METHODS OF DRILLING USING MIXED PROPORTIONAL INTEGRAL DERIVATIVE CONTROL

A proportional integral derivative (PID) controller implements control over a drilling system based on an integral term and a proportional term. The integral term is the integral of an operating drilling fluid pressure compared to a target drilling fluid pressure. The proportional term is the difference between an operating weight on bit and a target weight on bit. The sum of the proportional term and the integral term is multiplied by a controller parameter to determine a surface rate of penetration. A drill pipe lowering rate may be changed based on the determined surface rate of penetration, and the process may repeat in an iterative cycle until the integral term is reduced to an acceptable degree.