Logarithmic Rounding for Multivariable Model Gain Matrix Modification
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Solution Overview
Problem
Current methods for modifying model gain matrices to improve Relative Gain Array (RGA) properties are time-consuming and prone to unstable optimization solutions due to iterative and manual processes, which can lead to large magnitude changes and reversal of fixes, especially when dealing with uncertainty in multivariable control systems.
Innovation Solution
A logarithmic rounding technique is applied to modify 2×2 sub-matrix elements in model gain matrices, adjusting the logarithm base to balance accuracy and RGA improvement, ensuring no sub-matrix RGA element exceeds a desired threshold, and implementing this method via a computer algorithm to simplify the process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If manual iterative methods are used to modify model gain matrices, then RGA elements can be improved, but the process is time-consuming and may require large magnitude gain changes
Solution Approach 1:
The patent applies logarithmic transformation to the gain matrix elements, converting multiplicative relationships into additive ones. This parameter transformation enables more efficient computation and reduces the number of iterations needed to achieve desired RGA properties, directly addressing the time-consuming nature of manual iterative methods
Solution Approach 2:
The patent replaces manual iterative adjustment with an automated computer algorithm that performs logarithmic rounding and matrix modification. This substitution eliminates the need for time-consuming manual iteration while maintaining or improving the quality of RGA element optimization
2Manufacturing precision
If manual iterative methods are used to modify model gain matrices, then some RGA elements can be improved, but the process is complex and may reverse previous fixes
Solution Approach 1:
By transforming the gain matrix into logarithmic space, the patent simplifies the modification process. The logarithmic rounding operation provides a systematic approach that prevents the reversal of fixes, as each modification is based on a consistent mathematical transformation rather than ad hoc adjustments
Solution Approach 2:
The patent replaces complex manual iterative procedures with a straightforward computer algorithm that applies logarithmic rounding. This automation eliminates the complexity of tracking multiple iterations and preventing reversal of fixes, as the algorithm systematically processes the entire matrix in a unified manner
3Manufacturing precision
If the base of the logarithm is increased to improve RGA properties, then RGA properties are improved, but the magnitude of possible change increases
Solution Approach 1:
The patent uses logarithmic transformation with a configurable base to control the trade-off between RGA improvement and gain change magnitude. By adjusting the logarithm base parameter, users can optimize the balance between achieving desired RGA properties and maintaining acceptable gain change magnitudes, providing a systematic way to manage the trade-off
Data Source
AI summary
A method is presented for adjusting the steady-state gains of a multivariable predictive control, planning or optimization model with uncertainty. The user selects a desired matrix relative gain criteria for the predictive model or sub-model. This is used to calculate a base number. Model gains are extracted from the predictive model and the magnitudes are modified to be rounded number powers of the calculated base number.