In this work, the observational constraints on the coupling parameter of the interaction between dynamical dark energy and cold dark matter were obtained using cosmic microwave background data, baryon acoustic oscillations, and type Ia supernova data. The dark energy in considered models is dynamic, and the evolution of its equation of state parameter depends on dark coupling and internal properties of the dark energy itself. Such a model is believed to be more physically consistent than models of interacting dark energy considered in previous works. Constraints were made for three types of interaction. The first two are the types which are often considered in other works on interacting dark energy and are linearly dependent on the energy densities of dark components. The third type has a non-linear dependence on these densities and is studied for the first time. Observational constraints on the Hubble constant  for the first two models strongly disagree with so-called local measurements of . And The third model aligns more closely with local measurements than the ΛCDM model. Also, for the first two types of interaction models, only the existence of small upper bounds of the interaction parameter was found,  as for the last non-linear model, the existence of non-zero interaction was found at greater than 1σ significance level.