In order to further develop and implement novel drift scan imaging experiments to undertake wide field, high time resolution surveys for millisecond optical transients, an appropriate telescope drive system is required. This paper describes the development of a simple and inexpensive hardware and software system to monitor, characterise, and correct the primary category of telescope drive errors, periodic errors due to imperfections in the drive and gear chain. A model for the periodic errors is generated from direct measurements of the telescope drive shaft rotation, verified by comparison to astronomical measurements of the periodic errors. The predictive model is generated and applied in real-time in the form of corrections to the drive rate. A demonstration of the system shows that that inherent periodic errors of peak-to-peak amplitude ~100 are reduced to below the seeing limit of ~3. This demonstration allowed an estimate of the uncertainties on the transient sensitivity timescales of the prototype survey of Tingay & Joubert (2021), with the nominal timescale sensitivity of 21 ms revised to be in the range of 20 - 22 ms, which does not significantly affect the results of the experiment. The correction system will be adopted into the final version of high cadence imaging experiment, which is currently under construction. The correction system is inexpensive (<$A100) and composed of readily available hardware, and is readily adaptable to other applications. Design details and codes are therefore made publicly available.
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