CONTROL SYSTEMS ANALYSIS & DESIGN SERVER. F. Morilla*, A. Fernández +, S. Dormido Canto*

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1 CONTROL SYSTEMS ANALYSS & ESGN SERVER F. Morilla*, A. Fernández +, S. ormido Canto* * pto de nformátia y Automátia, UNE, Avda. Senda del Rey 9, Madrid, Spain. Phone: , Fax: , fmorilla@dia.uned.es; sebas@dia.uned.es + nstituto de Automátia, Faultad de ngeniería, Universidad de San Juan, Avda. Libertador General San Martín 1109 Oeste, 5400 San Juan, Argentina. arnoldo@inaut.unsj.edu.ar; afernandez@dia.uned.es Abstrat: This paper desribes an implementation of the tool SSTEMAS in order to use as WWW Server for analysis and design of ontrol systems. t an be used via an ntranet or nternet, alone or integrated in the virtual and remote ontrol laboratory. This laboratory is being developed in the nformátia y Automátia epartment of UNE. The tool overs widely the key onepts of Automátia (an annual ourse of feedbak automati ontrol. t has been used sine the aademi year 94/95 as support material in the subjet and in one of the pratial sessions that take plae in the laboratories of the Faultad de Cienias (Sienes Faulty of UNE. With the new idea of WWW servie, the student ould be able to use the tool as many times as he needs (to study or to take a pratial session from his house or from his Assoiated Centre; he will need only an nternet onnetion. Copyright 2001 FAC eywords: Compensation, omputer-aided ontrol system design, laboratory eduation, distane learning. 1. NTROUCTON Sine 1994 the nformátia y Automátia epartment of UNE has a CACS (Computer-Aided Control Systems esign tool that makes easier the design of linear feedbak ontrol systems in Matlab-Simulink (ormido Canto, 1994; Morilla, et al., 1994; Morilla, et al., The tool overs widely the key onepts of Automátia (an annual ourse of feedbak automati ontrol and sine aademi year 94/95 has been used with the name SSTEMAS, with suessfulness between the students (approximately 70 students per year, in one of the pratial session of the subjet (ormido Canto, et al., n the same ourse, it was removed its dependene of Simulink and it was made an implementation for the student version of Matlab 4.0 in order to use it in the students s home, previous request to the teahing team. Sine the aademi year 99/00 the tool is inluded as support material in the C-ROM edited with the guidebook ourse of the Faultad de Cienias of UNE. Sine 1999, the epartment is working in the projet of news virtual an remote laboratories for the distane learning of automati ontrol, whose results has been presented in (ormido, et al., 2000; Sánhez, et al., Sine 2001 the projet has a little finaning for next three years within the Researh s Promotion Plan of the UNE This paper desribes an implementation of the tool SSTEMAS in order to use as WWW Server for analysis and design of ontrol systems. t an be used via an ntranet or nternet, within the new onept CSAS (Control Systems Analysis & esign Servers, alone or integrated in the virtual and remote ontrol laboratory of the nformátia y Automátia epartment. To implement the tool in Matlab Web Server have been neessary signifiants hanges in the *.m files and a full development of the new interfae, based on dynami HTML pages. But also its funtionality has been inreased in order to report the designs and to make easy the evaluation of the pratial sessions. 50 students have used the server this aademi year via the ntranet of the Faultad de Cienias (Siene Faulty of UNE, but also some students and the teahing team have tested it from their houses. A overview of the SSTEMAS s features is shown in setion 2. The harateristis of the Web version of SSTEMAS are desribed in setion 3. Where also is mentioned the usual sequene of a pratial session.

2 Finally the paper is ompleted with the onlusions in setion FEATURES OF SSTEMAS Given a proess model and established the ontrol system speifiations, the SSTEMAS tool is able to advise about the ompensator type and to find the analytial solution. SSTEMAS uses the design methodology summarised in setion 2.1, desribed with more detail in (ormido Canto, 1994; Morilla, et al., The following general features delimit the sope of the tool: - The ontrol system an be analog (ontinuoustime, disrete (disrete-time or digital (sampleddata, with unity feedbak gain, as it is shown in Figure 1. - The proess model and the ontroller are desribed by their transfer funtions. Both transfer funtions are ontinuous when the ontrol system is ontinuous and disretes when the ontrol system is disrete-time. But if the ontrol system is digital, the proess transfer funtion will be ontinuous and the ontroller transfer funtion will be disrete. - The ontrol system speifiations ombine steadystate auray (steady-state errors for unit step and for unit ramp and the relative stability (phase margin and gain margin. - The ompensator to design an be: a P ontroller or its alternatives (P, P, a lead network (LEA or a lag network (LAG. This is shown in Table 1. Fig. 1. Control systems onsidered in SSTEMAS. The tool also allows to analyse the ontrol system, with a view to the subsequent design or to hek the latest design. The analysis omprises: the step response (of the proess, of the ontrol system, the open-loop frequeny response (Bode and Nyquist plots and the root lous. Therefore, the stability and the main features of the design are studied. An example is illustrated in Figure 2. Table 1: Continuous and disrete transfer funtions of the ompensators z Lead-lag network s +1 so s +1 o zp sp z +1 ( 1+ z p zo ( 1 + z zo + 1 zp P 1+ Fig. 2. An example of analysis. P P ontroller T s T s T 2 T z +1 2 T + z -1 T z -1 z esign with SSTEMAS. Any ontrol system must be stable, and so the stability is one of the main speifiations in the ontrol system design. n addition to the absolute stability, a ontrol system must have an adequate relative stability; that is to say, the transient system response must be relatively fast and with small overshoot. The ontrol system must also gets good traking auray. The relative stability and the steady-state auray are sometimes inompatible speifiations; hene a trade-off is needed between these onfliting requirements. The SSTEMAS tool approahes the automati ontrol system design in two steps: 1º Steady-state error ompensation: as the proedure that, given a proess and the steady-state speifiations, selets the set of possible ompensators and determines the value of some ontrol parameters. 2º Compensation by phase margin: as the proedure, next to the steady-state error ompensation, that selets the more adequate ompensator and determines the remainder of ontrol parameters in order to get the speified phase margin (PM (Phillips and Harbor, 1991; Saadat, The

3 ompensator seletion is sometimes onditioned by the speified gain margin (GM. Table 2 shows all possible ases of steady-state ompensation with the ompensators onsidered in SSTEMAS, they are grouped in two families, (LEA, LAG, P and (P, P, beause: - The lead-lag network and the P ontroller allow to modify the finite error of the unompensated ontrol system seleting appropriately one of its parameters, the d gain or the proportional gain P respetively. - The P and P ontrollers allow anel the finite error of the unompensated system, and its integral gain P /T an be used to get a finite and steady-state error of upper degree. Table 2: Possible ompensators for the steady-state error ompensation unompensated system ompensated system possible ompensators unit step unit ramp unit step unit ramp finite and unbounded finite and unbounded LEA,LAG,P finite and unbounded zero finite and P, P zero finite and zero finite and LEA,LAG,P zero finite and zero zero P, P zero zero zero zero LEA,LAG,P P, P n Table 3 the ompensation formulas by phase margin for ontinuous ontrol systems are shown, they were proposed by Phillips and Harbor (1991 and an also be used for disrete and digital ontrol systems in the bilinear transformation domain. G(j is the frequeny response of the proess and θ is the angle that the ompensator must ontribute in order to get the desired phase margin PM desired at the frequeny. ts value is given by θ PM desired 180º - arg(g(j (1 To use the formula of Table 3 it is neessary to have the frequeny design seleted and without any restritions to the ontrol parameters (, so y sp in lead-lag network ase; P, P /T and P T in P ontroller ase. But this is not the usual situation in SSTEMAS, beause is still unknown and also beause previously, as onsequene of the steady-state ompensation, the parameter of the lead-lag network, the P parameter of the P ontroller or the parameter of the P or P ontrollers has been determined, but the ompensator is still unseleted. Therefore the ompensation by phase margin in SSTEMAS inludes also the seletion of the ompensator, one between the members of the family (LEA, LAG, P or (P, P, and the determination of the frequeny range for (Saadat, Leaving as degree of freedom the seletion of the design frequeny, joined with another degree of freedom (the seletion of the integral gain or the derivative gain when the ompensator is P and its integral gain is not determined by the steady-state ompensation. Table 3: Compensation by phase margin Lead-lag network s o 1 osθ G(j s p osθ G(j P P ontroller osθ G( j G(j 2.2 Types of design. SSTEMAS offers three types of design. They differ in the degrees of freedom allowed the user. n AUTOMATC ESGN, the user don t has degrees of freedom, the seletion of the ontroller and the seletion of the design frequeny are made by the appliation. n MANUAL ESGN, the user ould be able to hoose the ompensator (one of the ontrollers that an ompensate the steady-state errors, the design frequeny (inside the frequeny range of possible solutions and the integral gain or the derivative gain if it would be neessary. The AE ESGN is an intermediate hoie, where the user hooses the design frequeny and the appliation selets the ontroller with the following riteria: P or P: just when the PM of the unompensated system is less than the PM desired, the P ontroller is seleted. (LEA, P or LAG: just when the PM of the unompensated system is bigger than the PM desired, the LAG network is seleted. LEA or P: just when the GM of the unompensated system is less than the GM desired, the P ontroller is seleted. SSTEMAS inludes the following rules in order to selet automatially the design frequeny: LEA, LAG, and P without ondition on P, P or P without ondition on : is seleted as the geometrial mean of the frequeny range extremes. P with ondition on : is seleted as the maximum value of the frequeny range that verifies also the equation: G(j + 0 (2 P with ondition on P : is seleted as the minimum value of the frequeny range that verifies also the equation: G(j osθ 0 (3 P

4 P with ondition on : is seleted as the minimum value of the frequeny range that verifies also the equation: sen 0 θ < + < G(j (4 t inludes also the following rules in order to selet automatially the integral or derivative gain when the ompensator is P without ondition on : f θ<0: is seleted as 20% upper the minimum possible, to be exat -1.2 (5 G(j f θ>0: is seleted as 20% upper the minimum possible, to be exat 1.2 (6 G(j 3. THE WEB VERSON OF SSTEMAS The main objetive of SSTEMAS projet in 1994 (Morilla, et al., 1994 was to develop a tool in Matlab for that beginning students in feedbak ontrol (students of Automátia ould be able to analyse and design linear ontrol system without have need of programming in Matlab, and only being enough with a minimum knowledge of its syntax. Nevertheless the user will need to have a Matlab version (the student fourth edition or upper. Sine then the tool has experimented several small hanges, mentioned in setion 1, and nowadays there is an implementation on version 5.3 of Matlab. However this work desribes the most important hange of SSTEMAS. This hange is beause of that the nformátia y Automátia epartment shows a onstant onern to give a ontrol teahing of quality and fitted to the new tehnologial hallenges. So, the Web version of SSTEMAS presents another advantages in relation to the loal version: The users will not need to have Matlab. They only need a standard and user-friendly browser. The teahing team of Automátia an shedule some praties that the students an make from their houses whenever and how they want, without timetable. Only there is a working opy of the tool, whih is in the server of the epartment. So, its maintenane and improvement an be almost ontinuous without disturb the users. At the same time is very easy to have a ontrol on the aess. The new version of SSTEMAS has all the original funtionality, where only the interfae has been hanged to dynami HTML pages. But it also inludes new funtionality in order to make easy to the teaher the evaluation of the student s designs. One of the most representative HTML pages of SSTEMAS is the Work Station page, see Figure 3, that shows the diagram of the ontrol system (analog, disrete or digital seleted in that moment and offers the following six options: Type of system: With this option the user will aess to the page of Figure 1, where he ould be able to hange the ontrol system. Configuration: This option allows the user aess to the HTML page where he an hek and hange the transfer funtions of the proess and the ontroller, and the sample time when the ontrol system is disrete or sampling. Analysis: This option presents some features of the ontrol system (stability, steady-state errors, phase margin and gain margin, an example is shown in Figure 2, leaving to the user another options of analysis (step response, frequeny response and root lous. Besides the user has an option to request a more omplete analysis, where he will be able to see the step response, the Bode plot and the root lous in the same HTML page. esign: This option provides information about the steady-state errors of the unompensated system and of the urrent ontrol system. Allowing the user: request a new design (with the same or different speifiations, selet the type of design or return to the Work Station. See as example the Figure 4. Report: This option allows the user to doument his designs. Exit: to quit the program. Fig. 3. A snapshot of the Work Station when an analog system is seleted. Another representative page HTML of SSTEMAS is the esigned Controller, see Figure 5, where as onsequene of the design, the user reeives information about the ontroller transfer funtion, its parameters and an automati justifiation of how the solution has been reahed. He an return later to the esign page for test if the speifiations have been ahieved, but also he has the option of make a omparative analysis between the unompensated system and the ompensated system.

5 Fig. 4. A snapshot of esign page after to make a manual design. Fig. 5. A snapshot of the esigned Controller page. Fig. 6. Example of report generated by SSTEMAS n Figure 6 an example of a report generated by SSTEMAS is shown: it onsists of a HTML page with outstanding information of the last design, the name of the user and a field with the omments that the user had wanted inlude. The user has then the option of print the report from the browser, but also he has the option of save the assoiate information of the report in his omputer. These types of reports have as aim that the student an doument the designs of a pratial session. But in addition, if the student have been onerned about to save one report by eah design, the teaher ould hek and evaluate them using the part of SSTEMAS developed with this purpose, the teaher only needs to know the user ode assigned to eah design. 3.1 Pratial session. The Web version of SSTEMAS is ready for use in spanish or english language. Next the usual sequene of a pratial session with it is desribed: Starting the session: The user aess to the way in HTML page of the server, see Figure 7, where after to selet the language he an start a session or retrieves a session that he had suspended by some reason. The last one is possible beause all session in SSTEMAS has assoiated a user ode. Seletion, onfiguration, analysis and design of the ontrol system: The user aess to the Work Station page of Figure 3, where he an unhain all the tasks aimed at the design of the ompensator. Reporting the design: From the Work Station page the user must generate the session report when he thinks over that the urrent design is the most suitable to the aims of the pratial session. Quiting the session: The user goes away from SSTEMAS and notes down the user ode just in ase he deides retrieve the session in another time.

6 Fig. 7. The way in page of SSTEMAS. 4. CONCLUSONS The ountless examples of design made by de students and by the teahing team of Automatia with SSTEMAS prove the great utility of this type of tool for teahing aims. With the version presented in this work, its utility is extended even more beause: - t is not mandatory that the users have Matlab in their omputers. - The new interfae is more user-friendly for anyone that had used sometime a standard Web browser. - The user ould aess at any moment and from anywhere to the last version of the tool (the only one, really available. - The teahing team will have more flexibility to shedule a set of pratial sessions, as well as for its pursuing and evaluation. - The nformátia y Automátia epartment of UNE an integrate it as another pillar of the virtual and remote laboratory of Automati Control, allowing the aess to the students of another subjets and of another universities. - The maintenane and improvement of the tool an be almost ontinuous without disturb the users. Ros and F. Vázquez (2001. Guiones de Prátias de la asignatura: Automátia. Revisión pto. de nformátia y Automátia, UNE. Morilla, F., S. ormido Canto and S. ormido (1994. iseño de Controladores en el entorno MATLAB-SMULN. Jornadas de Automátia, Málaga. Morilla, F., S. ormido Canto and S. ormido (1995. Herramienta para el análisis y diseño en el entorno Matlab-Simulink. MATLAB 95 Congreso de Usuarios de Matlab, Madrid. Phillips, C. L. and R.. Harbor (1991. Feedbak Control Systems, Seond Edition. Prentie-Hall nternational, n. Saadat, H. (1993. Computational Aids in Control Systems Using MATLAB. MGraw-Hill nternational Editions, Eletrial Engineering Series. Sánhez, J., F. Morilla, S. ormido, J. Aranda and P. Ruipérez (2000. Coneptual Learning of Control by Java-based Simulations. FAC/EEE Symposium on Advanes in Control Eduation (ACE 2000, eember, Gold Coast, Australia. ACNOWLEGEMENTS The authors wish to aknowledge to the Universidad Naional de San Juan (Argentina and to the UNE by allow and finane the stay of leturer A.W. Fernández in the nformátia y Automátia epartment. REFERENCES ormido Canto, S. (1994. Proyeto de diseño y ajuste de ontroladores en el entorno Simulink. Esuela Ténia Superior de ngenieros ndustriales,.c.a.., Mayo. ormido, S., J. Sánhez, and F. Morilla (2000. Laboratorios virtuales y remotos para la prátia a distania de la Automátia. Sesión Plenaria, XX Jornadas de Automátia. Sevilla 18, 19 y 20 de septiembre. ormido Canto, R., S. ormido Canto, N. uro, R. Hernández, J.C. Lázaro,. López, F. Morilla (Coordinador, R. Pastor, A. Pérez de Madrid, S.