Research Of Almost Disturbance Decoupling With Pole Placement

The disturbance decoupling problem is a research focus in the mathematics and control community, it occupies a central position in classical and modern control theory. Some important control problem, such as model reference, robust control, tracking control and decentralized control are all linked to disturbance decoupling problem. Almost disturbance decoupling problem is the extension of disturbance decoupling problem.It is well know that the locations of the closed loop system poles play an important role in the main performance of the system, such as stability, overshoot and adjustment time. In order to achieve the maximal pole placement,(almost) disturbance decoupling problem with pole placement emerges as the times require.On the premise of ensuring the solvability of (almost) disturbance decoupling problem, the locations of the closed loop system poles is studied in a geometric approach in this paper, seek out the optimal geometric solution with maximal pole placement, and figure out the corresponding state feedback control matrix. The main work contents include the following points.Firstly, to prepare for the study of almost disturbance decoupling problem, the almost invariant subspace of the original system equivalent to the invariant subspace of the new system by changing the input control parameters of the system. With the purpose of studying the general case, namely without controllability assumption, for uncontrolled system, the original system is decomposed into controllable and uncontrollable two subsystems through decomposition structure, and find out the relationship between the subspace of the original system and the subspace of the controllable subsystem.Secondly, analyze the distribution of the closed loop system poles, figure out the parametric representation of the fixed poles and infinite poles. On the foundation of this, the parametric representation of the optimal geometric solution is figured out, and the algorithm for such an optimal geometric solution is also proposed.Finally, several examples are proposed, and the correctness of the algorithm is verified through the simulation result.