1993-07-01

Equal Effort Level in Eigenvalue Assignment for Nominally Linear Systems Having Multiple Control Variables 932285

Actuator equal effort level and dynamic control authority are defined. A procedure for eigenvalue assignment which results in each actuator contributing equal weighted effort in the assignment of each eigenvalue set is presented for four frequently encountered cases. Restrictions on applicability are identified, and an example is given.
It is common knowledge that the majority of mathematically rigorous control theory is applicable to those systems which are sufficiently accurately modeled as linear time invariant (LTI) and in which the model reflects all relevant system dynamics. These conditions may be applicable to some systems under development as part of the CELSS Program when they are operated within appropriate regions of the adjoined state and control effort space (ASCS), e.g., near fixed set points or some tracking command paths. Actuators are limited in the effort they can exert, that is, they saturate if commanded to exert greater effort that their design capability, and this limitation destroys approximate linearity when any actuator saturates during a transient. It is therefore important to select feedback gains so as to minimize the possibility of actuator saturation during control system operation, or stated alternatively, to make the region of applicability of the LTI assumption in ASCS as large as possible.
In this paper, a procedure for assigning eigenvalues while establishing equal effort levels is presented. It is based on dynamic control authority, and is accomplished in asymmetric Real Jordan Canonical state space. Four frequently encountered cases are addressed all for conditions of distinct eigenvalues.

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