Linear and nonlinear discrete-time state-space modeling of dynamic systems for control applications
This research proposes a methodology to model a class of nonlinear dynamic systems, known as linear-analytic systems, by discrete-time state-space models. The method is based on a series of deterministic simulations of the differential equations of motion using well designed step-like input functions. The simulation results are processed to generate a vector series characterizing the selected discrete-time state-space model. A realization algorithm developed in this research is then applied to the computed vector series in order to obtain the matrices describing the state-space model. It is shown that the vector series obtained from the simulation results are discrete-time triangular Volterra kernels. Therefore, the designed simulations can be viewed as a new method to identify discrete-time Volterra kernels. Nevertheless, the emphasis here is in generating state-space models, since they are more attractive for design and analysis of control systems than the Volterra system representation. The novelty of the methodology being proposed is the fact it does not require continuous-time state-space modeling of the system as an intermediate step in the process: it goes from nonlinear differential equations directly to discrete-time state-space models. Such a philosophy seems attractive in the modeling of dynamic systems immersed in air flow fields, with aerodynamic forces being computed through the use of CFD codes. The main disadvantage in the methodology is that the number of simulations grows exponentially with the discrete-time model order, a direct consequence of the number of parameters needed to be fed into the nonlinear realization algorithm. Nevertheless, since each simulation is independent of the others, the simulations could be carried out by parallel processing in modern computers, reducing the total time necessary to obtain the simulations by a factor equal to the number of processors available in the parallel processing. Applications are first made to the modeling of simple dynamic systems containing nonlinearities caused by the presence of trigonometric functions on the differential equations of motion. Subsequently, the methodology is applied to an aeroservoelastic system containing nonlinear phenomena caused by transonic unsteady aerodynamics.
Weisshaar, Purdue University.
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