The Model Reduction Algorithm For Frequency-Weighted Based On LMI And Its Application

Modern engineering often encountered very large systems similar integrated circuit,distillation and other with the rapid development of society. The order is more and more higher with the complexity of such systems is also increasingly high which mathematical model of system and the controller. A higher order means that the cost is higher and engineering difficulty is greater. So the people often want to the order of model and controller not too big, because the lower order means that more concise simulation program and less computer time and higher reliability for design, simulation,and implementation systems. Based on this, model reduction and the reduced-order controller design obtained widespread application in engineering practice and development.Dependent on the outcome of already existing, Consider the model reduction problem in limited frequency, a new design method of model reduction base on linear matrix inequality(LMI). Combining with the bounded real lemma, model reduction problem can approximate to a mathematical problem which is a non-convex feasibility problem. Take the full-order controller as the controlled object, design robust reduced-order controller by the method of model reduction. The main content of the article are:1. Elaborated recent development and research methods of model reduction and reduced-order robust controller. Analyzed and summarized existing model reduction algorithm. These reduction algorithms will be applied to a fourth-order system at the same time, and compare the advantages and disadvantages of each method.2. Proposed a method which is model reduction algorithm for frequency-weighted based on LMI. The model reduction problem in the limited frequencies is converted into a non-convex optimization problem by the new design method which joint LMI and frequency weighting function. An effective model reduction method base on cone complementarity algorithm(CCA) to solve the non-convex optimization problem with rank constraints. Prove the feasibility of the method through the corresponding numerical examples and simulation analysis. It is the advantage of this method that reduced-order model is stable, and realized the error in the limited frequencies is much smaller than similar methods exist.3. Take the full-order controller as the controlled object, using the method design robust reduced-order controller which frequency-weighted optimal model reduction base on LMI. In the application, using the 8-order linear model of helicopter(the space velocity of helicopter is 46.2 m/s), take the robust controller of 16 orders fell to 12 orders in success. And the reduced closed loop system has stability and decoupling.