For 2D package chips, a group of one dimensional (1D) partial differential equations (PDEs), which is derived from the 3D PDE heat conduction equation, is proposed to describe the thermal behavior of each core. Thereafter, an optimal controller is designed to manage the power consumption and balance the temperature among the cores based on the proposed 1D model.
Different from 2D package chips, a liquid cooling system should be installed among the layers to reduce the internal temperature of 3D chips. Due to the complexity of the system, the thermal behavior of the whole system is modeled as an ordinary differential equation (ODE) system. For balancing the temperature a two step control policy is proposed. In the first step the micro-channel liquid velocity is set based on a logical algorithm. Thus, the system is described as a switched linear system. In the second step the model predictive control method is employed to design the thermal and power management/balancing controller.