Welcome everyone. Today we have Georg Uriya from the University of Hannover and also from

the University of Antiochia. And he will be speaking about Contrability Analysis of Multi-Gate

Systems, Application of State Theoretical Approach to a Semi-Batch Implementation Polymerization

Process. Georg, you have the floor. Thank you. Thank you very much for the nice introduction

and thank you for having me today. I am from Colombia. I did my PhD work in joint cooperation

between University of Antiochia in Colombia and Leibniz University. And today I will present

some of the results I obtained. So this is the outline of my presentation. So first I

will give you a brief introduction into the topic. I will present briefly the state of

the art. Then I will focus on the multiscale model we developed and how we use that model

for analyzing the controllability of the system. So our motivation for working in this topic

is the high, the demand of the high performance polymers in the market. Polymers we use in

everyday life. Now I'm trying to, people are trying to produce polymers which increase

their performance in terms of the heat. They can support of the mechanical stress. They

can support and so on. So because of the increasing market and the necessity of development of

specialized technologies for producing polymers, we try to adopt a multiscale approach for

studying how to synthesize a specific type of polymers that are thus conformed by a core

and a shell. So basically our starting point was studying a single polymer particle in

which we have a nucleus or a core from one polymeric material with some specific characteristics.

And then we have a shell with a completely different characteristics but performs better

when they are combined. So basically what we did was to feed in a chemical reactor a

seed of a polymeric material, in this case polystyrene, and then we feed a monomer, in

this case a acetate, and then we somehow monitor how the core shell structure is formed. For

tracking that process, what we did was to try to model how a whole population of the

particles, the growing particles inside the reactor behaves. Of course not all particles

will form as we expect. So what we will try to do is to minimize the side effects of having

this kind of polymer materials, for instance, secondary nucleation. So here in Figure B

you can see more or less how core shell polymer particles look like, and then you can see

here as well secondary nucleation, which basically means polymer particles of the material of

the monomer we are feeding into the reactor. We would like to minimize the number of these

particles. The question is how to produce high quality polymers in this kind of environment.

Well, what we need to do sometimes is just control at the microscopic level how polymer

particles are formed. But what we have is a whole chemical reactor and most important,

the only thing we can have sometimes from the control perspective is the macroscopic

information. So how to control events at the macroscopic scale? Okay, what we did was linking

process inputs with outputs. What that means? That means that the macroscopic scale what

we have are some inputs in our case, flows from the monomer and initiator, and then we

have the traditional mass and energy balances composed by ordinary differential equations.

And then we found a way to link the macroscopic scale with another two scales, the microscopic

scale. At the beginning we only tried to model the microscopic scale for capturing events

in a surrounding of a polymer particle, but quickly we realized that we additionally need

another scale, an intermediate scale that serves to connect all the scales, to couple

all the system. So here you can see more or less the general scheme of a multi-scale approach

in which you have at the macroscopic scale ordinary differential equations. At the mesoscopic

scale what you have is a partial differential equation describing how the population of

polymer particles are evolving inside the reactor and you have a microscopic scale composed

by a stochastic simulation. In our case was a kinetic Monte Carlo simulation. But then

our next question was, okay, if we are able to link our inputs to our macroscopic outputs,

how to assure the controllability of the multi-scale system? Because what we want is that manipulating

the inputs we can obtain the macroscopic output we would like. So we need to find a way to

guarantee that this output will be affected by our manipulated inputs. So additionally