In Software Defined Networks (SDNs), a number of controllers are placed in a given data plane network. In a standard logically centralized control plane, each controller acts simultaneously as a primary controller for some switches and as a backup controller for other switches, and the controller placements must meet given switch-controller (SC) and controller-controller (CC) delay bounds. Then, the SDN should be resilient to network disruptions such as node-targeted attacks. To improve the SDN resilience to this kind of disruptions, we assume that some controllers are deployed only as backup controllers so that they take over the functions of primary controllers only in case of disruption. We propose an optimization model that solves a relevant primary and backup controller placement problem, where a minimum number of primary controllers minimizing the maximum SC delay is first established, and then a joint primary and backup controller placement maximizing the resilience of the SDN against a list of the most dangerous node-targeted attacks is determined. A numerical study illustrating the merits of the proposed optimization methodology is presented.