A fixed-time control strategy based on the port controlled Hamiltonian system model (PCHSM) is proposed for a class of coupled liquid level systems. The Hamiltonian function is selected from the perspective of material balance and the PCHSM is constructed for the coupled liquid level systems. The fixed-time controller is designed based on a novel objective Hamiltonian function, combined with matching conditions, to enable the system to converge in the stable domain within the fixed time. The method for tuning the parameters of the target structure matrix is proposed to reduce the complexity of the controller solving process, and the intrinsic correlation between the target matrix parameters and convergence time is provided. Based on the $L_{2}$ gain disturbance attenuation theory, the global fixed-time $H_{\infty}$ controller is designed. The proposed control method can better achieve set-points tracking, has good robustness, and the controller is more concise. The effectiveness of the control strategy is verified through simulation results.