A distributed direct model free adaptive PID control algorithm based on controller dynamic linearization is designed to address the unified tracking problem of unknown heterogeneous nonlinear multi-agent systems, the tuning of controller parameters is only based on the input and output data of the controlled system and the topology relationship between intelligent agents, and is not limited by the mathematical model of the controlled system. Firstly, the controlled system and ideal controller are equivalently transformed into corresponding dynamic data models using dynamic linearization technology. Based on the dynamic data model of the ideal controller, the controller structure and parameter adaptive update algorithm are proposed. Then, error convergence analysis is conducted using compressed mapping and the Gale disk theorem. Finally, a large number of simulation comparisons are conducted to verify the effectiveness and superiority of the designed control algorithm.