We present a novel photonic beamformer for a fully integrated transmit phased array antenna, together with an automatic procedure for tuning the delays in this system. Such an automatic tuning procedure is required because the large number of actuators makes manual tuning practically impossible. The antenna system is designed for the purpose of the broadband aircraft-satellite communication in the \mathrm{K_u}-band to provide satellite Internet connections on board the aircraft. The goal of the beamformer is to automatically steer the transmit antenna electronically in the direction of the satellite. This is done using a mix of phase shifters and tunable optical delay lines, which are all integrated on a chip and laid out in a tree structure. The \mathrm{K_u}-band has a bandwidth of 0.5 GHz. We show how an optical delay line is automatically configured over this bandwidth, providing a delay of approximately 0.4 ns. The tuning algorithm calculates the best actuator voltages based on past measurements. This is the first time that such an automatic tuning scheme is used on a photonic beamformer for this type of transmit phased array antenna. We show that the proposed method is able to provide accurate beamforming ({<}\text{11.25}^{\circ} phase error over the whole bandwidth) for two different delay settings.