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We present a solution for velocity control in permanent magnet synchronous motors. We formally prove that velocity converges to the constant desired value from any initial condition. Our controller is so simple that it only differs from the linear control strategy commonly implemented in commercial drives by two simple adaptive terms. Moreover, identical velocity responses are obtained with both controllers. Hence, our results explain how the linear control strategy implemented in most commercial drives works and also provide tuning guidelines for that control strategy. We remark that this has been a long standing unsolved problem.