Abstract
This paper presents an efficient proportional-plus-integral (PI) current-output observer-based linear quadratic discrete tracker (LQDT) design methodology for the non-minimum-phase (NMP) discrete-time system with equal input and output number, for which the minimalized dynamic system contains the unmeasurable system state and unknown external matched/mismatched input disturbances. Illustrative examples are given to demonstrate the effectiveness of the proposed approach.
Highlights
The unknown input observer (UIO) design methodology involves the state estimation for a dynamic system subject to unknown input excitation [1], in which it may contain internal uncertainties and exogenous loads that cannot be measured or inconvenient to measure
Most UIO design methodologies presented in the early literatures require that the transfer function from the unknown input to the system output is minimum-phase and of relative degree one
For the NMP square strictly proper discrete-time transfer function matrix, for which the minimalized dynamic system with unmeasurable system state and its unknown external matched/mismatched input disturbances, we propose a PI current output-based observer (PICO) design methodology to simultaneously estimate the system state and its equivalent input disturbance
Summary
The unknown input observer (UIO) design methodology involves the state estimation for a dynamic system subject to unknown input excitation [1], in which it may contain internal uncertainties and exogenous loads that cannot be measured or inconvenient to measure. For the NMP square strictly proper discrete-time transfer function matrix, for which the minimalized dynamic system with unmeasurable system state and its unknown external matched/mismatched input disturbances, we propose a PI current output-based observer (PICO) design methodology to simultaneously estimate the system state and its equivalent input disturbance. To have a desired observer gain L in terms of (Lo , L1, L2 ) for the current output-based observer in (8)-(12) Such that the closed-loop observer error dynamic system poles are optimally assigned inside a circle with a pre-specified radius α ( 0 < α ≤ 1 ), let us perform the following transformations Gɶ = G α , Cɶ = C α , and 0 < α ≤ 1 , which yield to a transformed equation as wt (k). The estimation errors will be constrained in the small region of O(Ts2 ) , since the sampling time Ts is assumed to be sufficiently small
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