A Speed Observer for Sensorless Control of an Induction Motor

Half a century has passed since the time F. Blaschke received a patent for vector control of an induction motor with a speed sensor and a Hall sensor. Since that time, the transformation of generalized vectors in the Park—Gorev equations as projections on the axes in different coordinate frames aft, dq, and xy has been regarded to be a commonly accepted one. With this approach, five differential and four algebraic equations with cross-links have to be solved for studying the processes in an induction motor, which involves certain inconvenience of analyzing the processes in the machine. Eventually, many versions of high-quality electric motor control systems have been developed. Owing to the progress achieved in computer engineering, it has become possible to solve a fewer number of the Park—Gorev equations in complex form without decomposing the vectors into projections on the coordinate ases aft, dq, xy. At present, the majority of widely used programming languages (FORTRAN, C+, MathCAD, MatLAB, etc.) offer efficient tools for implementing the operations of summing and multiplying complex quantities. In the article, the Park-Gorev equations are solved without decomposing the vectors into their projections on the coordinate axes вб, dq, xy. In so doing, the induction motor complex speed observer uses only two voltage equations and two flux linkage equations. The rotor motion equation is not used to determine the speed. The obtained algorithms for solving by means of a complex speed observer made it possible to determine the currents, electromagnetic torque and motor’s moment of inertia. The proposed algorithms written in the б-в and x-y coordinate systems made it possible to determine the motor speed in its fast start-up process (0.2 s) with an error of less than 1%.