetic levitatin device fr reinfrcement f cntrl educatin Shiakl as, P.S.; Piyabngkarn, D.Educatin, IEEE Transactisn Vlume 46, Issue 1, Feb 2003Page (s):79-87digital Object Identifier /TE [4] Real Time Windws Targrt fr mdelling, Simulatin and Implementatin.User Guide versin 2. by MathWrks,Inc. Fig19. Mdel fr Cntrlling Magnetic Levitatin System RESULTS AND CONCLUSION The cntrl gal f suspending a steel sphere by means f a magnetic field cunteracting the frce f gravity, and t be able t apply a cntrlled disturbance t frce the sphere t fllw a predetermined trajectry is achieved using Real time Matlab Simulink tl. In peratin the cntrl utput frm the I/O bard in the PC is a vltage, but the magnetic levitatin unit cntains inbuilt vltage t current cnverter circuitry. The electrmagnetic is therefre driven with a current utput surce and the system avids the prblems assciated