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The limiting zero dynamics of discrete-time system based on forward triangle sample-and-hold
Minghui Ou1,2, Mingkun Ou3, Haiyang Wang1
1School of Big Data and Internet of Things, Chongqing Vocational Institute of Engineering, Chongqing, China.
Plos One
|April 11, 2023
Summary
This study introduces forward triangle sample-and-hold (FTSH) for discrete-time systems. It reveals stable conditions for limiting zeros, showing FTSH offers advantages over BTSH for controller design.
Area of Science:
- Control Systems Engineering
- Signal Processing
- Discrete-Time Systems Analysis
Background:
- Zero dynamics significantly impact control system analysis and controller design.
- Unstable zero dynamics can degrade overall system performance.
- The properties of limiting zero dynamics in discrete-time systems require further theoretical exploration.
Purpose of the Study:
- To investigate the properties of limiting zero dynamics for continuous-time systems reconstructed using forward triangle sample-and-hold (FTSH).
- To establish a framework for analyzing limiting zero dynamics under varying sample periods (small or large).
- To determine the stability conditions for limiting zeros in discrete-time systems employing FTSH.
Main Methods:
- Development of a theoretical framework for limiting zero dynamics with FTSH.
- Analysis of system behavior for sufficiently small and large sample periods.
- Comparative theoretical analysis against backward triangle sample-and-hold (BTSH).
Main Results:
- Introduction of a framework for limiting zero dynamics in discrete-time systems reconstructed via FTSH.
- Identification of stable conditions for limiting zeros in both small and large sample period scenarios.
- Demonstration that FTSH offers superior performance compared to BTSH.
Conclusions:
- FTSH enables the selection of a variable parameter to position discrete-time system zeros within the stable region.
- The study provides theoretical validation for the advantages of FTSH over BTSH in signal reconstruction.
- Simulation examples confirm the practical effectiveness of the derived results for FTSH-based control systems.
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