Nonlinear droop compensation for current waveforms in MRI gradient systems

The paper entitled “Nonlinear droop compensation for current waveforms in MRI gradient systems” published in Magnetic Resonance in Medicine by Reza Babaloo. In this paper, nonlinear feedforward controller was introduced to control the gradient coils current and compensate for the nonlinearities arises from gradient power amplifiers.

The modified state space averaging method was used to characterize the switching GPAs, both steady-state and transient behavior, by considering nonlinear equations. The digital inversion of the acquired model is then used in the feedforward open-loop configuration to provide the required voltage to control the output gradient currents. Using a nonlinear controller compensates for the current droop in the plateau region of the trapezoidal gradient waveforms and provides slight corrections in the transients. Low-cost gradient power amplifiers were driven using high-switching (1 MHz) pulse width modulation signals with the resolution of less than 80 ps.


The paper can be accessed:



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.


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.


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.


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.