The High Energy cosmic-Radiation Detection (HERD) facility onboard the Chinese Space Station will provide high quality data on charged cosmic rays from few GeV to PeV energies and gamma rays above 100 MeV. HERD will employ a Plastic Scintillator Detector (PSD) to discriminate charged from neutral particles to help identify gamma rays and to measure the nuclei charge up to iron. For these reasons, the HERD PSD needs to have high detection efficiency ($\sim99.998\%$) and a good charge resolution ($\sim30\%$ at low $Z$). During 2022 and 2023, beam test campaigns were performed at CERN and at CNAO (Centro Nazionale di Adroterapia Oncologica) in Italy, aimed at studying the overall performance of the PSD detector. A prototype detector composed of 8 plastic scintillator trapezoidal bars of two different lengths was equipped with Silicon Photomultipliers (SiPMs) arranged in different positions along the bars. We tested SiPM of different sizes to increase the dynamic range and study the charge resolution in the range of Z between 1 and $\sim26$. The prototype was irradiated with relativistic protons and pions at CERN PS, an ion beam at CERN SPS and with low momentum protons and C ions (with energy release similar to those of high-Z relativistic particles) at CNAO. In this work we present and compare the results from these campaigns. Moreover, we present a characterization of plastic scintillator detectors for the future generation of space missions, with respect to their capabilities for nuclei identification, in terms of quenching effects.