Design Of Reduced-Order LQG Controller By The Principle Of Minimal Information Loss

Model and controller reduction are long-term discussed topics in the fields of control theory and application.For systems with higher order plant model,the realization of controller would be harder to implement.The purpose of controller reduction is that,on the one hand, there are fewer things to go wrong in the hardware or bugs to fix in the software by using the reduced-order controller and they are easier to understand and the computational requirements are less;on the other hand,investigating the high-order closed-loop system is also beneficial to the comprehension of system dynamic structure.Based on the dynamic and information theoretic properties of control systems,this thesis investigates the problem of controller reduction by using information theoretic measures.One controller reduction method is firstly to reduce the plant model,and then design the LQG controller based on this reduced model;the other is to find the optimal LQG controller tbr the full-order model,and then get a reduced-order controller by information theoretic methods.Two LQG controller reduction methods are proposed based on the principles of minimal information loss method(MIL) and minimal cross-Gramian information loss method(CGMIL),respectively. The simulation results are given to illustrate the performances of reduced-order controllers.The innovation and contribution of this thesis are as follows:(1) This thesis investigates the problem of designing reduced-order LQG controller based on information theoretic method.By studying the controller inner structure,the reduced-order LQG controllers are obtained by combining the methods of model reduction and controller reduction based on information theory.We extend the methods of MIL model reduction and CGMIL model reduction method to the problem of controller reduction that complete the algorithms.(2) In order to compare our methods,which include MIL controller reduction and CGMIL controller reduction method,to the KL information distance controller reduction method,a 10-order lightly beam model and a realistic 30-order distillation model are adopted for simulations.We compare these three controller reduction methods by using output square error of Gaussian white noise input and specific input signal,respectively.The simulation results show that the reduced-order controllers derived by the proposed two controller reduction methods approximate the full-order controller satisfactorily.Our work indicates that,the proposed methods of model reduction and controller reduction based on information theory possess clear physical meaning,satisfactory performance and properties.The derived results suggest new instruments of controller reduction and extend the application of the minimum information loss principle.