On Matrix Linear Diophantine Equation-Based Digital-Adaptive Block Pole Placement Control for Multivariable Large-Scale Linear Process

This paper introduces a digital adaptive control framework for large-scale multivariable systems, integrating matrix linear Diophantine equations with block pole placement. The main innovation lies in adaptively relocating the full eigenstructure using matrix polynomial representations and a recursive identification algorithm for real-time parameter estimation. The proposed method achieves accurate eigenvalue placement, strong disturbance rejection, and fast regulation under model uncertainty. Its effectiveness is demonstrated through simulations on a large-scale winding process, showing precise tracking, low steady-state error, and robust decoupling. Compared with traditional non-adaptive designs, the approach ensures superior performance against parameter variations and noise, highlighting its potential for high-performance industrial applications.