Elektronika 2012-08 I.pdf - Instytut Systemów Elektronicznych

Fig. 6. Control quality deterioration index β for the suboptimal matricesS s(α) and S s0Rys. 6. Wskaźnik β pogorszenia jakości regulacji dla suboptymalnychmacierzy S s(α) oraz S s0As the use of a suboptimal controller with parameters dependenton the state of the system is unacceptable, therefore theapplication of constant S smatrix denoted S s0has been analysed,and S s110and S s220have been given their average values over α:901Ss110=Ss11= ∫Ss11( α)dα180−90(13)901Ss220=Ss22=∫Ss22( α)dα180−90The diagram in Fig. 6 presents the deterioration index β, determinedfor both the gain matrix S swith variable elements and thegain matrix S s0with averaged elements. The β index for S s0matrixat the plane of initial states of inputs (u p1, u p2) is shown in Fig. 4.It results from the diagram in Fig. 6 that for positive α, the indexβ deteriorates (rises) less than 1.3 times, which is relativelynot much. Positive α corresponds to the deviations of u p1and u p2of the same polarity, while for the deviations of opposite polarity(α 0. The essential a few days’ long crystallizationphase requires very slow temperature changes, and fromthe control point of view it can be treated as a stabilization. Thecases in which the significant changes of power for α < 0 occurcan happen in emergency states, e.g. after the heating power decay.According to the initial assumptions the performance index,the deterioration for such untypical states is acceptable.As mentioned before, during the furnace designing a strongradiation coupling between the bottom of upper heater and thetop of lower heater at crystallization temperature level had beenassumed. In lower temperatures this coupling is weaker, whichcauses an additional deterioration of performance index in relationto the control with the additional temperature measurementsof the top of the lower heater x 5. It concerns e.g. the preliminaryphase of the process, when the filling of the vacuum chamber withtechnological gas having a controlled temperature above 1000°Coccurs. However, the analysis has proved that the above-discussedcontroller can work well at this level too.Equation (8) describes a simple proportional controller (P).In the real system the structure corresponding to this controllerhaving two independent control loops is retained, but with PIDalgorithms substituted for P.14The furnace temperature controller is based on a PLC controller.As the PID loops commercial controllers are used. The mainPLC controller, according to the temperature program of the crystallizationprocess, sends the actual set values to the PID controllers.Its other task is changing the dynamic parameters of the PIDloops according to the actual temperature level. As the measuringrange of the applied two-colour pyrometers is above 900°C, sobelow this level the main controller works with open loops. Theauto-tuning functions of the PID controllers enable to tune thewhole controller to various temperature levels. The main controlleris provided with autodiagnostic function also.Temperature control of the plantThe computer controlled system for SiC monocrystallization describedin the paper is intended for R&D works in SiC crystallizationtechnology. The goals of these works are a significant improvementof the process productivity and of the quality of crystals.The tests of this system in the production conditions have provedthat it meets all requirements.Fig. 7 shows a typical programmed temperature diagram beforethe crystallization process and during the beginning of thisprocess. The temperature level is reached with an overshoot lessthan 2.5°C. The state when the temperature is approaching theworking level corresponds to positive initial angle α (Fig. 6). In thenext phase the pressure is reduced from 500 mbar to 50 mbar.Fig. 7. Programmed temperature control before and at the very beginningof the monocrystallization processRys. 7. Regulacja temperatury programowana dla faz przed procesemmonokrystalizacji i dla początku tego procesuFig. 8. Dynamic response for α < 0Rys. 8. Odpowiedź dynamiczna dla α < 0Elektronika 8/2012