A small volume of liquid is a big deal

Language barrier
‘We had something of a language barrier to overcome at first,’ says Ghatkesar. ‘I explained the concept of my so-called femtopipette, a cantilever with a hollow needle that can be precisely manoeuvred with an accuracy of less than a micrometre, which is a millionth of metre, and push out a femtolitre of liquid, which is equivalent to a cubic micrometre of liquid. I thought that would be sufficient for my colleagues to design the control system envisioned, but that’s not how it works. It took a few weeks of discussions for us to find common ground: we first had to develop a model of the system, clearly defining the physics, the parameters and the links between the parameters. As an engineer, I don’t usually think of the technology I’m developing in terms of model parameters.’ The model definition allowed the disciplines to connect.   

‘We had something of a language barrier to overcome at first. It took a few weeks of discussions to find common ground. A model definition allowed the disciplines to connect.’  

Single-cell biopsy
There are many possible applications for a pipette system that can dose femtolitre droplets. ‘Imagine a femtopipette depositing a drop of fluorescent marker fluid onto a single living cell and extracting an element of interest, guided by the markers.’ Such a tool would help researchers understand how the complex system of life functions, by allowing them to zoom in on its basic building block – the cell – and study the many different components inside it. ‘The only way to succeed in such a single-cell ‘biopsy’ is to limit the amount of liquid that is dispensed or sucked up. Too much would damage the cell.’ For this and other applications, being able to precisely control the liquid volume that is transported by the pipette is essential.  

Many parameters
So, the researchers first had to come up with a model of how dosing the fluid depends on the various parameters. Complicating matters, there were a lot of parameters involved: the properties of the surface onto which the droplet is deposited, the material properties and size of the hollow needle, the viscosity and density of the fluid, and so on. To reveal the role of each parameter, lots of experiments using lots of pipettes were done. ‘The femtopipettes are fabricated using techniques common to microchip fabrication, which is quite an expensive process,’ explains Ghatkesar. As a result, the cohesion project’s budget allowed only a Master’s student to assist Ghatkesar and HosseinNia in the work. ‘Luckily, we found Mr. Xi Cao, who was very good in both the physics and control engineering aspects. It was a perfect project for him.’ And a successful one as well, as concluded from the presentation Cao was invited to give at the prestigious world congress of the International Federation of Automatic Control (IFAC). The results were well received and published as a conference paper.

‘The results were well received and published as a conference paper’    

Iterative-adaptive-fractional control
Based on the resulting picture of the physics at play, HosseinNia and Baldi designed a control scheme. They came up with an integrated approach in which (1) an iterative learning control loop allows the system to learn by comparing the intended and realised droplet volumes, (2) an adaptive controller stabilises the iterative loop, adapting it to different experimental circumstances, and (3) the control loop features so-called fractional order properties to make the process more robust against unwanted disturbances. HosseinNia is especially excited about the third element. ‘The overwhelming majority of control systems used in industry are of a simple, linear type. Whenever better performance, such as higher precision or speed, is needed, the control systems become so complicated that it scares off practical use. The fractional-order approach has great potential as it represents a middle ground between high performance and easy compatibility with industry standards. He continues: ‘The combination of adaptive and fractional-order control is a theoretical novelty, which has not yet been applied to practical systems. Our cohesion project is the first.’

‘The combination of adaptive and fractional-order control is a theoretical novelty, which has not yet been applied to practical systems. Our cohesion project is the first.’

Next on the agenda
While Ghatkesar notes that they are not done yet, he looks back at a fruitful project. ‘I certainly enjoyed the collaboration.’ For control engineers HosseinNia and Baldi there were even surprises along the way. ‘We’re used to working with much larger systems. When moving to such small scales, the situation becomes so much more complex and troublesome.’ HosseinNia adds: ‘In a way, it made proud to be an experimental control engineer. The project reaffirms that control theory cannot be mindlessly applied in practice, it requires diving deep into the experimental reality.’ Although the cohesion project has ended and their MSc student moved on to a PhD position at the University of Eindhoven, the collaboration continues. Testing their newly developed control approach in real-time experiments is next on the agenda of Ghatkesar, HosseinNia and Baldi.