A Robust Control System Design.

Abstract

Abstract : A representation of controllable linear systems is introduced, which permits assigning poles or characteristic parameters to a state feedback system by a matrix multiplication. This is used as a link between state space and classical parameter plane methods. The system representation maps a point in a nxp dimensional parameter space of characteristic parameters into the nxp dimensional parameter space of state feedback gains, where p is the number of actuators. For p counts one the coordinates of the characteristic parameter space are the coefficients of the closed loop characteristic polynomial, for p greater than one they are coefficients in a characteristic polynomial matrix and its determinant is the characteristic polynomial. By this computationally simple mapping procedure it becomes feasible to map not only a fixed set of eigenvalues but also regions in the s or z plane, in which the eigenvalues shall be located. This relaxation of the dynamic specifications permits satisfying other typical design specifications like robustness with respect to sensor and actuator failures, large parameter variations, finite word length implementation, and actuator constraints. All tradeoffs between such requirements can be made in the feedback gain space. Three examples illustrate the variety of problems which can be tackled with this new tool. (Author)