Unified gain formula for control diagrams with matrix-based transfer functions
1The College of Electrical and Information Engineering, Hunan University, Changsha City.
ISA Transactions
|March 24, 2023
Summary
A new unified gain formula extends control system analysis beyond single-input single-output (SISO) systems to complex multi-input multi-output (MIMO) systems. This novel approach uses matrix operations for broader applicability in control engineering.
Area of Science:
- Control Systems Engineering
- Matrix Theory in Engineering
Background:
- Conventional Mason's gain formula is limited to SISO systems.
- Inadequate for MIMO systems due to lack of matrix operations.
Purpose of the Study:
- Introduce a novel unified gain formula for control diagrams.
- Address limitations of existing formulas for MIMO systems.
Main Methods:
- Utilized partitioned matrix theory and feature extraction.
- Derived transfer functions for three types of control diagrams.
- Developed a unified gain formula based on feature extraction and equivalent input nodes.
Main Results:
- Proposed a unified gain formula applicable to both SISO and MIMO systems.
- Demonstrated effectiveness through case studies.
- Successfully extended gain formula analysis to matrix-based transfer functions.
Conclusions:
- The novel unified gain formula effectively analyzes control diagrams in MIMO systems.
- The formula offers a more general approach compared to conventional methods.
- Validated potential for broad application in control system design and analysis.
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