Need to adjust the speed every time I turn on turntable

There is of course the well-proven quartz oscillator based PLL method used in better direct drive turntables. 

AC synchronous motors rely on stability of AC frequency, which before accounting for noise from other sources can vary by up to +/-2Hz, which is an error range of 6.7%. Noise that breaks the synchronization can increase this to 10% depending on the power factor of the source. Bottom line is to use a line frequency conditioning device for equipment that has AC synchronous motors. This is why quartz oscillator disciplined phase locked loop controlled DC motors maintain speed with much greater precision and reliability.