Feedback based toolface control system for a rotary steerable drilling tool

A non-transitory machine-readable medium comprising instructions stored therein, the instructions executable by one or more processors to facilitate performing a method of forming a wellbore, the method comprising:

• determining a desired toolface of a drilling tool;
• calculating a toolface error by determining a difference between a current toolface of the drilling tool during a drilling operation and the desired toolface;
• calculating a correction to correct the toolface error, the correction including solving for a signal to send to an input component by:
• estimating, using a model of a series of components of the drilling tool, an output of each of a plurality of states of the model based on an input to each of the states of the model;
• and
• determining a desired input to each of the plurality of states, beginning at the toolface, based on a desired output of at least one of the plurality of states connected to a particular state, the desired output of the at least one of the plurality of states connected to the particular state being calculated by using the model;
• transmitting the signal to the input component of the drilling tool, the signal being based on the correction;
• adjusting the current toolface based on the signal to match the desired toolface;
• and
• drilling a wellbore with a drill bit oriented at the desired toolface.

A downhole drilling tool control system comprising:

• a processor;
• a memory communicatively coupled to the processor with computer program instructions stored therein, the instructions configured to, when executed by the processor, cause the processor to:
• determine a desired toolface of a drilling tool;
• calculate a toolface error by determining a difference between a current toolface of the drilling tool during a drilling operation and the desired toolface;
• calculate a correction to correct the toolface error, the correction including solving for a signal to send to an input component by:
• estimating, using a model of a series of components of the drilling tool, an output of each of a plurality of states of the model based on an input to each of the states of the model;
• and
• determining a desired input to each of the plurality of states, beginning at the toolface, based on a desired output of at least one of the plurality of states connected to a particular state, the desired output of the at least one of the plurality of states connected to the particular state being calculated by using the model;
• transmit the signal to the input component of the drilling tool, the signal being based on the correction;
• adjust the current toolface based on the signal to match the desired toolface;
• and
• drill a wellbore with a drill bit oriented at the desired toolface.