Observer Synthesis for Linear Time Invariant Systems with Unknown Inputs via Eigenstructure Assignment and Its Application to Disturbance Attenuation

概要

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Unknown input observer (UIO) has been used to estimate the states of dynamic systems in the presence of unknown inputs. The UIO can also be applied to the systems with disturbance inputs or unknown varying parameters. It is well known that there exists the UIO for linear time invariant systems (A, B, C) if and only if (i) rankCB=rankB and (ii) all invariant zeros are stable. However, in many cases, these may be very strict conditions. In this paper, a new synthesis method of the UIO is studied in order to estimate system states influenced by unknown inputs. The proposed method can be applied in the case when the above condition (ii) is not satisfied. The basic idea is to assign poles of uncontrollable subspace and controllable subspace for observer systems to desired locations via eigenstructure assignment methods. The dynamic behavior of the states which belong to the controllable subspace depends on the pole locations and so these poles are assigned so that the estimation error caused by unknown inputs and/or disturbance inputs is reduced as small as possible. In order to indicate the effectiveness of our proposed method, a numerical example of the control system with disturbance inputs is given.
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