How to Shorten First Order Unit Testing Time. Piotr Mróz 1

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1 How o Shoren Firs Order Uni Tesing Time Pior Mróz 1 1 Universiy of Zielona Góra, Faculy of Elecrical Engineering, Compuer Science and Telecommunicaions, ul. Podgórna 5, , Zielona Góra, Poland, phone , Fax , p.mroz@iie.uz.zgora.pl Absrac- One of he mehods of shorening he response ime of firs order inerial device is using he sep signal wih overshooing. In he aricle i is discussed he source of sep signal wih overshooing wih one calibraor and wih wo calibraors and analog muliplexer. There are described resuls of simulaion ess of he response ime on inpu signal from boh sources. Resuls of ess proved accuracy of he soluions proposed. I. Inroducion Developmen of engineering of he measuring equipmen involves increasing reques for esing devices used for verificaion of performance of he measuring equipmen on he producion line. Tesing is based on he suiable conrolling of seleced parameers in specified condiions [1]. I is very imporan o reduce coss by shorening of esing ime and reducing esing sysem price. Modificaion of exciaion signal form is one of mehods of shorening he response ime. The exciaion signal sources are very expensive and difficul in handling. The devices response ime can be shorened by consraining suggesed signal form. Using he signal source wih one calibraor or using signal source wih wo calibraors and analog muliplexer allows generaing his signal. This mehod makes possible o shorening device response ime. II. Sep signal wih overshooing Applicaion of he sep signal wih overshooing, shown on figure 1 allows o shoren ime response of firs order inerial device [2]. P Figure 1. Sep signal wih overshooing 428

2 Theoreical maximal shorening of he objec ime response is achieved, when he equaion (1) is fulfilled [4]. P T ln 1 = K P (1) where: P overshooing ime, T objec ime consan, sep signal ampliude afer ime P, overshooing ampliude. Overshooing ampliude mus be of he maximal value ha would no desroy he objec under es. For his overshooing ampliude he overshooing ime P is obained from equaion (1). III. The sep signal source wih calibraor Sep signal wih overshooing can be obained eiher from a single calibraor or from wo calibraors and analogue muliplexer. A. Source wih a single calibraor Figure 2 shows sep signal source wih overshooing wih a single calibraor. I consiss of a calibraor and a conroil uni. Calibraor Tesed device Y N Conrol uni Figure 2. Sep signal source wih overshooing wih one calibraor To he inpu of he calibraor i is given a se N P, corresponding o he oupu signal of ampliude. Afer ime P, seing is changed o N K, corresponding o he oupu signal of ampliude. Theoreically on he oupu of he source one should ge he signal abou he shape shown on figure 3 (curve 1). In he real condiions one ges he signal abou he shape shown as curve 2. These resuls from dynamic characerisics of he calibraor, being a second order inerial uni [3]. On figure 4 here are shown objec responses o ideal inpu signal (curve 1) and real inpu signal (curve 2) compared o objec responses o sep inpu signal (curve 3). Giving he real inpu signal o he objec inpu causes exension of is ime responses. Shorening of he ime response, wih using real inpu signal, can be achieved eiher by shorening of overshooing ime P (curve 3, figure 3), so ha he objec answer would be conforming o curve 4 on figure 4 or by use of calibraor wih smaller values of he ime consans. 429

3 curve 3 curve 2 curve 1 P Figure 3. Sep signal wih overshooing wih one calibraor Y curve 2 Y K curve 1 curve 4 curve 3 P Figure 4. Response of esed objec o he sep signal wih overshooing 43

4 B. Source wih wo calibraors To generae he signal wih he shape approaching he ideal signal i is proposed a circui shown on figure 5. This circui consiss of wo calibraors, an analog muliplexer and a conrol uni. Calibraor 1 Analog muliplexer Tesed device Y Calibraor 2 N P N K swich Conrol uni Figure 5. The circui of he source wih wo calibraors generaing he sep signal wih overshooing Calibraor 1 is supplied wih se N P. I corresponds o oupu signal wih ampliude. Calibraor 2 is supplied wih se N K. I corresponds o oupu signal wih ampliude. Afer ime P he analog muliplexer swiches he signal from value o value. The signal generaed by he sep signal wih overshooing source wih wo calibraors is shown on figure 6. Shape of his signal is nearly ideal and any differences resul from dynamic characerisic of analog muliplexer. The objec answer (curve 2) o he signal from signal source wih wo calibraors is shown on figure 7. The objec ime response o his signal is close o overshooing ime P. Figure 6. The shape of inpu signal P 431

5 Y curve 2 Y K curve 1 curve 3 P Figure 7. Response of he objec o he exorion from signal source wih wo calibraors IV. Tesing Verificaion has been made by compuer simulaion wih MahLab and Simulink. The es was carried ou for differen values of objec ime consan T and for differen values of overshooing ampliude and overshooing ime P. The ess resuls are shown on figure 8. objec ime response O [s] objec ime response on ypical sep signal overshooing ampliude overshooing ime P [s] Figure 8. Objec ime response in funcion of overshooing ampliude and overshooing ime P 432

6 They confirmed he accuracy of he equaion (1). The horizonal surface indicaed by black edges illusraes he objec ime response on he sep signal. There were performed ess of objecs ime response for differen values of objecs ime consan T and for differen values of overshooing ampliude and overshooing ime P calculaed from he equaions (1). Resuls of es confirmed ha he using of he sep signal wih he overshooing makes possible shorening of he objecs ime response up o seveny imes. V. Conclusions Proposed shape of he sep signal wih he overshooing allows shorening considerably he ime response of he firs order inerial objecs. There is presened relaion beween signal parameers in he funcion of he objec ime consan. In he aricle here is analyzed a mehod of generaing of such signal from he source wih one calibraor and source wih wo calibraors and he analog muliplexer. Resuls of simulaions research showed ha he signal generaed by he source wih wo calibraors and he analog muliplexer is nearly ideal, bu is cos is much higher han he cos of he source wih one calibraor. References [1] J. Gajda, M. Szyper: Modelowanie i badania symulacyjne sysemów pomiarowych. Firma JARTEK S.C., Kraków, [2] P. Mróz, Analiza wpływu wybranych paramerów sygnału wymuszającego na czas odpowiedzi obieku, Maeriały konferencyjne KNWS 5, 25. [3] J. Szmykiewicz, Analiza możliwości poprawy paramerów merologicznych kalibraora uniwersalnego napięć i prądów sałych i przemiennych, Rozprawa dokorska, Zielona Góra, 2. [4] P. Mróz, Pewien sposób skrócenia czasu odpowiedzi urządzenia, Maeriały konferencyjne MKM 5,

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