Model Refinement Of Second Order Dynamic Systems

Since in general there are errors between the theoretical models and the practicalsystems, error correction, i.e., model refinement, is highly desired. This thesis studies themodel refinement problem of second order dynamic systems using eigenstructureassignment approach. The basic idea is to transform the model refinement problem intothe eigenvalue and eigenvector assignment problem in linear time-invariant systems viaoutput feedback. By using output feedback eigenstructure assignment approach,eigenvalues and eigenvectors of the refined system are assigned to the desired targetvalues. First, based on eigenstructure assignment approach sufficient conditions for theexistence of solutions to damping matrix refinement problem, stiffness matrix refinementproblem, and simultaneous damping matrix and stiffness matrix refinement problem areestablished, and parametric expressions for the associated model refinement gainmatrices are given. The parameters contained in the gain matrices specify the non-uniqueness of thesolutions of the corresponding model refinement problems, which may be used to achieve othersystem property specifications beyond model refinement. Next, based on the obtained parametricsolutions to the model refinement problems, algorithms for the solutions to minimum gain modelrefinement of damping matrix, stiffness matrix, and both damping and stiffness matricesare proposed. The algorithms may give control systems with much optimality. The mainachievements of this thesis are as follows:(1) A sufficient condition for existence of a solution to the damping matrix (stiffnessmatrix) refinement problem is proposed, and parametric expressions for eigenvectors andgain matrix of the refined system are given.(2) A sufficient condition for existence of a solution to the simultaneous dampingmatrix and stiffness matrix refinement problem is proposed, and parametric expressionsfor eigenvectors and gain matrix of the refined system are given.(3) Based on the general parametric solution to the damping matrix (stiffness matrix)refinement problem, an algorithm for the solution to minimum gain model refinement ofdamping matrix (stiffness matrix) is proposed.(4) Based on the general parametric solution to simultaneous damping matrix andstiffness matrix refinement problem, an algorithm for the solution to minimum gainmodel refinement of both damping matrix and stiffness matrix is proposed.