Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System One-Dimensional Model

Abstract

In this paper, a one-dimensional unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multistage axial compressor experimental rig configured for single-stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of nine first-order ODEs. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open-loop uncontrolled and closed-loop controlled behaviors. These comparisons focus on (i) forced transients and (ii) global nonlinear dynamics and bifurcations. In all cases the agreement between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed-loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed-loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first-order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control-oriented high-frequency turbomachinery modeling being developed by the authors.