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We report on experimental investigations of proton acceleration from solid foils irradiated with PW-class laser-pulses, where highest proton cut-off energies were achieved for temporal pulse parameters that varied significantly from those of an ideally Fourier transform limited (FTL) pulse. Controlled spectral phase modulation of the driver laser by means of an acousto-optic programmable dispersive filter enabled us to manipulate the temporal shape of the last picoseconds around the main pulse and to study the effect on proton acceleration from thin foil targets. The results show that applying positive third order dispersion values to short pulses is favourable for proton acceleration and can lead to maximum energies of 70 MeV in target normal direction at 18 J laser energy for thin plastic foils, significantly enhancing the maximum energy compared to ideally compressed FTL pulses. The paper further proves the robustness and applicability of this enhancement effect for the use of different target materials and thicknesses as well as laser energy and temporal intensity contrast settings. We demonstrate that application relevant proton beam quality was reliably achieved over many months of operation with appropriate control of spectral phase and temporal contrast conditions using a state-of-the-art high-repetition rate PW laser system.