Òåõíè÷åñêèå íàóêè/ 12.Àâòîìàòèçèðîâàííûå ñèñòåìû óïðàâëåíèÿ íà ïðîèçâîäñòâå.

Student Kryvopyshyn T. M., Candidate of Engineering Sciences Ladieva L. R.

National Technical University of Ukraine “Kiev Polytechnic Institute”, Ukraine

Optimal robust control system of a reactor synthesis to form urea melt

The synthesis process of urea involves the stages of synthesis and dehydration of urea ammonium. Ammonia is compressed by the compressor and through the refrigerator at a temperature of 25 0Ñ enters the reactor. There is carbon monoxide (IV) with a temperature of 35 0Ñ, compressed by the compressor. Given that the process involves recycling, one of the basic reagent is a carbamate ammonium (NH4)2CO2  which enters the reactor after the decomposition of a 75% solution of urea. Since this synthesis reactor type "ideal mixing", all the reactants are mixed throughout its volume, and using the heating jacket pressure reached to 2 ÌÏà, and the temperature of 170…190 0Ñ. The resulting floating output contains 34-35 % urea, 18-19 % ammonium carbamate,  34-35 % ammonia and 10-11 % water. The flow temperature is – 175 0Ñ.

The resulting solution of the carbamate recirculates in the reactor. The ratio of  NH3 : CO2  = 3-5 : 1 . At the first stage distillation at a pressure of 1,4 ÌÏà and temperature of  390 0Ñ output becomes to 84 % of excess ammonia.

In the process of creating urea melt one of the most important technological parameters on which depends the quality of the produced raw material is the temperature of the urea melt at the exit of the reactor. Therefore, the main channel of the regulation: "the consumption of ammonia - temperature urea melt".

The dynamical equation of heat balance of the reactor:

where Q – volume flow, m3/s; Ñ – the heat capacity of a substance, J/(kg∙Ê);          Òw– the temperature of the casing wall, Ê; Ò – the temperature of the substance, Ê;  ñ – the density of the substance, kg/ m3; V – the volume of the reactor, m3; q – thermal effect of reaction, J/mol; Ê – the reaction rate, mol/(m3∙s); αT – the heat transfer coefficient, J/(m2∙s∙Ê);  F – the surface heat transfer, m2.

The dynamical equation of thermal balance of heating the shell:

                                                    

where αT1 – the heat transfer coefficient between the casing wall and environment, J/(m2∙s∙Ê); Òe – the temperature of the environment, Ê;    m – the hull weight, kg; Ñ – the heat capacity of the wall material, J/(kg∙Ê).

Highlight here two thermal capacity afloat urea and heating wall: 

Hence the matrix status and control acquires the form:

But, there are certain parametric uncertainty is the action of the catalyst in the reactor changes with time, and therefore, the thermal effect is unpredictable. As a result, have a nominal mathematical model and mathematical model with perturbations. The question arises whether the system is robust stable?

To verify that the system is robust stable on the Kharitonov theorem it is necessary that the interval  characteristic polynomial was of the type Hurwitz, as well as necessary and sufficient what its four angled versions was of the type Hurwitz are of the form:

 

                   

The synthesized optimal linear regulator and the calculated gain:  

                                                     

where  P(t) – matrix Riccati coefficients, R – weighting factor.                                                

This control object with an interval matrix ΔÀ=À0+À, for which the controller implements a control law so that the matrix of the system state has the form:

  .                                              

This control system is of order n=2 with characteristic frequency ω0=4ñ-1 set in probeam basis and the matrix F0 becomes:

Interval part  matrix condition has the form:

The matrix F then there is an interval of the characteristic polynomial:

Tested the stability of the system showed that the system is robust stable, all the Kharitonov polynomials were of the type Hurwitz.
         Optimal control with a given quality criterion for such a law regulation:

                                                                             ,                                              

having a linear matrix inequality:

                                                                                   

Multiplying this expression to the left and to the right on Q=P-1, we obtain:

                                                                      

The criterion value is determined when the choice of a stabilizing control. To this end, we introduce the parameter γ >0:

                                             

If for a given γ >0 will be his decision Q, having feedback:

the value of the functional is:

                                                 

The parameter γ plays the role of a parameter is its optimal value corresponds to the minimum of the functional J.

 

Pic.1. Schedule changes of the state variables and the control vector

X1v, X2v – state variables; Uv – the control vector; Upconstv – set the control vector

 

Was calculated parametric uncertainty is the action of the catalyst was set to    30 % and was calculated its effect on the circuit.

 

Literature:

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