Oil drilling rigs are used for drilling holes for identification of oil or natural gas sources and for extraction. An oil drilling system can be thought of as a drill inside a straw, which is placed inside a glass. The straw assembly represents the drill string, the drill surrounded by fluid, and the glass represents the volume, the annulus, around the drill string through which slurry and eventually oil will flow as the drilling progresses.

Assume that we want to control the drill pressure output, P_d (t), with a reference voltage input, V_d (t). A control loop model (Zhao, 2007) consists of a drill-pressure controller, drill motor subsystem, pulley subsystem, and drill stick subsystem. The output signal of the latter, the drill pressure, P_d (t), is measured using a transducer, which transmits a negative feedback voltage signal, V_b(t), to the drill pressure controller. That signal is compared at the input of the controller to the reference voltage, V_r (t), Based on the error, e(t) = V_r (t) – V_b(t), the drill pressure controller sets the desired drill speed, ω_d, which is the input to the drill motor subsystem whose output is the actual drill speed, ω_a, which is the input to the pulley subsystem. The output of the pulley system drives the drill stick subsystem. The drill stick subsystem may be severely affected by environmental conditions, which may be represented as disturbances acting between the pulley and stick subsystems.

Draw a functional block diagram for the above system, showing its major components as well as all signals.