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RZ Cas is a short-period Algol-type system showing episodes of mass transfer and Delta Sct-like oscillations of its mass-gaining primary component. We analyse high-resolution spectra of RZ Cas that we obtained during a spectroscopic long-term monitoring lasting from 2001 to 2017. Spectrum analysis resulted in precise atmospheric parameters of both components, in particular in surface abundances below solar values. We find that the variation of orbital period is semi-regular and derive different characteristic timescales for different epochs of observation. We show that the radial velocity variations with orbital phase can be modelled when including two cool spots on the surface of the secondary component. The modelling leads to precise masses and separation of the components. The seasonal variation of several parameters, such as vsin(i), rotation-orbit synchronisation factor, strength of the spots on the cool companion, and orbital period, can be characterised by a common timescale of the order of nine years. We interpret the timescale of nine years as the magnetic activity cycle of the cool companion. In particular the behaviour of the dark spots on the cool companion leads us to the interpretation that this timescale is based on an 18-year magnetic dynamo cycle. We conclude that the mass-transfer rate is controlled by the variable depth of the Wilson depression in the magnetic spot around the Lagrangian point L1. In the result, based on available data, we observe a damped activity cycle of the star, starting with a high mass-transfer episode around 2001, followed by quiet periods in 2006 and 2009, slightly higher activity around 2013 and 2014, and again followed by quiet periods in 2015 and 2016. However, owing to missing data for years 2010 and 2011, we cannot exclude that a second high mass-transfer episode occurred within this time span.