Interpolation of homotopic operating states

A method for real-time modeling of a compressor that is designed to operate between a stall line beyond which the compressor operates in a stall condition, and a surge line beyond which the compressor operates in a surge condition, the method comprising:

• storing, in a memory, an operating condition matrix that plots multiple compressor pressure ratios to each of a plurality of compressor speeds;
• storing, in the memory, an operating state matrix that plots multiple compressor flow rates to each of the plurality of compressor speeds, the operating condition matrix being related to the operating state matrix such that a first compressor pressure ratio at a first location of the operating condition matrix corresponds to a first compressor flow rate at a corresponding location of the operating state matrix, the operating condition matrix including a first plurality of rows each corresponding to one of the plurality of compressor speeds and a first plurality of columns each corresponding to equally spaced locations along the plurality of compressor speeds between the stall line and the surge line, each cell of the operating condition matrix including a pressure ratio value;
• determining, by a compressor controller, a current or target compressor speed and a current or target compressor pressure ratio;
• identifying, by the compressor controller, a current or target location in the operating condition matrix based on the current or target compressor speed and the current or target compressor pressure ratio;
• determining, by the compressor controller, a current or target compressor flow rate by interpolating values in the operating state matrix based on the current or target location;
• and
• controlling, by the compressor controller, the compressor based on the current or target compressor flow rate.

A method for real-time modeling of a compressor comprising:

• obtaining, by a model controller, test data including combinations of compressor speeds, compressor pressure ratios, and compressor flow rates, the test data being obtained by at least one of detecting the test data from a physical compressor or calculating the test data using a model of the compressor;
• generating, by the model controller, an operating condition matrix that plots multiple compressor pressure ratios to each of a plurality of compressor speeds based on the test data;
• generating, by the model controller, an operating state matrix that plots multiple compressor flow rates to each of the plurality of compressor speeds based on the test data;
• providing the operating condition matrix and the operating state matrix to a compressor controller as a model of the compressor such that the compressor controller can control the compressor based on the model;
• and
• generating the operating condition matrix includes generating the operating condition matrix to include multiple equally-spaced compressor pressure ratio values for multiple compressor speeds, and generating the operating state matrix includes generating the operating state matrix to include multiple equally-spaced compressor flow rates for each of the multiple compressor speeds.