Characterization and control of dimensionally similar systems

When a model (i.e. experimental facility) and prototype (i.e. the real system) are dimensionally similar, then it is possible to extrapolate experimental results from model to prototype. In particular, in this article we consider the problem of prototype controller design on the basis of controlled model experimental results. The problem is considered in both continuous time and discrete time, showing that if the model controller is properly scaled in gain and time, it can be used for prototype control achieving a similar performance level. In the case of partial similarity, it is shown that robustness considerations can be applied to the model controller in order to guarantee stability and performance on the prototype. From a control viewpoint the control design of similar systems is useful when families of products sharing the similarity relation must be controlled, maintained and upgraded. The approach is also useful when it is not possible to directly experiment with prototypes due to economic and/or safety issues.