Suboptimal control of linear systems by state vector partitioning

Abstract

Several research workers [1-5] have studied the problem of designing suboptimal/near optimal regulators for high order plants. The implementation of the sub-optimal controllers has the advantage that a significant saving in computational effort may be realized with a small deterioration in system performance. The methods available for designing suboptimal controllers for large scale systems may be classified in the following broad categories: i) State vector partitioning methods [1] ii) Singular perturbation methods [2] iii) The use of aggregated reduced order models [3] iv) Control law reduction [4] The methods (ii) through (iv) yield good results if the original system eigenvalues are clearly separable into dominant and non-dominant modes. However, the state vector partitioning method is applicable to all cases. In this method suboptimal controllers are derived by partitioning the given system state vector into two or more parts and then solving the matrix Riccati equations for the subsystems. Finally, the controllers for each partitioned system are combined linearly to provide a suboptimal control for the original system. Meditch [1] introduced a set of constant matrices for deriving the lower order subsystems. These matrices play a crucial role in obtaining the suboptimal controller. However, no systematic procedure has been given for choosing these constant matrices apart from the work of Reddy and Rao [5] who presented a procedure for a multi-output system making use of Crossley's [6] canonical form. In this paper a method is presented to derive systematically the constant weighting matrices from the modal matrix of the original system. These constant matrices can be termed as aggregation matrices. It is proved that the resultant suboptimal closed loop system is always stable with this particular choice of aggregation matrices.