Simplification of nonlinear controllers: balancing approaches

Hong Min

doi:10.17918/00009661

This thesis concerns the controller reduction for nonlinear systems with dynamic output feedback controllers. Using the concept of nonlinear balancing, algorithms to reduce controller order are proposed. The balancing involves a series of state coordinates transformations in which the contribution to controllability by each state is measured by a singular value function and this singular value function also indicates the contribution to observability by the same state. By truncating states associate with smaller singular value functions, the order of the controller is reduced. In the case when controller is stable, controller reduction is extended from model reduction. The discussion for unstable controller reduction focuses on H[infinity] suboptimal output feedback controller and other controllers that employ observer-based structures. An unstable controller is reconstructed based on its stable left (right) coprime factorization, so that the above controller reduction technique can be applied. Four such algorithms are proposed. It is essential that a reduced controller still stabilizes the closed system and does not significantly degrade performance. Three of the five reduction approaches are evaluated with respect to stability and H[infinity] performance. Using small-gain theorem, it is found, in each of the three cases, that when the error between the full order and the reduced controllers has an L2-gain less than certain value as determined by singular value functions in balancing, the closed-loop stability is guaranteed. The above finding is used to choose the order r of the reduced controller to ensure stability. As a measure of the degradation in performance, a formula has been derived to compute the increase in the disturbance attenuation level. The increase is smaller if less states are truncated. Computational issues for balancing reduction are discussed. The impact of approximate controllability and observability functions on balancing and reduction is investigated. Another issue discussed is the construction of the diffeomorphism in balancing controllability and observability functions.

Simplification of nonlinear controllers: balancing approaches

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Simplification of nonlinear controllers: balancing approaches

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