Design of Precision Motion Controllers Based on Frequency Constraints and Time-Domain Optimization

As the requirement for precision motion is increasingly demanding in manufacturing and automation industry, it becomes more and more challenging to design motion controllers for higher tracking accuracy and better robustness with respect to uncertainties and disturbance. Since the performance and robustness specifications are usually expressed in terms of time and frequency domain characteristics of the system, it is useful to integrate both time and frequency-domain properties for controller design. In this article, we propose a
frequency constrained time-domain optimization
(FreCTO) controller design method for single-input, single-output, linear time-invariant systems. The controller is parameterized by a finite impulse response filter whose coefficients are determined from a constrained optimization problem that minimizes time-domain errors subject to upper or lower bounds on the magnitude of the loop transfer function at a set of selected frequencies. This constrained optimization problem is turned into a quadratically constrained quadratic programing problem, allowing efficient solvers to find the solution. Then, the FreCTO controller is applied to the biaxial motion stage of a computer-numerical-control lathe. We demonstrate a systematic and insightful design procedure for the FreCTO controller and experimentally verify its performance in accurate trajectory tracking and simultaneous vibration suppression.