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This paper develops new results on the use of model predictive control to regulate the speed of a permanent magnet synchronous motor where the design is based on a linearized state-space representation of the nonlinear model that describes the dynamics. The model predictive controller employs integral action, resulting in zero steady-state error and load torque disturbance rejection. Design in the presence of constraints is considered, where a quadratic programming procedure is used to solve the resulting on-line optimization problem during experimental verification by application to an industry-sized motor.