Robust observer for multiple time-delay systems with unknown inputs

Abstract

In this paper, a design of a full-order observer for linear time-invariant (LTI) multivariable systems with multiple time-delays and unknown inputs (UI) is proposed. The main idea is to reduce the problem of the unknown input observer (UIO) for systems with multiple time-delays to that of a standard one. To that purpose, the orthogonal collocation method is used to transform the infinite dimensional model of the delayed system described by a set of linear partial differential equations (PDEs) to a finite dimensional one described by a set of linear ordinary differential equations (ODEs). Even using an approximation method, the asymptotic stability of the UIO is well proven. The efficiency of the proposed algorithm is shown using the quadruple-tank benchmark. The two cases of minimum and non-minimum phase models are considered.

Full and Reduced-Order Unknown Input Observer Design for Linear Time-Delay Systems with Multiple Delays

“…Motivated by the authors' early works for linear systems without delays [44], in this paper, we expand the problem of full-order unknown input observer (FOUIO) and reducedorder unknown input observer (ROUIO) design for linear systems with multiple time delays in states and inputs affected by unknown inputs. In this framework, it is important to note that a FOUIO is designed in [45][46][47] for linear systems with a single delay in the states and two delays in the inputs whereas another FOUIO is proposed in [48] for linear systems with a single delay in the states and a single delay in the inputs. For the last works, only the state information is used to design observers in open loops and to the best of our knowledge, there are no related works for which both the state vector and the input vectors are used to design the observer.…”

“…(i) The designed observers' approaches do not require approximation of the infinite dimensional model of the delayed system in a lumped one as described in our previous works [45,46]. (ii) Different from [46] where only the state vector is used to construct observers in open loop, in this paper, we construct the novel observers by using both state and input vectors.…”

Full Order Unknown Inputs Observer for Multiple Time-Delay Systems

“…Consider the following class of the infinite dimensional LTI multivariable systems with multiple time-delays and unknown inputs described by [28]:  are known and constant delays of the system (1). Consider now from (1), an approximated finite dimensional LTI system with free-time delays described by:…”

“…Consider the following class of the infinite dimensional LTI multivariable systems with multiple time-delays and unknown inputs described by [28]:…”