Several Classess Of Controller Order Reduction Algorithm Comparison And Application

For a long time, research on H_∞controller design is the main content ofmany areas. It is tend to have a high-order when we use the robust control theory todesign the H_∞controller, which is difficult to easily use in practical engineering,while the reduction is an effective way to solve such problems. The main significanceof reduction is changing a complex and high-order system into a simple and low-ordersystem, while ensuring the reduction system with the original system performance,such as stability, speed and so on. The paper first discussess and compares withseveral reduction methods, and then uses the robust control theory to design andreduce the order based on these methods. And the detailed work are as follows:1. Discussed the reduction algorithm based on Singular Value Decomposition, themain idea of the method is to solve the Hankel singular values and consider the orderof reduction system according to the size of singular values. Then find a balancetransformation matrix to balance the original system, and then deal with convertedsystem based on SVD algorithm.Finally, compare and analyse advantages anddisadvantages of the balanced trucation method and frequency weighted method. Thealgorithm can guarantee stability of the reduction system, it is the basis of reductiontheory.2. Discussed the reduction algorithm based on Krylov subspace theory, the mainidea of this method is to seek transfer function of a low-order system, and spread at apoint by Taylor, the low-order system can match several moments of the originalsystem. Then use two important ways that Arnoldi algorithm and Lanczos algorithmfor order reduction in Krylov subspace theory. algorithm.Finally, compare and analyseadvantages and disadvantages of these two algorithms.These algorithms could makethe calculation greatly reduced, and they are excellent reduction methods.3. Discussed the reduction algorithm based on Least Squares, the main idea of thismethod is combined with the characteristics of Singular Value Decomposition andKrylov subspace theory, and compare and analyse advantages and disadvantages of several reduction algorithms. The algorithm can not only ensure stability of thereduction system, but the calculation process is convenient, easy to realize and theerror norm is also very small, so it is a kind of good reduction method.4. Discussed the design and reduction process of the diesel H_∞controller. Themain engine controller K design ideas include making a complete control systemstructure, confirming the controlled object and the controller, geting the generalizedobject, calculating the weighting matricesW1,W2,W3, designing the required H_∞controller. And then for the closed-loop system consisting of the controller and thecontrolled object, use the three algorithms discussed above to reduce, compare and analyse,and get their advantages anddisadvantages.