Pulse-compression probing for nonlinear systems with additional hard nonlinearity at the input

The effects of input hard nonlinearities on probing outputs are analyzed with respect to the pulse-compression probing method. The pulse-compression probing method identifies a local, linear model around an operating point of a nonlinear system by processing the system response to a probing input. The outputs of probing systems with one of six common input hard nonlinearities, including deadband, saturation, relay, backlash, and rate limit are derived. Pulse-compression probing is effective for the first five hard nonlinearities listed, where the probing outputs retain the same waveforms as if the probing inputs were scaled and offset. When probing an input with a rate limit, pulse-compression probing is effective when the bit duration of the probing input exceeds some threshold, which is based on the rate limit. As long as the probing input is properly designed with respect to the input nonlinearities present, the shape of the probing output is preserved. As a numerical example, pulse-compression probing method is applied to the NASA generic transport aircraft model with nonlinearities at the probing input.