Tank filling with control delay -- Szymon Rajchel

                                                       

 

 

 

 

Project for the course 
Simulation Modeling  

 

 Title:

"Tank filling with control delay"

 

 

 

Student name: Szymon Rajchel 

Student ID: 167558 

 

 

Vensim PLE is a professional tool for system dynamics modeling that enables the creation of advanced simulations based on differential equations and complex logical relationships between variables. The software is particularly useful for analyzing complex systems typical of fields such as engineering, economics, ecology, or social sciences, which are characterized by delays, nonlinearities, and complex feedback loops. 

Basic elements of modeling in Vensim: 

• Stocks 

Represent the accumulation of resources in a system. In the case of a water tank model, a stock corresponds to the current level of liquid in the tank. 

• Flows 

Define the dynamics of changes in stock levels over time. For example, they can model the rate of water inflow or outflow from the tank. 

• Connectors 

Visualized as arrows, they represent causal relationships between different elements of the model. 

• Auxiliary variables (Variables) 

Serve as intermediate parameters that modify the behavior of flows or influence the state of stocks. 

Key functions used in the model: 

• DELAY1 – first-order delay function with the syntax: 

DELAY1(input, delay_time) 

 

Models the effect of a gradual adjustment of the output value to a changing input signal, according to an exponential characteristic. 

• IF THEN ELSE – conditional function with the structure: 

IF THEN ELSE(condition, value_if_true, value_if_false) 

Implements decision logic in the model, triggering appropriate scenarios depending on whether certain criteria are met. 

 

Specifics of the analyzed model: 

The model includes the following key components: 

Water Tank 

A stock with a maximum capacity of 200 liters 

Represents the current water level in the system 

Flow Mechanisms 

• Inflow (water entering the tank) – regulated in liters per minute 

• Outflow (water leaving the tank) – controlled in liters per minute 

Control Parameters 

• Set water level – a variable that defines the target water level in the tank (expressed in liters) 

• Control elements based on delay and conditional functions 

The model demonstrates typical behaviors of control systems with delays, highlighting characteristic transient effects such as oscillations around the setpoint value. 

 

Fig. 1. Tank filling model 

 

Fig. 2. Change in water level over time 

 

Fig. 3. Change in outflowing water over time 

 

Fig. 4. Change in the water outflow over time 

 

Fig. 5. Simulation of the example 

 

The model represents a closed-loop control system for regulating the liquid level in a tank. In the initial phase, the inflow dominates, causing a rapid increase in the water level. Once this value exceeds a defined threshold, the outflow mechanism is activated, reducing the amount of liquid until the target level is reached. Upon reaching the desired value, both inflow and outflow are turned off. 

The observed fluctuations in the level during stabilization result from delays in the operation of the control valves, implemented in the model using the DELAY1 function. This effect illustrates the typical transient oscillations found in real-world systems during regulation processes.