Design of controls at guaranteed performance

Whenever the problem of the designer has to do with the control system design of a specific plant with specific requirements already widely studied by other people, or whenever one deals with a limited technological sector, as f.i. the robotics, then it is possible to make available to the designer solutions already successfully experimented elsewhere. However the designer will be always the one responsible of his choice.

An evaluation – which is at the same time absolute and efficient – of the uncertainty of the model chosen as a foundation of the control design is never possible.

In fact, since no mathematical model can give a complete and precise description of a plant, any model appears always widely uncertain in absolute terms.

For being efficient the evaluation of the uncertainty should not be absolute, but relative to the specific aspects of the plant dynamics, which are of interest in connection with the specific control requirements established.

One aim of the EICAS methodology is an efficient evaluation of the model uncertainty.

After having chosen the model on which the design will be based (the so called approximate model) the designer builds a new model (called fine model) apt to show the validity limits of the first one concerning the expected performance of the control to be designed.

The fine model should not give necessarily a more precise description than the first one, but instead it should be extended up to including the modeling of behavioral phenomena of the plant which the first model willingly neglected and could possibly have influence on the control performance if it were extended beyond the limits established by the design requirements.

The fine model will be often non-linear, and will include an approximate description of the above mentioned behavioural phenomena of the plant.

In general the plant model is not apt to be taken as a basis for designing a control system of the plant.

After having chosen the approximate model to be taken as a basis for the control design, the designer can avail himself of identification techniques for an accurate estimation of the model parameters.

Within the EICAS methodology an identification method has been developed, which optimises the parameter estimation in relationship with the model objective to build up the foundation for designing the control.

Note how – being the model an approximation of the plant – it does not exist the true value of its parameters and how furthermore it does not make sense to talk about their optimum estimate except in connection with a clearly defined objective.

The objective of the EICAS identification method is the control performance for whose design the model has been conceived.

The design of the control system is carried out on the basis of the chosen approximate model. For designing sophisticated control systems giving the best performance the designer must have specific - sometimes even very advanced - competences essentially in the mathematical field.

This is the reason of the wide use of elementary control techniques like the PID control, which can easily be set up in-field by applying simple (but long) experimental procedures.

Within the EICAS methodology there were developed Automated Algorithm and code generation techniques assisting the designer during all design steps in which complicated calculations are required, until a completely automatic development of the control algorithms and related code are made possible.

When the designer decides to follow one of the available automatic design techniques, he must choose the control architecture that he believes to be more suitable, give the approximate plant model and define the control performance required.

Algorithms and software for the control are immediately developed and the designer can then verify the performance through the numerical simulation which uses the fine model for reproducing the plant.

The control performance is verified in the simulated environment where the plant behaviour is reproduced through the fine model already introduced at point 2.

Following the EICAS approach by using in particular the available automatic design methodology, the designer must always keep in mind the requirements to be satisfied by the control system. Recall three steps of the design:

- the approximate model is chosen for meeting the control requirements;
- the fine model is chosen for emphasizing the limits of the plant representation through the approximate model;
- the control is designed for meeting the same pre-established requirements.

When the project is carried out properly it must be possible to verify through the simulation that the control system which was designed meets the pre-established requirements.

However it is possible to carry out also another important check.

If, starting from the approximate model, a control is designed for obtaining a performance better than the one defined as a validity limit of the approximate model itself, then - if the fine model was properly selected – the above control tested through the numerical simulation should result unstable. Such event will confirm that the design procedure was properly followed. The designer will then be able to push the required performance up to the limit at which the simulated system tends to become unstable and therefore to deteriorate its performance.

As a part of the EICAS methodology it is available a numerical optimisation tool which makes possible the automatic search of optimum performance to be achieved through a control system based upon a pre-established approximate model of the plant.

In fact the EICAS approach shows that the best achievable performance is an inherent feature of the pair “approximate model”–“fine model”.

By the definition of the pair, it is defined the approximation level of the plant representation through the approximate model and it must be assumed as a known fact, that the closed-loop control performance results theoretically limited only by the uncertainty of the model used for the control design.