Nonlinear droop compensation for current waveforms in MRI gradient systems
Purpose: Providing accurate gradient currents is challenging due to the gradient chain nonlinearities, arising from gradient power amplifiers and power supply stages. This work introduces a new characterization approach that takes the amplifier and power supply into account, resulting in a nonlinear model that compensates for the current droop. Methods: The gradient power amplifier and power supply stage were characterized by a modified state-space averaging technique. The resulting nonlinear model was inverted and used in feedforward to control the gradient coil current. A custom-built two-channel z-gradient coil was driven by high-switching (1 MHz), low-cost amplifiers (<$200) using linear and nonlinear controllers. High-resolution (<80 ps) pulse-width-modulation signals were used to drive the amplifiers. MRI experiments were performed to validate the nonlinear controller's effectiveness. Results: The simulation results validated the functionality of the state-space averaging method in characterizing the gradient system. The performance of linear and nonlinear controllers in generating a trapezoidal current waveform was compared in simulations and experiments. The integral errors between the desired waveform and waveforms generated by linear and nonlinear controllers were 1.9% and 0.13%, respectively, confirming the capability of the nonlinear controller to compensate for the current droop. Phantom images validated the nonlinear controller's ability to correct droop-induced distortions. Conclusion: Benchtop measurements and MRI experiments demonstrated that the proposed nonlinear characterization and digitally implemented feedforward controller could drive gradient coils with droop-free current waveforms (without a feedback loop). In experiments, the nonlinear controller outperformed the linear controller by a 14-fold reduction in the integral error of a test waveform.