This document discusses a framework for modeling the remaining useful life (RUL) of feedback control systems with degrading actuators. The framework combines the deterministic dynamics of the control system with a stochastic model of actuator degradation. A particle filtering approach is used to estimate the system state and predict the RUL distribution based on sensor observations. As an example, the framework is applied to a double water tank level system. The results show the RUL prediction becomes more accurate over time as more sensor data is obtained. The conclusion states that the proposed modeling approach can estimate the probability distributions characterizing the true failure time of degrading control systems.

1. DEEKSHA VERMA
B.Tech (2014-18)

2. INTRODUCTION
• The feedback control system (FCS) has the ability
to compensate for disturbances
• Failure of actuators and sensors lead to instability
of control loop
• Main aim is two folded
• One, propose an integrated model to describe
state of the FCS
• RUL assessment -a major valuable information
• The RUL at time t is defined as the remaining time
(from t) before the system can no longer fulfil it’s
mission.

3. PROBLEM DEFINITION
• Decreasing performance of Feedback Control
System due to component’s wear or degradation
• Includes stochastic degradation process for the
actuator
• To improve :
reliability,
durability of production systems, and
reduce the cost

4. PURPOSE
The main aim of this paper is to deal from a
dependability point of view with a closed-loop system
combining a deterministic part related to the system
dynamics and a stochastic part related to the actuator
degradation
FCS
Structure
Actuator
deterioration
modeling
Condition
monitoring
process
RUL
estimation
Double tank
level system

5. HYPOTHESIS
• H1:The measurement noises are independent
random variables from process state
• H2: consider classical Proportional-Integral Derivative
(PID) controllers which are widely used in industrial
applications.
• H3: an actuator is subject to shocks that occur
randomly in time.
• H4: In degradation model the shocks occur according
to a Poisson process with intensity λ.
Note: The Poisson point process is related to the Poisson distribution, which
implies that the probability of a Poisson random variable is equal to is given
by: P { N = n } ...

6. APPROACH
RUL estimation
at time Tprop
Particle filter
state
estimation
Filtering
Density
Monte Carlo
Simulation
Approximate
filtering
distribution
Key objective of FTC system design may not offer optimal performance
Can reduce the effects of system components failures.
Remaining Useful Life (RUL) of the system become a valuable
information
Aim to find a satisfactory trade-off between FCS performances and its
reliability
procedure based on filtering methods is used to predict the RUL of open
loop systems.

7. SCHEMATIC REPRESENTATION

8. Behavior of deteriorating closed loop system at time t resumed
by a random vector (Zt)
 System state is a Piecewise Deterministic Markov Process
RUL computed at Tprop
P(RULTprop> s|Y1 = y1, . . . , Yn = yn)
=∫Rz(s)μy1,...,yn(dz)
μy1,...,yn(dz) =probability law of the system state at time Tprog
Rz(s)= reliability of the system at time s
METHODOLOGY

9. EQUATIONS

11. CASE STUDY
The level of the tank 2 is considered as the only available health information
of system

12. ANALYSIS

13. THE FAILURE ZONE
CALCULATION(contd..)

14. GRAPHICAL REPRESENTATION

15. • 10 excitation signals are
introduced in the system at
time instants Tb(i) for i = 1, .
..10
• Observations of the system
response (measurement of
water tank level 2) are then
recorded until Tprog = 1209.
• compute the pdf of the system
state regarding the available
observations till Tprop
• simulation of trajectories of
3000 particles to obtain pdf of
RUL
OBSERVATIONS RECORDED

16. 1. Particles populations is then fitted by the kernel density
estimation
2. As frequency progresses, prediction become significantly
more accurate and precise.
3. Black dashed curve presents the density of the RUL with
Monte Carlo simulation in the idealistic case

17. CONCLUSION
Paper presents a modeling framework
Framework combines the deterministic
behavior of FCS
Probability distributions all cover the true
failure time of system
Fault Tolerant Control strategies to overcome
the faults of FCS