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The observer-based linear quadratic sub-optimal digital tracker for analog systems with input and state delays

机译：基于观察者的线性二次次优数字跟踪器，用于具有输入和状态延迟的模拟系统

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摘要

This paper presents a new observer-based sub-optimal digital tracker for the continuous-time system with input and state time delays. We directly convert the continuous-time input-state delayed system into an equivalent discrete-time input-state delayed model and its extended discrete-time delay-free model. In addition, we directly discretize the linear quadratic performance index specified in the continuous-time domain into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. As a consequence, the well-developed discrete-time optimal control theory for discrete-time delay-free system can be applied to determine the optimal digital tracker for the continuous-time input-state delayed system. When the states of the continuous-time input-state delayed system are not available for measurements, we develop a sub-optimal digital observer for the original continuous-time input-state delayed system using the state-matching digital redesign technique and the digital-to-analog model conversion technique. As a result, the proposed observer-based linear quadratic digital tracker is able to make the output of the digitally controlled continuous-time input-state delayed system sub-optimally track the desired reference signals. An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology.
机译：本文针对具有输入和状态时延的连续时间系统，提出了一种新的基于观测器的次优数字跟踪器。我们将连续时间输入状态延迟系统直接转换为等效的离散时间输入状态延迟模型及其扩展的离散时间无延迟模型。此外，我们使用新开发的扩展无延迟模型将连续时间域中指定的线性二次性能指标直接离散化为等效的解耦离散时间性能指标。结果，可以将针对离散时间无延迟系统的完善的离散时间最优控制理论应用于确定连续时间输入状态延迟系统的最优数字跟踪器。当连续时间输入状态延迟系统的状态无法进行测量时，我们将使用状态匹配数字重新设计技术和数字量测技术为原始的连续时间输入状态延迟系统开发次优数字观察器到模拟模型转换技术。结果，提出的基于观察者的线性二次数字跟踪器能够使数控连续时间输入状态延迟系统的输出亚最佳地跟踪期望的参考信号。给出了一个说明性示例，以证明所提出的设计方法的有效性。

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