ENG5031 Fault Detection, Isolation And Reconfiguration Assignment - University of Glasgow, UK

Attempt ALL questions. An electronic calculator may be used provided that it does not have a facility for either textual storage or display, or for graphical display.

Question 1 - Figure Q1 illustrates an offshore separator that is used to extract gas from fluid containing a mix of oil, gas and water.

In normal operation the gas is collected from the Gas Outlet pipe and the oil/water by-product is collected via the Fluid Outlet pipe. This separator has a double redundant safety system to prevent the gas pressure from exceeded the structural design pressure. If the gas pressure rises significantly (e.g. if the gas outlet is blocked) then the first stage of the safety system is to stop the flow into the separator by means of 2 pressure switches connected to 2 automatically actuated Flow Valves (FV₁ and FV₂). The second stage is provided by 2 Pressure Sensitive Valves (PSV₁ and PSV₂) which send excess gas to the flare. The final stage is provided by a Rupture Disc (RD) which only breaks when the pressure reaches the maximum design pressure for the separator.

(a) Construct an event tree diagram and fault tree diagram based on the description of the offshore separator in Figure Q1 when the gas outlet is blocked.

(b) Hence or otherwise, given the fault probability of the components shown in Table Q1, calculate the probability of the separator exploding.

(c) By considering the main failure modes for this separator, construct an appropriate FMEA for this system using the values given in Table Q1. Use the resulting PRN to determine the most critical component within the system described above.

Table Q1.

Question 2 - A propeller drive system from a multi-rotor UAV is illustrated in Figure Q2.

This systems consists of a dc motor. The electrical side of the motor has inductance L_A(H), resistance R_A(Ω), back emf constant K_e, current i_A(A) and voltage V_IN(V). The mechanical side of the motor has moment of inertia J_m(kgm²), shaft damping coefficient B_s, rotational speed ω_m (rad/s) and torque constant K_T. The shaft of the motor is connected to the propeller, which has moment of inertia J_p(kgm²) and rotational speed ω_p(rad/s). The following equations describe the dynamic motion of this system.

(a) With respect to the description given above, show how the following faults would manifest themselves in the propeller drive system:

(i) Additive faults.

(ii) Parameter faults.

(b) By taking the Laplace transform of these differential equations, derive the structured residuals and the residual generation matrix for the system described above.

(c) Hence or otherwise, construct a fault signature table for the additive and multiplicative faults that could affect this system.

Question 3 - A typical first order system can be presented by the following transfer function:

G_P(s) = y(s)/u(s) = K/(Ts+1)

Here K is the gain of the system and T is the time constant.

(a) With respect to the system shown above, describe in detail what is meant by the following terms:

(i) Multiplicative Faults

(ii) Additive Faults

Illustrate your answer with appropriate diagrams.

(b) In the context of fault detection, describe in detail what is meant by output error residual. Illustrate your answer with appropriate diagrams.

(c) Derive the output error residual parity equation for the following faults in the first order system described above:

(i) Faults present in the gain K and time constant T.

(ii) Faults present in the input and output.

(d) Hence or otherwise define the associated output error residual time domain equations for stepwise faults of the types discussed in part (c).

(e) Sketch the output error residual time histories for both stepwise and drift-wise faults in the presence of a step input to the system. Consider both Multiplicative and Additive Faults.