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Methods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the inverse of the system exists in the proposed parameterisation of the precompensator, the LPV transfer functions commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the parameters of the system inverse despite the presence of stochastic disturbances. For the more general case, when the system inverse does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error.