Uncertainty Of Modal Parameters Research Articles

Uncertainty Models and Robust Complex-Rational Controller Design for Flexible Structures

Realparametricuncertaintiesin themodal dampingratiosandfrequenciesofe exiblestructuresarerepresented by complex uncertainties that can lead to robust controller designs satisfying robust performance specie cations. Thesecomplex uncertaintyblocksareusefulina π-synthesiscontrollerdesignprocedure.Twomodelsareproposed for modal parameter uncertainties. The e rst model uses a coprime factorization representation of the perturbed plant, whereas in the second model, a diagonal representation with complex eigenvalues is used. The innovation in the second method proposed is the use of a complex-rational controller design strategy, which offers tight uncertainty bounds and leads to a robust performance controller. The frequency response of the complex-rational controller is then approximated by a real-rational controller achieving the robust performance specie cations. LEXIBLE structures are generally characterized by the un- dampednaturalfrequenciesand dampingratiosoftheire exible modes. These parameters are subject to errors when they are esti- mated. Such uncertainties are important and should be taken into account in a robust controller design. The proper capture of modal parameter uncertainties in dynamic models of e exible structures for robust control has been the subject of ongoing efforts. Previ- ous research 1;2 used additive or multiplicative uncertainty models to take into account the variation in the dynamics of the plant. An- other way is to use certain heuristics to facilitate the representation of the parametric uncertainties in the e exible modes by a para- metric model. 3 These heuristics represent approximations in the parameter variation that are not generally realistic and lead to con- servative controller designs, that is, designs that cannot provide the desired performance in the face of realistic levels of parametric uncertainty. Recently, a model representing parametric uncertainties in the modes of a e exible structure was discussed in Ref. 4. Note that such models were developed 5 a few years ago. In Ref. 5, a model of dynamic uncertainty covering parametric variations in the e exible modes of a e exible structure was developed. This dynamic uncer- tainty has the virtue of being nonconservative, but only when the frequencies of the e exible modes are close to each other. In this paper, we propose to represent perturbations in the frequency and damping ratio of each e exible mode by a tight low-order dynamic uncertainty. Thus, we reduce the order of the augmented plant by half and transform the mixed real/complex uncertainty robust per- formanceπ-synthesis problem into an easier complex π synthesis. We use two techniques: The e rst is based on the coprime factor- ization framework, 6 and the second uses a complex diagonal modal representation to model the dynamics of the e exible structure and

µ Synthesis for a Large Flexible Space Structure Experimental Testbed

An application is presented of π synthesis to the robust control of a large e exible space structure experimental testbed called Daisy. A perturbed left-coprime factorization of Daisy’ s dynamics is used to capture the uncertainty in the modes. Designs of the π synthesis controller based on left-coprime factorizations of 46th-order collocated and noncollocated models of Daisy are presented together with simulation and experimental results. These results are compared to those obtained with H1 H1 controllers, and it is shown that the π controllers performed better. These controllers provide robust performance with respect to given bounds on modal parameter uncertainties without resorting to computationally complex techniques involving real structured perturbations.

Uncertainty modeling and experiments in ℋ/sub ∞/ control of large flexible space structure

Approaches to uncertainty modeling for robust control of large flexible space structures (LFSSs) such as additive or multiplicative perturbations in /spl Hscr//sub /spl infin// do not work very well because of the special properties of LFSS dynamics. We propose the use of a left-coprime factorization (LCF) of LFSS dynamics in modal coordinates in order to get improved stability margins and performance in robust control design. The plant uncertainty is then described as stable perturbations of the coprime factors accounting for modal parameter uncertainty and unmodeled dynamics. Two multivariable /spl Hscr//sub /spl infin// designs based on LCFs of 46th-order collocated and noncollocated models of an LFSS experimental testbed are presented together with simulation and experimental results to illustrate the technique.