Industrial networks demand centrally controlled quality of service (QoS), often in the form of hard real-time guarantees. Software-defined networking (SDN) provides a convenient paradigm for central QoS control. However, existing SDN-based solutions cannot guarantee hard real-time QoS as they rely on a control loop over the forwarding (data) and control planes. We propose a novel SDN-based QoS control framework that maintains an accurate network model through network calculus to avoid a control loop over forwarding and control planes, allocates resources to and routes flows over a network of "queue links," whereby each physical network link houses multiple queue links (with different QoS levels), and manages QoS through a function split between delay-constrained least-cost routing on the network of queue links and the resource allocation to the queue links. This function split greatly reduces the computational complexity while achieving hard real-time QoS with high bandwidth utilization. Our evaluation results indicate that our function split approach allows for online runtime admission control and can achieve bandwidth utilization above 80% while meeting deterministic real-time QoS requirements.