This paper provides a framework of designing distributed model predictive controller to reach consensus of a heterogeneous time-varying multi-agent system, and the dynamics of heterogeneous agents are modeled by double integrators and Euler-Lagrange (EL) equations. Firstly, a DMPC-based consensus algorithm is proposed, where the constraints in the algorithm depend on the heterogeneous dynamics. We prove that the resultant DMPC optimization problem is feasible with the designed controllers, which is stable when the system reaches consensus. To further reduce communication cost and solve the problem with asynchronous discrete-time information exchange, self-triggered mechanism is introduced into the framework. Trigger intervals are alternatively optimized with the control inputs, and the influence on the system performance is analyzed. Numerical examples are provided to verify the effectiveness and advantages of the proposed algorithms.