This paper proposes an improved nonlinear extended observer with adaptive gain (ANESO), which can be applied to systems with large disturbance amplitude changes without parameter re‐tuning. An ANESO is added an adaptive factor Ai$$ {A}_i $$ to the gain of the original NESO. The expression of Ai$$ {A}_i $$ is obtained by assuming that nonlinear extended states observer (NESO) and linear extended states observer (LESO) has the same characteristic of steady‐state error when the amplitude of disturbance turns. On this basis, an adaptive adjustment algorithm based on tracking error is designed. In addition, the stability of the proposed ANESO is analyzed by using the Routh‐Hurwitz criterion. Finally, through simulation experiments, the observation performance of ANESO was compared with NESO and switching extended state observer (SESO). The experimental results demonstrate that the observation performance of ANESO is hardly affected by the disturbance amplitude, and moreover, its observation precision is higher than that of NESO and SESO.
Non-member Zhiqiang Long * 5 Non-member As an alternative to bang-bang control, a time optimal control (TOC) algorithm for discrete-time systems was first reported by Han (1) . This algorithm not only acts as a noise-tolerant tracking differentiator (TD) to avoid setpoint jumps in control processes, but also has wide applications in the design of controllers and observers. However, determination of the real-time state position on the phase plane involves complex boundary transformations, which renders this algorithm impractical for some engineering applications. This paper proposes a methodology for discrete-time optimal control (DTOC) of double integrators with disturbances. The closed-form solution with lower computational burden can be easily extended to general second-order systems. Further, in consideration of the inevitable disturbances in the systems, a rigorous and full-convergence proof is presented for the proposed algorithm. The results show finite-time and fast convergence as well as provide the ultimate stable attraction regions for the system states. Examples and experiments are also presented to demonstrate the effectiveness of the proposed algorithm for solving a signal processing problem in a maglev train.
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