Real-time optimal commutation for minimizing thermally induced inaccuracy in multi-motor driven stages

In this paper minimum power commutation laws of permanent-magnet synchronous linear motors are extended to multiple-motor driven systems. A system-wide view of commutation is shown to exploit the redundancy of motor coils and motor force generation that exist in over actuated motion platforms. We propose a novel commutation law, that is only realizable by a multiple-motor system view, which minimizes total power subject to the constraint that the thermal distortion at the motion platform work space, caused by the motor coil heating, is minimized. Due to the added constraint, there is no closed-form solution and the problem is shown to be non-convex. This problem solution is proven to be equally solved by the combination of an algebraic and convex problem. To realize the commutation laws, a custom embedded solver, using an interior-point method, is described to solve the convex problem in real-time and is shown to converge to a solution, in under 35 μs, within the update rate of our system running at over 9 KHz.