An Instrumental Variable Method for Continuous-Time Transfer Function Model Identification With Application to Controller Auto-Tuning

Abstract

An instrumental variable algorithm is presented that estimates the coefficients of a continuous transfer function model directly from sampled data. The algorithm is based on instrumental variables extracted from an auxiliary model and input and output signal derivatives estimated by filtered difference equations. As a result, this method does not require any prior knowledge of the output noise. To ensure the validity of the filtered derivative estimates, a criterion based on the Nyquist frequency and the system bandwidth is established. Then the concept of asymptotic consistency is applied to the proposed instrumental variable algorithm to identify the conditions for convergence of the model parameter estimates. Specifically, the asymptotic consistency conditions impose a continuous and persistent exciting constraint on the input signal. This is analogous to the persistent excitation condition for identification of discrete models. The proposed instrumental variable algorithm is demonstrated within an auto-tuning algorithm for feedback controllers based on plant inversion. In this application, the algorithm is only suitable for lower-order transfer functions that are minimum-phase and stable. These types of systems are common in industrial applications for manufacturing and process control. Here, the algorithm is experimentally validated for automatic tuning of the idle speed controller on a 4.6L Ford V-8 spark ignition engine.