Abstract
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Highlights
The automatization of industrial processes currently makes the application of based-model control schemes be more complex, resulting in the need to model this type of systems using piecewise linear systems
In the present work we examine the switching sequence for each dynamic model, which represents a significant contribution to the field of discrete-time piecewise linear systems with unknown active mode varying at arbitrary times
In order to define the observability of piecewise linear systems in a discrete time, a finite number of output measurements of the system affected by the commutation law is required
Summary
The automatization of industrial processes currently makes the application of based-model control schemes be more complex, resulting in the need to model this type of systems using piecewise linear systems. In order to face new challenges Babaali y Egerstedt [16] presented a proposal to solve the observability problem for unknown modes (of piecewise linear systems) switched by an arbitrary switching signal Those authors do not take into account the control input. In the same line this paper proposes a methodology in order to prove observability for piecewise linear systems under conditions of arbitrary switching like a function of system output when it is assumed that sufficient residence time exists for each active mode and the distance between modes is null. This paper proposes a methodology to probe the observability and a new approach to estimate the states of a piecewise linear system under the conditions of unknown commutation modes depending on the system’s output
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