Modeling for control of centrifugal compressors

Abstract: Downsizing and turbocharging of engines provide a way to meet increasing demands for efficiency and performance in the automotive industry. An engine design is a result of compromises, e.g. the selection of charging system, and the trend is to reduce these compromises by increasing system complexity. Models have come to play a central role to handle this rise in complexity, and are used for simulation, system optimization and control synthesis. The models should describe the entire operating range, be capable of extrapolation, be easily parameterizable, and wide cover a range of applications.A novel compressor model is developed which, in addition to the nominal operation, also covers surge, choke and operation at pressure ratios less than one. The model is based on data from more than 300 compressor maps, measurements from engine test stands, and a surge test stand. The general knowledge gained from the in-depth analysis is condensed in the model equations. The model can be automatically parametrized using a compressor map, is based on static functions for low computational cost, and is shown to extrapolate low speed compressor operation well. Furthermore, it is shown to be applicable to compressors of different size, ranging from small car applications to large heavy duty vehicles. Compressor restriction operation is modeled down to a standstill compressor, and shown to agree well with gas stand measurements. Further, the analysis contributes with new knowledge and models for choking pressure ratio and flow.A method to automatically determine a turbo map, when the turbo is installed on an engine in an engine test stand is developed. The method can be used to validate manufacturer maps or expand the region covered in a map. An analysis of the limits that an engine installation imposes on the reachable points in the compressor map is performed. The addition of a throttle before the compressor is suggested to increase the reachable map region, and an engine and test cell control structure that can be used to automate the measurements is proposed. Two methods that compensate for the deviation between measured and desired speeds, are proposed and investigated. A gas stand map is compared to the map generated in the engine test stand, and a generally good agreement results.An experimental analysis of the applicability of the commonly used correction factors, used for estimating compressor performance when the inlet conditions deviate from nominal, is performed. Correction factors are vital, to e.g. estimate turbocharger performance for driving at high altitude or to characterize second stage compressor performance, where the variations in inlet conditions are large. Measurements from an engine test stand and a gas stand show a small but clearly measurable trend, with decreasing compressor pressure ratio for decreasing compressor inlet pressure, for points with equal corrected shaft speed and corrected mass flow. A method that enables measurements to be analyzed with modified corrections is developed. As a result, an adjusted shaft speed correction quantity is proposed, incorporating also the inlet pressure in the shaft speed correction.