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Guaranteed robust stability of the closed-loop systems for digital controller implementations via orthogonal
1Department of Electrical Engineering, Tatung University, Taipei, Taiwan 10451, ROC.
Summary
This study proposes a robust stability analysis for digital control systems affected by finite word length (FWL) errors. It determines the minimum mantissa bits for stabilizing controllers, reducing implementation costs.
Area of Science:
- Control Systems Engineering
- Numerical Analysis
- Computer Arithmetic
Background:
- Digital control systems are susceptible to errors from finite word length (FWL) effects, impacting stability.
- Floating-point arithmetic introduces uncertainties due to roundoff and computational errors, dependent on mantissa bit number.
Purpose of the Study:
- To develop a robust stability analysis method for digital closed-loop systems under FWL effects.
- To derive a sufficient stability criterion and determine the minimum mantissa bit number for digital controller implementation.
Main Methods:
- Uncertainties from FWL effects are modeled based on mantissa bit number in floating-point arithmetic.
- The Small Gain Theorem and Bellman-Grownwall Lemma are used to derive a stability criterion.
- Eigenvalue sensitivity is analyzed using mixed matrix-2/Frobenius norms, and an optimal similarity transformation is obtained via minimization.
Main Results:
- An analytical closed-form solution for optimal transformation is provided.
- The proposed method determines the minimum mantissa bit number for stabilizing digital controllers.
- Simulation results demonstrate the effectiveness of the proposed scheme in reducing required mantissa bits.
Conclusions:
- The approach offers a robust method for stability analysis of digital control systems with FWL effects.
- It enables the implementation of stabilizing controllers using fewer mantissa bits, leading to more efficient digital implementations.