Team:KULeuven/Design/Integrated Model

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__NOTOC__
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=Control model=
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=Controller design=
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Because we want to optimize the design of the feedback loop in our system, we developed a more abstract block scheme of the bacteria. It shows each component as a block performing a specific task. The diagram is used to develop some theories about the performance of the feedback loop.
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Because we want to optimize the design of the feedback loop in our system, we developed a more abstract block scheme of the bacterium. It shows each component as a block performing a specific task. The diagram is used to develop some theories about the performance of the feedback loop.
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[[Image:Blockmodel.jpg|750px|center|thumb|Block model of the system (Simulink)]]
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==Proportional design (P controller)==
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=Control theory=
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Because the controller has to be implemented in 'biological technology', we choose the simplest possible design of
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controller, the proportional controller. The output signal in this type of controller is directly proportional to the error signal. The error signal is the substraction of the input and the control signal. however this type of controller has one importent flaw. When the input is a step function, as in most cases, there will be a steady state error. To make this steady state error as small as possible, the gain in the feedback loop must be as large as possible.
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The gain in the feedback loop can be adjusted by using low/high copy plasmids for the genes in the loop.
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Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The purpose is to design a controller which controls the system so that it behaves as desired. The controller in our system will implemented in 'biological technolgy', it will be used to control the production of vanillin so that the concentration of (extracellular) vanillin is regulated to a certain value, dependent on the irradiation of blue ligth. There exists several criteria to measure the performance of the controller, some are listed below.
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[[Image:Proportional10.JPG|750px|center|thumb|Block model of the system with proportional controller (Simulink)]]
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==Stability==
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==Proportional and Integral design (PI controller)==
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The system can be called stable if, no matter what the input signal (in our case: blue light) is, the output (extracellular vanillin concentration) will remain finite after an infinite amount of time.
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==Tracking problem==
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This criteria is an indication of how well the output will follow the wanted reference, we want the difference between the output and the wanted reference signal as small as possible.
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The more input signals the controlled system can follow the better the controller will perform on this criteria. We will see that with our controller we want to minimize the steady state error on a step signal as reference signal.
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==Disturbance rejection==
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Most controlled system are disturbed by other systems in their neighbourhood, in our case, imagine someone adding an extra amount of vanillin to the environment. We don't want to see these disturbances in our output of vanillin, meaning that the vanillin concentration remains at the desired level independent of disturbances.
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The disturbance rejection criteria indicates the ability of the system to reject those inputs.
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==Robustness==
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As with every model, our model of the bacteria is not perfect. Robustness is a property of a property, meaning if the system is stabilized in a robust way, it means that all similar systems that will also be stabilized by the same controller designed for the simulated model. It's possible to define a distance between to different models, now imagine a sphere around the nominal model of models how are still stabilized by the controller.
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The bigger the 'radius' of this sphere, the more robust the controller meets another criteria.
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It's then hoped that the controller will also stabilize the real system as it's assumed to be similar to the modelled system.
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=Biological implications=
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Because the controller has to be implemented in 'biological technology', we choose the simplest possible design of
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controller, the proportional controller.
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The gain in the feedback loop can be adjusted by the use of low/high copy plasmids for the genes involved in the transduction of the signal in the feedback loop.
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= Simulations =
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Because the steady state error on a step input signal will always be nonzero without an integrator, we considered to add some integral action, in the form of an proportional and integral controller. The input of the controlled system is, in this type of controller, a weighted sum of the error and the integral of that error signal. This way the staedy state error is avoided. However because of the limited amount of time and resources we stayed with the P controller design, which is more straightforward to implement in a biological systems.<br>
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In order to check the set-up of the model and to estimate the behaviour of the real bacterium, we performed a number of simulations.  
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As an extention the integrator could be implemented in the cell by producing a species with a rate proportional to the amount of mRNA key.
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[[Image:PI.JPG|750px|center|thumb|Block model of the system with proportional controller (Simulink)]]
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Latest revision as of 19:06, 13 October 2009


Controller design

Because we want to optimize the design of the feedback loop in our system, we developed a more abstract block scheme of the bacterium. It shows each component as a block performing a specific task. The diagram is used to develop some theories about the performance of the feedback loop.

Proportional design (P controller)

Because the controller has to be implemented in 'biological technology', we choose the simplest possible design of controller, the proportional controller. The output signal in this type of controller is directly proportional to the error signal. The error signal is the substraction of the input and the control signal. however this type of controller has one importent flaw. When the input is a step function, as in most cases, there will be a steady state error. To make this steady state error as small as possible, the gain in the feedback loop must be as large as possible. The gain in the feedback loop can be adjusted by using low/high copy plasmids for the genes in the loop.

Block model of the system with proportional controller (Simulink)

Proportional and Integral design (PI controller)

Because the steady state error on a step input signal will always be nonzero without an integrator, we considered to add some integral action, in the form of an proportional and integral controller. The input of the controlled system is, in this type of controller, a weighted sum of the error and the integral of that error signal. This way the staedy state error is avoided. However because of the limited amount of time and resources we stayed with the P controller design, which is more straightforward to implement in a biological systems.
As an extention the integrator could be implemented in the cell by producing a species with a rate proportional to the amount of mRNA key.

Block model of the system with proportional controller (Simulink)

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