Motivation
Founding Motivation of Little Pine Ltd.
Little Pine Ltd. has been established in an effort to allow access to the practical use of scientific knowledge in the area of Control Theory.
We aim to enable people to develop original solutions regardless of their level of knowledge of this multidisciplinary field.
The field of Control Theory has a long history (see
Control Theory Timeline — IFAC Control Resources
) and is continually evolving mainly thanks to computers and microelectronics which allow for both complex process modelling
and for the execution of direct digital control with input from many different data sources.
The knowledge of the mathematical model of the regulated system is essential for the creation of an automated control algorithm.
This because the specific systems and their layouts might be very varied. In practice however,
the engineer who is assigned the task of automated regulation has no upfront knowledge of the exact mathematical model of the regulated system
and little prior knowledge about it. Such prior knowledge also often tends to be only qualitative.
The second fundamental challenge is that Discrete Automated Regulation Theory demands, apart from knowledge of common mathematical concepts
(such as classical analysis), a familiarity with Z, DL Transformation, Theory of Polynomials, Theory of Probability and so on.
The third important problem is that those who design the system regulation should have knowledge about the nature
(physical, chemical, biological ...) of the processes which form the dynamic system.
Generally, the above-described complexity cannot be met by one person and so there no other way but to institute teams of experts
who are able to solve the task. The solution therefore tends to be expensive. For this reason such solutions are only
developed in situations where quality and safe regulation are absolutely vital (e.g. in the Energy or Transportation sector),
or where it can pay for itself by the volume of sold products.
Often we find that solving a task of automated regulation using methods designed for linear systems only leads to an approximate solution
as the real system is not, in actuality, linear. It is typical that the final control elements, such as control valves, for instance,
often have non-linear outputs. The magnitude of the time constants which characterise the process dynamics tend to be the function
of the system state. Additionally, when examining a regulation circuit sufficiently closely we may never eliminate the presence
of random signals such as break-downs, parasitic noise and useful noises. It is possible to find many such examples.
We therefore often find ourselves in a situation where, for various reasons, we don’t know the exact model of the regulated system
and its parameters, and sometimes even the type of system is only estimated. This is an unfavourable situation in the light
of the importance of modelling for the synthesis of the control. Therefore, very often the model concentrates on a linear solution which,
from an engineering perspective, brings limitations to its employment.
However, even though an exact description of the regulated system is “better” than a linear description,
it is often reasonable to employ typical widely described systems in the above situation, as it is important to note
that from an engineering perspective the optimality of the regulation process itself is not as important as its stability
and compliance with the operating and technological criteria.