Graduate Attribute $5($GA $5)$: Engineering methods, skills, tools, including Information technology: Figure $1$: Water Tank Level Control Background of the Mathematical model: The linear model of a single tank system can be derived using Bernoullis principle of mass conservation. In this system, two key parameters are considered: resistance and capacitance.in flow rate; that is: The resistance for liquid flow is defined as the change in the level difference to a unit change$()=()()2$ Capacitance $($C$)$ is nothing but is cross sectional area $()$ of the tank: $==$ The transfer function of the single tank water level system is:$()=()+$ Where:The parameters of the system are defined in Table $1$:Table $1$Case $1$Case $2$Case $3=$ Cascaded transfer function of Case $1$ & Case $2=$ h $3=$ h $3$ h $=$ h $()()4\mathrm{.}3792\mathrm{.}939$Capacitance $()$ Resistance$1025$ Use case $1$ & case $2$ values as applicable $2$Figure $1$ illustrates a typical Single Tank Water Level Control System. With the single$-$loop control system, the level sensor $($LT$)$ provides the feedback, which gives the error signal to the controller and then initiates the controlling action on the rate at which fluid exits the tank. By increasing or decreasing the discharge rate $($varying the speed of the pump$)$ the level of the liquid inside the tank can be controlled. A level measurement sensor provides a $4-20$mA feedback signal to a controller.By addressing this real$-$life problem, you will apply your knowledge of process control and PID controller design to ensure optimal performance and operational safety in a liquid tank setting.Problem Statement:You are working as a process control technician in a water processing plant. One of the critical tasks is to maintain the level of water in a large storage tank. Due to the tank$\text{'}$s large capacity and the relatively slow inflow and outflow rates, changes in the water level occur rather slowly. Precise control of the water level is essential to ensure smooth plant operations and prevent overflow or underfill situations.Task: Design a PID controller for the water level control system. You need to simulate both the open and closed loop control systems to manage the water level accurately in the storage tank. Section $1$: Understand Tools $(20\%)$ Ability to describe and explain the principles behind and applicability of engineering tools.Understanding the System Dynamics & Simulation of Open Loop System$1\mathrm{.}1$ DeterminethenumericalmathematicalmodelsofthewatertankpresentedinFigure$1$for the three cases$\mathrm{.}1\mathrm{.}2$ Simulatethesystemsresponsesforallcasestovariousinflowandoutflowcaseswithout feedback to understand the natural behavior$\mathrm{.}1\mathrm{.}3$ Measure the responses of the water level cases to changes in the inflow and outflow rates$\mathrm{.}1\mathrm{.}4$ Identifythetimeconstantanddelayofthesystemsinallthreecasesduetothelargetanksizeand slow rate of level change.Section $2$: Identify and Use Tools $(20\%)$ Ability to identify and use relevant tools for an engineering activity.Designing the PID ControllerDetermine the appropriate PID parameters $($Proportional$,$ Integral, and Derivative gains$)$ using methods like Ziegler$-$Nichols tuning, trial and error, or software$-$based optimization. To achieve that, choose the model of your choice between Case $1,$ Case $2$ and Case $3\mathrm{.}3$Section $3$: Create Tools $(30\%)$ Ability to create engineering tools.Simulation of Closed Loop System$3\mathrm{.}1$ Build the system with the PID controller in Matlab$/$SIMULINK environment$\mathrm{.}3\mathrm{.}2$ Simulate the closed loop system to observe how well the controller maintains the desiredwater level setpoint$\mathrm{.}3\mathrm{.}3$ Adjust the PID parameters as needed to minimize overshoot, oscillations, and steady$-$stateerror.Section $4$: Evaluate Tools $(30\%)$ Ability to identify the limitations in the use of engineering tools, and their underlying assumptions$\mathrm{.}4\mathrm{.}1$ Validate the simulation results with real testing in a simulated controlled environment$\mathrm{.}4\mathrm{.}2$ Make further adjustments based on actual performance to ensure the system maintains therequired water level within the specified range $($specify and evaluate all levels$)\mathrm{.}4\mathrm{.}3$ Ensure the tank reaches the desired water level quickly without significant overshoot$\mathrm{.}4\mathrm{.}4$ Prove that your system can maintain the level of stability and prevent any deviation that coulddisrupt plant operations or cause safety hazards$\mathrm{.}4$