Distributed H ∞ $H_\infty$ control for roller kiln temperature based on adaptive dynamic programming

The roller kiln with multi-temperature zones used for cathode material sintering is an interconnected system with time delay in energy transfer and precise control of the temperature for the preparation of cathode materials for lithium-ion batteries. However, the interconnection between the temperature zones, the time delay of the temperature state, and the disturbance of the external environment make it difficult to control the sintering process. For this reason, this paper develops a distributed $H_{\infty }$ control of the temperature of roller kiln based on adaptive dynamic programming (ADP). Firstly, the heat transfer mechanism of sintering process is discussed; the law of energy conservation provides the physical basis for the sintering process on which the autocorrelation function method identifies the time delay. Then, the cost function is constructed by combining the Lyapunov–Krasovskii function containing the time delay, the temperature state, the heating power of the silicon carbon rod and the perturbation. Subsequently, Hamilton–Jacobi–Isaac equation with the optimal cost function and the optimal distributed control strategy are approximated by neural network of ADP. Finally, the stability of the closed-loop system is proved by Lyapunov functional analysis, and the effectiveness of the proposed method is verified by the simulation results of roller kiln temperature control.