Virtual Sensors for Discrete-Time Nonlinear Systems

The problem of virtual sensor design is described for a given technical system equipped with sensors to measure the components of its state vector. Such sensors can be useful in cases where existing physical sensors are insufficient or a failed sensor needs to be replaced. The use of additional physical sensors to achieve the necessary result may require extra costs; in addition, the reliability of such sensors is usually low. The authors state and solve the problem of designing virtual sensors for technical systems described by dynamic models representing nonsmooth nonlinearities (dry friction, play, hysteresis, and saturation) under external perturbations. Relations are presented that enable the design of a sensor of minimum complexity that can estimate given state vector components of the system. A sensor synthesized in this way will be insensitive or minimally sensitive to external perturbations and can complement existing physical sensors or replace a failed physical sensor. Theoretical principles are illustrated using the design of virtual sensors for a known three-tank system as an example. The conducted Matlab-based simulation confirms the accuracy of computations and design. The obtained results can be applied in the design of fault-tolerant systems.