# Integrating Process Re-Engineering Models in Cement Production to Improve Energy Efficiency
## 3 Results
### Klin System Simulation  
The average temperature of the gas entering the burner was 26.7 \({}^{\circ}\)C, the volume was 25 m\({}^{3}\), and the density of air was 1.2 kg/m\({}^{3}\). The system response using the equation can be solved as follows:  
\[\frac{\theta_{(s)}}{v_{(s)}}=\frac{\theta_{int}}{\tau s+1}=G_{burner}(s)=\frac{ 26.7}{60s+1} \tag{15}\]  
The transfer function of the klin for Plant A, calculated using the actual volume of the klin and inlet temperature, is as follows:  
\[\frac{\theta_{in}}{\tau s+1}=G_{klin\ A}(s)=\frac{1450}{180,695.5s+1} \tag{16}\]  
For Plant B, the transfer function of the klin is as follows:  
\[G_{klin\ B}(s)=\frac{1450}{148,490.1s+1} \tag{17}\]  
The transfer function of the heat sensor is calculated using Equation (8) and indicates the transfer function results as follows:  
\[G_{sensor}(s)=\frac{2.8}{0.05s+1} \tag{18}\]  
The transfer function of the PID is calculated using Equation (4):  
\[G_{PID}(s)=\frac{0.03s^{2}+1.803s+0.08}{s} \tag{19}\]  
The transfer function for the heat loss is calculated using Equation (2):  
\[G_{Heat\ loss}(s)=\frac{\text{Ys}}{s+26.17} \tag{20}\]  
where Ys is defined as 26.17T\({}_{env}\), and T\({}_{env}\) is the heat loss to the environment. Figure 9: Logarithmic energy consumption curve with confidence intervals for Plant B. Therefore, the closed-loop equation for the kiln system model is as follows:  
\[G_{closed-loop}(s)=\frac{G_{PID}(s)\cdot G_{burner}(s)\cdot G_{klin}(s)}{1+G_{PID}( s)\cdot G_{burner}(s)\cdot G_{klin}(s)\cdot G_{heat\ loss}(s)} \tag{21}\]  
The energy efficiency of the system can be defined as follows:  
\[\eta(s)=\left|G_{closed-loop}(s)\right| \tag{22}\]  
The improvement is established as shown in Equation (23). \[E_{i}=\int_{Y_{0}}^{Y_{1}}\left|G_{closed-loop}(s)\right|dt \tag{23}\]  
Figure 10 shows a Simulink schematic of a PID-controlled system that maintains the cement kiln temperature at 1450 \({}^{\circ}\)C. The system determines the difference between the desired and actual temperatures, which are subsequently controlled by a PID controller with proportional, integral, and derivative components. This PID controller controls the damper to manage the airflow and fuel mixture to the burner, with a transfer function indicating the dynamic response. The thermal dynamics of the kiln are also represented by a transfer function, which specifies how it responds to heat input. In addition, the system accounts for heat loss using another transfer function. A complete heat detector measures both generated and lost heat, providing feedback to maintain accurate temperature control. Figure 11 shows the dynamic response model for the burner in the cement kiln system, which is modelled using the transfer function in Equation (13) to control inputs over time. This function describes a first-order system, in which the temperature response increases exponentially towards a steady-state value. The response curve indicates that the burner output can be modified to attain the ideal kiln temperature of 1450 \({}^{\circ}\)C, which is required for clinker formation. The constant of time \(\tau\), obtained from the denominator of the transfer function, is 60 s, showing the time required for the system to achieve approximately 63.2% of its final value. The time constant shows small values, which indicate how fast the system responds. Figure 11 also indicates that the system stabilises after around 100 s without exceeding the specified temperature, proving that the PID controller is effectively tuned. The absence of overshoot and oscillations in the graph indicates that the control system provides stability and has the ability to efficiently handle process disruptions, emphasising the significance of an optimised burner response for energy efficiency. Figure 12 presents the response function of a heat sensor in a cement kiln system.