Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems

Data-driven actuator fault identification and accommodation in networked control of spatially-distributed systems

“…Remark 1: It can be seen from the expression in (11) and the definitions of L F and L G k that the given bound on the minimum stabilizing communication rate is dependent on the degree of mismatch between the dynamics of the slow system and the model, the controller design parameters, and the spatial locations of the actuators. The stability condition can therefore be used to characterize the networked closedloop stability region in terms of these various factors.…”

“…choose h that satisfies (11) and set θ k = θ k = 1 and i = 0 2. solve (17) for θ * and estimate Ψ(θ * l ) for each θ * l , l ∈ {1, · · · , m} 3. if for any ϑ l ∈ Ψ(θ * l ), (11) is violated with θ k l = ϑ l 4. if for all ς l ∈ Ψ(θ * l ), θ * l satisfies (11) with θ k l = ς l and θ k l = θ * l 5. update θ k l using θ * l at the next transmission time and GOTO step 12 6. else if any K * satisfies (11) 7. update K using K * at the next transmission time and GOTO step 12 8. else 9. replace l-th actuator with a new actuator that satisfies (11), set θ k l = θ k l = 1 at the next transmission time and GOTO step 12 10. end if 11. else 12. i = i + 1 and GOTO step 2 13. end if Remark 5: As mentioned earlier in Remark 4, when a perfect model is implemented for control and fault identification (i.e., ∆G = 0), the estimation confidence interval for θ k l , Ψ(θ * l ), shrinks to a point, θ * l . In this case, the fault accommodation logic can be modified as shown in the following algorithm.…”

“…choose h that satisfies (11) and set θ k = θ k = 1 and i = 0 2. solve (17) for θ * 3. if for any θ * l , (11) is violated with θ k l = θ * l 4. if for any θ * l , θ * l satisfies (11) with θ k l = θ k l = θ * l 5. update θ k l using θ * l at the next transmission time and GOTO step 12 6. else if any K * satisfies (11) 7. update K using K * at the next transmission time and GOTO step 12 8. else 9. replace l-th actuator with a new actuator that satisfies (11), set θ k l = θ k l = 1 at the next transmission time and GOTO step 12 10. end if 11. else 12. i = i + 1 and GOTO step 2 13. end if Comparing Algorithm 2 with Algorithm 1, it can be seen that the difference exists in steps 2-4 which are related to the way in which the process can be stabilized by adjusting the plant-model mismatch.…”

“…To illustrate the key ideas, we first consider the case when a perfect model is applied for control and identification (i.e., g(z a ) = g(z a )), and analyze the dependence of closed-loop stability on the choice of the fault parameters in the process and in the model, θ and θ, as well as on the feedback gain, K. The contour plot in Fig.1(a) depicts the dependence of Γ(h) (see (11))on θ and θ when the feedback gain is fixed at K = −5. The uncolored area which lies inside the unit contour line represents the stability region.…”

Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos

“…Many chemical processes such as heat conduction problems, however, are modeled by partial differential equations (PDEs). The application of FDD methodologies to distributed parameter systems described by PDEs is lacking (Ghantasala and El-Farra, 2009). …”