Dynamic System Modeling Assignment: Buffer System Analysis Project

This project focuses on modeling and analyzing the dynamics of a buffer system, a single-element system designed to supply a commodity from a source to a sink. The assignment involves using MATLAB Simulink to simulate and analyze the system, focusing on two main components: the charger and the reservoir. The charger's operational status and the reservoir's emptiness are key variables. The project explores the concept of system reliability, specifically the mean time to failure (MTTF). The solution details the modeling of reservoir dynamics, charger status, and the implementation of a pseudocode algorithm to determine the system's health (H) using a truth table. The simulation results, including the determination of the charger's failure rate and downtime, are presented. The project also discusses the importance of a reliable system and provides insights into how to determine the MTTF through simulations, ultimately assessing the system's ability to continue normal operation. The solution provides a comprehensive understanding of the buffer system's behavior under various conditions and the factors influencing its reliability.

DYNAMIC SYSTEM MODELLING ASSIGNMENT
BUFFERING SYSTEM DYNAMICS
INTRODUCTION
The system has a single element, the purpose of which is to supply a sink with a commodity
from a source. This could be a liquid tank modelling system, a monetary income and outgoings
problem, an energy supply and demand problem. The output is the same as the input without
delay, regardless of demand or supply. The flow must on average remain the same. The flow on
average is an approximation if the supply is too fast for too long, then the reservoir will overflow
or if the demand is too great for too long, then the reservoir will underflow.
A top-level model of the system is represented as,
The two main elements of the system are the charger which determines a known failure rate and
subsequent downtime and the reservoir. The charger can be operational or not, the reservoir can
be empty or not. There are two resulting variables from this, U and V, to represent charger
operational and reservoir empty respectively. The most important feature of a system is its
reliability which is the mean time of operation before failure occurs. The health of the system is
denoted by the state variables H to show if it is healthy. When healthy, the buffer system can
ultimately supply the user Demand mass flow rate of liquid.

PROBLEM STATEMENT
The problem of determining the health of the system is reduced to three sub problems of
determining the U, V, W at any instant in time. Implementation of the pseudocode algorithm
determines the health, H. using a truth table, it can be broken down as,
The modelling is performed using the MATLAB Simulink to model, simulate and analyze the
buffer system. To model the dynamics of the reservoir, it is prudent to describe the system
mathematically,
BUFFER SYSTEM MODELLING
(i) Model Reservoir Dynamics
Simulink block model

The output
A relay was added to the block model and the simulation was performed,

The output was obtained as follows,

Confirmation that,
V = {1 L>0
0 L<0 }
(ii) Determine W
W = {1 D> S
0 otherwise }
Incorporating another relay as a 2-state switch into the model, the required logic is simulated.
Setting the values as S=20 and D=100, the value of W=1

Setting S=500, D=150, the value of W=0,
Creating hierarchies
It can be observed that with continuous addition of components the block model becomes more
complex. A neat way of handling such systems is to bundle parts of it together as a simple sub-
system module that has relevant inputs and outputs.
(iii) Model Charger Status (U)
Modelling the status of the charger considers that the failure of the charger is governed by
random chance. This can be achieved by generating a random number between 0 and 1. Tests are
carried out to check if the failure chance lies between α and α+f. f is the failure rate given in sec-
1.

The output of the failure rate where f=1/30 sec-1

And the charger functionality is 1

Downtime (g seconds)
Statically model when a failure of the charger is going to occur. There is need to model how long
the failure will last, i.e., the length of the time the charger is not operational following a failure.
The variable g is used to model the downtime.

To interface the two models, one must consider that when the charger is operating correctly, it
lets S of the liquid flow into the reservoir unimpeded.
The results are as shown below,

Part 4
Pseudo-code algorithm for determining system health (H)
The buffer system should be in a position to determine when the system will fail such as not to
continue normal operation. The truth table in the first section of this report shows the truth table
used to determine the system health based on the inputs, U, V & W.
Combinatorial
Logic
1
U
2
W
3
V
1
Out1

Part 5
Discussion
The mean time to failure refers to the amount of time or length of time before a failure occurs in
an equipment or system. The system is considered reliably healthy when the MTTF is as least as
possible. It also seeks to describe the time between one failure and the next. A reliable system is
more preferred as compared to the unreliable system which tends to be unavailable when needed
or produces the unexpected results. According to the simulations, using a time margin of 300
seconds for the simulation, when the system is halted, it is found that the failure occurred at 45
seconds. In this practical exercise, the MTTF from various tests was estimated to 49 seconds
when the simulation is halted randomly.