A reduced-order unknown input observer scheme for a class of nonlinear fractional-order systems

Abstract For fast drive mode transitions by shifting clutches equipped in the dedicated compound power-split hybrid transmission, correct estimations of pressure and torque of the clutches are crucial for control strategies. A hierarchical estimator is proposed herein for individual estimation of the clutch torques, consisting of not only the reference layer containing the unknown input observer of vehicle resistance and the reduced-order observer of drive shaft torque, but also the estimation layer combining the unknown input observer with the reduced-order observer. The estimator is implemented to strike a balance between estimation accuracy in the steady state and real time response in the transient state. For validation of the estimator, simulations and real car tests are carried out in specific drive conditions. By numerical results, it’s demonstrated that excellent predictive abilities are found including reasonably small estimation error and adaptive capability and, as a result, shift to shift induced driveline oscillations and vehicle jerks are reduced significantly.

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H ∞ and Sliding Mode Observers for Linear Time-Invariant Fractional-Order Dynamic Systems With Initial Memory Effect

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4027289 ◽

2014 ◽

Vol 136 (5) ◽

Cited By ~ 7

Author(s):

Sang-Chul Lee ◽

Yan Li ◽

YangQuan Chen ◽

Hyo-Sung Ahn

Keyword(s):

Memory Effect ◽

Fractional Order ◽

Dynamic Systems ◽

Sliding Mode ◽

Linear Time ◽

Unknown Input ◽

Unknown Input Observer ◽

Linear Time Invariant ◽

Sliding Mode Observers ◽

Time Invariant

The H∞ and sliding mode observers are important in integer-order dynamic systems. However, these observers are not well explored in the field of fractional-order dynamic systems. In this paper, the H∞ filter and the fractional-order sliding mode unknown input observer are developed to estimate state of the linear time-invariant fractional-order dynamic systems with consideration of proper initial memory effect. As the first result, the fractional-order H∞ filter is introduced, and it is shown that the gain from the noise to the estimation error is bounded in the sense of the H∞ norm. Based on the extended bounded real lemma, the H∞ filter design is formulated in a linear matrix inequality form, and it will be seen that numerical methods to solve convex optimization problems are feasible in fractional-order systems (FOSs). As the second result of this paper, not only state but also unknown input disturbance are estimated by fractional-order sliding-mode unknown input observer, simultaneously. In this paper, it is shown that the design and stability analysis of the two estimation techniques are not related with the initial history. Through two numerical examples, the performance of the fractional-order H∞ filter and the fractional-order sliding-mode observer is illustrated with consideration of the initialization functions.

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