Study On The Order Reduction Algorithm For H_∞ Controller Based On Model Reduction

In the modern control field,the physical objects we meet are always complex system with high orders.In recent years,the robustH_∞ control theory has a mature development and used widely.The scale of the designed controller by using robustH_∞ control theory is much more bigger.No matter from the view of easy to programming in the engineering or the economic cost,we hope the order of the model and controller can as less as possible.In this paper,using the model reduction methods in the reduction ofH_∞ controller and a new improved algorithm based on Information Loss Minimum Theory has been proposed.Detailed work are as follows:1.Discusse the Balanced Truncation Reduction based on Singular Value Decomposition systematically and detailedly.The key is according to the order of system’s Hankel values to obtaining the reduced order.Then truncation reduction by using the transformation matrix T which get through balancing transformation method.For stabilized original system,it can makes reduced system stable,and has a good performance in low-orderH_∞ controller reduction.2.Search the Least Squares algorithm based on Krylov subspace theory.The law is reduced system can match several moments of original system.Made an exposition of continuous and discrete method.The Least Squares algorithm simulation shows not good inH_∞ controller reduction.3.Search the Information Loss Minimum Theory in reduction,sometimes it has a low probability inH_∞ controller reduction.So a new improved algorithm has been proposed,it combining Balanced Truncation Reduction with Information Loss Minimum Theory.Simulation results have shown the effectiveness of the new technique by comparing with the above-mentioned.