The phenomena related to charge trapping are among the most relevant open issues that affect the long-term stability of perovskite-based devices. According to this, the objective of this paper is to report experimental results in which a charge control strategy is used for the first time in a solar cell structure that has a high trap density perovskite absorber. This device has also noticeable J-V hysteresis, produced by non-capacitive effects. The control strategy proposed, based on sigma-delta modulation, applies to the device an appropriate sequence of voltage waveforms determined after periodical current measurements made at a constant voltage. The experimental results obtained and the fittings made with a phenomenological model indicate that this approach allows controlling several charge-related effects. As a consequence, the J-V characteristic of the device is successfully shifted and stabilized to predetermined positions.