Orthogonal Eigenstructure Control with Non-collocated Actuators and Sensors

Abstract

An orthogonal eigenstructure control method with collocated actuators and sensors was recently developed by the authors. In this paper the application of the method is extended beyond the collocation of the actuators and sensors, including the cases that different numbers of actuators and sensors are used. Orthogonal eigenstructure control is an output feedback control for multi-input multi-output linear systems. This method uses singular value decomposition to find the matrix that spans the null space of the closed-loop eigenvectors. This method regenerates the open-loop system while simultaneously determines a set of eigenvectors that are orthogonal to the open-loop eigenvectors. This method does not attempt to place the eigenvalues of the closed-loop system, nor does it require defining a set of closed-loop eigenvectors. The closed-loop eigenvectors will be within the achievable eigenvector set and the closed-loop poles will be consistent with them. As a result, no extra constraints have been imposed to the system trying to place the closed-loop poles at certain locations such that excessive force in actuators is prevented. Since there are usually some limitations on the location of the actuators and sensors, collocation of actuators and sensors is not always possible. Also, some systems might not have equal number of actuators and sensors. The proposed method in this paper is based on adding virtual actuators and sensors to the closed-loop system in order to extend the application of the orthogonal eigenstructure control to the systems with non-collocated actuators and sensors as well as the systems with different numbers of actuators and sensors.