MICROPROCESSOR SYSTEM DESIGNATED FOR CONTROL PNEUMATIC ACTUATOR

Transcription

1 MICROPROCESSOR SYSTEM DESIGNATED FOR CONTROL PNEUMATIC ACTUATOR *Přemysl MATOUŠEK *Technical University of Liberec, Faculty of Mechanical Engineering, Department of Applied Cybernetics Studentská 2, , Liberec, Czech Republic Phone: + (420) , premysl.matousek@tul.cz This article describes the design of the electric circuit which is intended for the control of the piston position of the pneumatic cylinder. The designed circuit includes a range of peripheral circuits that not only enable to join the indispensable sensors but also to control the electro - pneumatic valves. The central component of the whole circuit is a 32- bit microcontroller Atmel AT91SAM9G20 of ARM9 architecture in which there is an implemented control algorithm. The position control of pneumatic cylinder is designed in the state space and is realized by means of a predictive controller of which part is an online identification of pneumatic system parameters and a reduced - order observer using it the process of state vector is estimated. Keywords: pneumatic system; microcontroller; controller; state space; 1 INTRODUCTION The pneumatic systems composed of a pneumatic cylinder and a valve are integrated and nonlinear systems at which the nonlinearity is caused mainly by the friction and the compressibility of the air. These systems are also characterized by a very fast response to the control signal. If the high sampling period should be gained, during which the control algorithm should be in the progress, there are great demands on the computing speed of the control technique. When the industrial computers, for example such as the NI PXI real - time system, are used for the control of the systems, it is not necessary to pay close attention to this demands, because these computers usually have enormous computing speed. In the case that the system should by controlled by the microcontroller it is on the other side important to pay attention to the choice of the microcontroller and chose the microcontroller depending on the demands of the chosen control algorithm and the demanded minimal sampling period. On the basis of the reached results [7] were chosen the predictive controller without the limiting conditions together with the online identifications of the parameters and with the reduced - order observer. The minimal sampling period of the control algorithm was experimentally determined, approximately to 350Hz. On the basis of this period the microcontroller Atmel AT91SAM9G20 was chosen. The pneumatic system including the design of the predictive controller without the limiting conditions and the design of the electric circuit are briefly described in the next several paragraphs. 2 PNEUMATIC SYSTEM The pneumatic system consists of the pneumatic cylinder with one - side piston rod and with the up-stroke of 960mm, a proportional directional control valve MPYE 5 1/8 HF B, a proportional pressure regulator VPPM 6L L L10H - A4P - S1C1 and an on - off valve HEE - D- MINI - 24 with the filters (Compressed air preparation). The position of the piston rod is measured by the displacement encoder with the 1000mm measurement length. The power supply of the system is realized by the power supply 24V/2,5A. This voltage serves for power supply the on - off valve, the proportional pressure regulator and the proportional directional control valve and it is also regulated to 10V voltage, by which the displacement encoder of the position is supplied. This displacement encoder is connected with the piston of the pneumatic cylinder and the voltage in the extent from 0 10V on the slider appropriate to the position of the piston. The air from the air compressor is brought to the input of the on-off valve, through which the air supply to the whole system is switched on or off and it is switched on by the 24V. Constant pressure in the system is ensured by means of the proportional pressure regulator and it is controlled by the current in the extent from 4-20 ma. When the air pressure is set to the required value, the air is brought to the input of the proportional directional control valve. This valve controls the flow of the air in to the working chambers of the pneumatic cylinder and it is controlled by voltage 0-10V. The system further contains of two pressure sensors DMP 331 that measure the running pressure over and below the piston and they also generate the 1

2 current in the extent from 4 20mA. The scheme of pneumatic components connection is shown in the Fig.1 and the pneumatic system is shown in the Fig. 2. Figure 1: Scheme of pneumatic components connection Figure 2: Pneumatic system 3 DESIGN OF CONTROLLER OF PNEUMATIC SYSTEM The pneumatic system control is realized adaptively and the control structure can be divided into three individual parts an online identification of model parameters, a reduced - order observer and a predictive controller. During the design of the online identification parameters it was necessary at first to determine the model structure and after that the algorithm of online identification. When determining the model three models in total were compared, ARX, ARMAX and Box-Jenkins. The last mentioned model cannot be used for the online identification because the error of the identification was to large with this model in comparison with the ARX and ARMAX models. At the choice of the suitable algorithm of identification the RLS algorithm with exponential forgetting, the RLS algorithm with fixed directional forgetting, the RLS algorithm with adaptive directional forgetting, the recursive method of instrumental variable for the ARX model were compared and for the ARMAX model the RELS and RPEM algorithms were compared. On the basis of the results of the comparison of these algorithms mentioned above the most suitable model for the online identification of the pneumatic system is the ARX model with the RLS algorithm with adaptive directional forgetting and the ARMAX model with the RPEM algorithm. With the identification with these algorithms the estimated parameters are not deviated and they are also more stable if the pneumatic system is not waken 2

3 sufficiently. The lack of the permanent waking usually leads to the numeric instability of the algorithms and so on the basis of this viewpoint finally the ARMAX model together with the RPEM algorithm were chosen for the online identification of the parameters. As the state controller minimizes the components of the state vector according to a quadratic criterion, the observer that ensures the observe of the state vector progress is also a part of the control algorithm. For the description of the pneumatic system in the state space the canonic form was chosen, Observer normal form of which structure was determined from the discrete ARX and ARMAX models structure. As the first state vector component, the measured piston position, does not have to be observed, it was chosen the reduced - order observer for the observe of the state vector. So the state vector is then composed of three components of which only two are observed and the component that is not observed is the measured piston position of the pneumatic cylinder. The last part of the control algorithm is the predictive controller that is nowadays often used in practise for the control of various technological processes. The predictive controller can be designed both without and with limiting conditions. The version without limiting conditions was implemented into the microcontroller because at the microcontroller with the limiting conditions there is the computation of control action converted to exacting quadratic programming task. At the high sampling period also the industrial computers have problems with the computation of the control action and thus it would not probably possible to realize this computation in the microcontroller. The predictive controller is based on minimize the certain quadratic criterion in which the predicted output is included, the criterion in form by the Eq.1 was chosen for the control of the pneumatic system [4]: N2 Nu i= N 1 i=1 J u = [ y k i w k i ]T Q[ y k i w k i ] u T k i 1 Ru k i 1, (1) where N1 and N2 are the minimum and maximum costing horizons, Nu is the control horizon, u k i 1 is the vector of control action, y k i is the vector of predicted output, w k i is the vector of future trajectory, R and Q are the weighting matrices. During the control of the pneumatic system in each sampling period the new estimates of the discrete model parameters are calculated and as soon as these estimates are gained the state matrices and the matrices of the reduced - order observer are updated. When the updating is finished the calculation of the control action of the predictive controller by means of Receding Horizon Control method follows. The scheme of the control with the predictive controller is shown in the Figure 3. Figure 3: Scheme of control of pneumatic system 4 DESIGN OF MICROCONTROLLER SYSTEM The microcontroller represents the central element in the designed circuit thus such microcontroller has to be chosen of which output would be sufficient for the computation of the control action at high sampling period. At present it is possible to chose from a huge variety of microprocessors (Atmel, Microchip, Texas Instruments, ), from these it was chosen at first a 32 - bit microcontroller of architecture ARM7 Atmel AT91SAM7256 with the 50 MIPS at 55MHz performance. The algorithm of the controller was written in programming language C and at the implementation of the algorithm the program code was optimized from 3

4 the point of view of the computational speed so that the highest sampling period would be gained. Unfortunately, despite the executed optimization of the program code it was gained the maximal computational speed in the range from 110 to 120Hz with the microcontroller Atmel AT91SAM7S256. This frequency is insufficient for the control of the pneumatic system and therefore was chosen the microcontroller of architecture ARM9 Atmel AT91SAMG20. The performance of this microcontroller is 400 MIPS at 400MHz and at the control of the pneumatic system the maximal sampling frequency 800Hz was gained. This frequency is absolutely sufficient for the system control of the pneumatic system and so this microcontroller is a part of the designed electric circuit. The next parts of the electric circuit are the peripheral circuits that enable for one thing to process the signals from the sensors and for another to control the electro - pneumatic components. For switching the voltage 24V, thanks to which the on-off valve (Compressed air preparation) is controlled, the relay with the NPN transistor is used, its base is joined to the microcontroller pin. The proportional pressure controller is controlled by current 4-20mA, for that reason the demanded pressure value is at first converted to voltage by means of the multichannel D/A converter and then this voltage is converted to the demanded current by means of the U/I converter. The second channel of the D/A converter is used for the control of the slide inside of the proportional directional control valve. This valve is controlled by means of voltage 0-10V and so the output voltage of the D/A converter is amplified to the demanded value by means of the operational amplifier. The voltage value in the range from 0 to 10 V corresponds with the piston position of the pneumatic cylinder. And since it is possible to convert the voltage in the range from 0-2,5V to the input of the multichannel D/A converter, the voltage from the displacement encoder is adjusted by the voltage divider to the proper range of this converter. The working pressures inside the pneumatic cylinder are measured by means of two pressure sensors of which the output signal in the range from 4 to 20mA is converted to the I/U converter to the voltage of 0-5V range. This voltage is then adjusted by the voltage divider to the proper range of the A/D converter and after that it is transferred to two channels of this converter. The communication with the computer is realized by means of RS and if it is necessary the user can set the parameters of the control algorithm by the user program written in programming language C#. The simplified scheme of the designed circuit is presented in the Figure 4. Figure 4: Scheme of electronic circuit 4

5 Figure 5: AT91SAM9G20 board Figure 6: User program for setting of controller 5 CONTROL PROCESS Figure 7 presents the progress of the demanded and real position of the pneumatic piston without the load. The demanded position is not assigned in the form of position step but in the form of speed step. This is why the part of the control program is the generator of position (Fig.3) that generates the appropriate progress of the position on the basis of the demanded speed. In the Figure 7 there is shown the progress of the appropriate control deviation. Figure 7: Progress of pneumatic piston position Figure 8: Progress of control deviation 5

6 6 RESULT From the mentioned progress of the position of the pneumatic piston it is observable, that with the predictive controller we can gain the high - quality control process with the accuracy in the range from 0 to 3 mm. Even if the control algorithm of the controller was maximally simplified it regards the usage of the faster microcontroller Atmel AT91SAM9G20, of which price is not so different in contrast with the lower series Atmel AT91SAM7S256. The nonlinear behavior of the pneumatic system also causes the auto - oscillation of the piston near the demanded value. This problem can be partly suppressed by the compensation of the friction and so the subject of the upcoming research will be the suppression of the influence of the friction so that also the higher accuracy of the positioning will be gained. The compensation of the friction will be then added into the control algorithm and the resulting electric circuit together with the pneumatic cylinder will create a separate module. REFERENCES [1] ASTRÖM, K.J., WITTENMARK, B. Adaptive control. Addison-Wesley Publishing Company, p. ISBN [2] BOBÁL, V., BÖHM, J., PROKOP, R., FESSL, J. Praktické aspekty samočinně se nastavujících regulátorů: aplikace a implementace. Brno: VUTIUM Publishing Company, p. ISBN [3] CAMACHO, E.F., BORDONS, C. Model Predictive Control. London: Springer-Verlag, p. ISBN [4] ORDYS, A. W., CLARKE, D. W. A state-space description for GPC controllers. Int. J. Systems Science. 1993, vol. 24, pp [5] LJUNG, L. System Identification: Theory for the User. Englewood Cliffs: Prentice-Hall, p. ISBN [6] STREJC, V. Stavová teorie lineárního diskrétního řízení. Praha: Academia, p. [7] MATOUŠEK, P., MOUČKA, M. Predictive regulation of pneumatic servomechanism. Journal of Applied Science in the Thermodynamics and Fluid Mechanics [online]. 2011, vol. 8, no. 1, [ ]. Available from: < ISSN ACKNOWLEDGEMENTS The work presented in this paper was supported by the Student Grant Project. 6