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An adjustable speed single phase induction motors are widely used in domestic applications and industries. It is difficult to get such a single phase induction motor practically. The present work deals with the analysis and design of a speed control for a single phase induction motor. There are several methods which may be used to control the speed such a motor: voltage control, frequency control and a voltage to frequency control, which is widely used in this application. Most of the previous methods are suffering from certain problems, e.g narrow speed range, starting problems, the low efficiency of the motor. Here a novel method is suggested to use for controller design. the suggested method computed the best values for the frequency and the voltage for any desired reference speed. The simulated open-loop system as well as the closed-loop one are analyzed and the result show that the actual speed is tracking the desired speed and the deference between the reference speed and actual is acceptable (less than 2%).