A digital orthogonal model for nonlinear processes with two-level inputs

This paper describes a method by which the class of nonlinear processes with switched two-level inputs and finite settling times can be identified and an adaptive model of the process constructed. The adaptive model uses only the process input-output records. After a suitable identification time (approximately 14-70 times the settling time of the process) the model approximates the plant performance using a mean square error criteria and tracks any changes in the plant parameters. The past of the two-level input is stored in a digital shift register tapped at
n
points, thus forming a function space comprised of 2
ⁿ
nonoverlapping or orthogonal cells. By averaging the output wave-form during the time that a cell is occupied a coefficient is obtained which characterizes the output for that input condition. A basic assumption about the input waveform statistics reduces the number of characterizing coefficients from 1024 to approximately 50. The model that is evolved is a small synchronous digital computer. The model is quite versatile as it is independent of the type of process nonlinearity and can adapt to systems with different settling times. The model is ideal for use in predictive adaptive control systems where a fast time predictive model is utilized.