Predictive Control Algorithm with Time Delay Based on State-Space Plant Model: An LMI Solution Example

This article presents a practical example of solving Linear Matrix Inequalities (LMI) for predictive control algorithms with time delays based on state-space plant models. The example aims to help readers better understand the implementation process through detailed steps and technical explanations, including code-level implementation considerations.

First, we will introduce the fundamental principles and key concepts of predictive control algorithms, emphasizing the mathematical formulation and constraint handling mechanisms. Next, we analyze the impact of time delays on control performance and present mitigation strategies through delay compensation techniques in the prediction horizon. Subsequently, we demonstrate how to apply this algorithm to state-space controlled objects, detailing the LMI formulation process using MATLAB's LMI toolbox or YALMIP framework, including key functions like lmivar and lmiterm for matrix variable declaration.

Finally, we illustrate the complete implementation through a numerical example, discussing stability analysis and performance evaluation using MATLAB simulations. The example will include code snippets showing how to set up prediction matrices, handle delayed states, and solve LMIs for controller synthesis.

Through this article, readers will gain comprehensive understanding of time-delay predictive control algorithms for state-space systems and practical skills in LMI problem-solving. The acquired knowledge can be directly applied to engineering projects for improved control performance in systems with inherent delays.