Automated control of trajectory of downhole drilling

A method for controlling drilling trajectory during directional drilling to a geological target, the method comprising:

• providing or using a predictive controller that interfaces to and cooperates with a downhole trajectory control system to automatically control a drilling direction of a drilling tool during the directional drilling, wherein the predictive controller is configured to receive data representing a new reference trajectory for a given measured depth and generate output data representing a sequence of set-points for the new reference trajectory, wherein the predictive controller is further configured to communicate the output data to the downhole trajectory control system to automatically actuate one or more pistons to tilt a swivel of the drilling tool to control the drilling direction of the drilling tool to follow the new reference trajectory, wherein the predictive controller includes a model and optimizer, wherein the model embodies a transfer function for at least one closed-loop controller of the downhole trajectory control system, wherein the transfer function is configured to account for response of the at least one closed-loop controller to input data supplied thereto, and wherein the transfer function is a function of a gain in degrees per distance, a Laplace operator, a target inclination of the drilling tool, a measured inclination of the drilling tool, and an output steering power of the drilling tool.