A Model-order-deduction Algorithm for Nonlinear Systems

An important aspect of mathematical modeling for controller design or system performance evaluation is obtaining an appropriate model order that meets the needs of the problem at hand. In modeling systems with distributed and discrete mechanical components, a model builder needs to decide the number of compliant elements to use to represent each distributed component — a potentially timeconsuming and error-prone process. Nonlinear component behavior, such as dry friction and backlash, is present in most mechanical systems and further complicates the modeling process. An algorithm was developed previously to coordinate the synthesis of the minimumorder linear system model that accurately characterizes the frequency response of the system over a frequency range of interest 〈0, ωreq〉. This is accomplished by iteratively determining which component refinement causes the smallest increase in model spectral radius when a more complicated component submodel is used in the system model. A more complicated submodel of this component is incorporated in the system model, and the iterative process continues until any further increase in model order results in poles beyond ωreq. In the current research, this algorithm has been extended to synthesize models of nonlinear systems. The extended algorithm follows a procedure similar to the original algorithm, but uses describing-function theory to develop an amplitudedependent quasilinear representation of the nonlinear system model. The extended algorithm synthesizes models that are also of minimum order. Algorithm operation is demonstrated using a nonlinear modeling example. Extending the original modeling algorithm to synthesize minimum-order models of nonlinear systems represents a significant extension of its utility, as a much broader class of modeling problems can be tackled.