Nonlinear system identification with an application to hydraulic actuator friction dynamics

The friction of lubricated sliding is a highly nonlinear, non-stationary process that depends on many physical parameters. Conventional studies of friction often address only the steady state characteristics. The analytic modeling of friction in dynamical sliding (e.g., time varying sliding velocity) is very difficult.; We use system identification theory to model the friction mechanism in dynamical sliding at low sliding speeds. We propose two nonlinear models for the identification of the friction process: a Hammerstein model and a state space model.; For the identification of the Hammerstein model parameters, we develop a series of adaptive algorithms where one algorithm becomes the basis of the next algorithm. Wavelet basis functions are used to represent the nonlinearity of the model, and a least squares criterion is used to estimate the model parameters. An effort has been made to develop algorithms in the most general terms, because the algorithms can be applied to other linear/nonlinear problems.; The state space model of the friction dynamics is developed from a close observation of the friction signal of the lip seal. First, a dynamic model of the seal, consisting of lumped linear and nonlinear components, is built by using a macroscopic point of view. Then, a discrete time state space model is derived from the governing equation of the dynamic model. The deformation of the seal is defined as the current state of the system, because the deformation is determined by the sliding history and represents the current state of the seal. A Kalman filter and a least squares criterion are used to estimate the state vector and model parameters, respectively.