Exothermic CSTR: modeling, control & simulation.

Tanuska, Pavol ; Kunik, Stanislav ; Kopcek, Michal 等

1. INTRODUCTION

The labs for distance education can be realized as remote controlled lab or as a virtual lab in web environment. The conceptions and ideas have been published in (Huba et al., 2004), (Bakosova et al., 2007) and (Ligus et al., 2005).

Disadvantage of physical models using is expensive operating, needful of technician support and scheduling of these equipment to users. The effective solution is to use analogue models.

The basic idea of the presented solution is using the connection of virtual ECSTR and virtual controller to perform control processes simulation after any control strategy design. Consequently, the validation of the design is performed in real time environment using the analogue ECSTR model and the real industrial controller, what is an original approach to the given problem.

2. MATHEMATICAL MODEL OF THE ECSTR

[FIGURE 1 OMITTED]

The model simulates a process of exothermic reaction in a stirred tank reactor (Fig. 1). More details can be found in (Mikles et al., 1994).

A dynamical process is described by non-linear system of differential equations (1) and (2).

[dx.sub.1]/dt = [k.sub.1] ([c.sub.Af] - [x.sub.1]) - y (1)

[dx.sub.2]/dt = [k.sub.1][T.sub.f] + [k.sub.4][T.sub.c] - ([k.sub.1] + [k.sub.4])[x.sub.2] - [k.sub.3]y (2)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

3. VIRTUAL MODEL OF ECSTR

The real-time virtual model represents the ECSTR described by (1) and (2) implemented in Delphi, using the 4th order Runge-Kutta method. The application works with/without a controller KRGN 90 real or virtual (Pollak, 2004) and (Remias, 2004) or the controller UDC 3000/3300 Honeywell (Kuzma, 2006) and (Rybar, 2005). The all input variables ([T.sub.f], [T.sub.c], [c.sub.Af], q) can be considered as the manipulated variable or the disturbance, and both the output variables (T, [c.sub.A]) as process variables.

[FIGURE 2 OMITTED]

3.1 Simulation Experiments

In the Fig. 3, the time response on a step change of [T.sub.f] from 350 K to 340 K of the reactor temperature T [K] is depicted. The time axis is in units of seconds. More detailed description can be found in (Mikles et al., 1994).

[FIGURE 3 OMITTED]

4. ANALOGUE MODEL OF ECSTR

The analogue model of ECSTR is based on the non-linear system of differential equations (1) and (2) as the virtual one. The principal structure of the analogue model is shown in Fig. 4. The differential equations are implemented using basic linear circuits with op--amps e.g. integrator, adder, multiplier etc. The non-linear behaviour of the temperature in the real ECSTR is approximated by the function generator, which uses several diodes with strictly adjusted operating points in the negative feedback of an op--amp. The time response characteristic of the model has been validated in comparison with a Matlab model of the ECSTR. The analogue model has implemented the same I/O signals as the virtual one (I/O signals are in standard voltage range 0 - 10V).

[FIGURE 4 OMITTED]

4.1 Simulation Experiments

The Fig. 5 (black line) documents the same experiment on the analogue model as described in section 3.1.

[FIGURE 5 OMITTED]

5. CONTROLLER KRGN 90

The controller KRGN 90 is an industrial controller namely for the control of continuous processes. The KRGN 90 is an eight loop controller with free configured I/O signals.

For education purposes, the virtual controller KRGN 90 has been developed. It consists of the reduced set of pre-programmed functions. However, the standard control strategies can be implemented in the virtual KRGN 90 as single control loop, cascade control loop, feed forward control, ratio control etc. More detailed description is presented in (Pollak, 2004) and (Remias, 2004).

6. EXOTERMIC CSTR CONTROL

The exothermic CSTR is not easy to control due its instability nature. The simple control strategy is to keep the ECSTR in the stable state under disturbances as the input concentration change or input feed temperature change. There are more sophistic control strategies, for example the robust control (Bakosova et al., 2007). To illustrate the presented solutions, the single loop PI control has been considered in this paper.

6.1 Real time control

The controlled variable (Fig. 5--gray line) is the reactor temperature T, the steady state value of this temperature is approximately 378 K; this value represents Set Point for the controller. A disturbance process variable is the feed temperature [T.sub.f], that will change in time t = 0 s from 350 K to 340 K. The control action is performed by temperature control of the coolant [T.sub.c]. The KRGN 90 control parameters are GAIN = 0.4, REPEAT = 0.015 [s.sup.-1] and RATE = 0.0 s.

6.2 Virtual control loop

The Fig. 6 documents the same experiment on the virtual model as is described in section 6.1, but the Set Point of the controller is approximately 385 K (the steady state value of T).

[FIGURE 6 OMITTED]

7. CONCLUSIONS

The new approach to ECSTR modelling, control and simulation has been presented in this paper. The virtual version of the ECSTR control has been extended by the non-linear analogue model of the ECSTR controlled by the real industrial controller. This solution gives many possibilities to realise real-time control, where the process signal processing, control action limiting, alarms processing, real time capabilities and another can be included. The using of the analogue model and an industrial controller offers the operator interface very similar to real one.

Further research is focused on the development of new types of process analogue and virtual non-linear models and virtual controllers.

8. REFERENCES

Bakosova, M.; Puna, D. & Zavacka, J. (2007). Robust stabilization of an exothermic CSTR. In: Proceedings of European Congress of Chemical Engineering (ECCE-6). CD ROM 990.pdf, ISBN 978-87-91435-57-9, Copenhagen (Denmark), September 16-20, 2007, EFCE

Huba M.; Bistak P. & Zakova K. (2004). Remote Experiments in Control Education. The IFAC Symposium in Telematics Applications in Automation and Robotics, pp. 161-166, 21.6.2004 Helsinky University of Technology, Finland

Kuzma, U. (2006). Virtual technological processes controlled by UDC 3300 Honeywell. In Slovak. Diploma work. STU Bratislava

Ligus, J.; Ligusova, J. & Zolotova, I. (2005). Distributed Remote Laboratories in Automation Education. Proceedings of 16th EAEEIE Annual Confrenece on Innovation in Education for Electrical and Information Engineering (EIE), ISBN 952-214-052-X, Lappeenranta, Finland, June, 2005

Mikles, J.; Dostal, P. & Meszaros, A. (1994). Control of technological processes--Process modeling and control basics. In Slovak. STU, ISBN 80-227-0688-4, Bratislava.

Pollak, P. (2004). Virtual controller KRGN90--Firmware. In Slovak. Diploma work. STU Bratislava

Remias, P. (2004). Virtual controller KRGN90--Operator interface In Slovak. Diploma work. STU Bratislava.

Rybar, P. (2005). Virtual controller UDC3300 Honeywell. In Slovak. Diploma work. STU Bratislava