# Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems
## 3 Classical Controller Methods for Coupled Tank System
### Feedforward Proportional Integral Controller for the Coupled Tank System (FF-PI)  
Feedforward action in process control technology counteracts the impact of the measured disturbance on the process output. In this situation, the feedforward action is used to counterbalance the water being taken out (due to gravity) through the orifices at the bottom outlets of Tank 1 and Tank 2. However, the effects of unaccounted dynamics and disturbances are addressed by the cascade proportional-integral controllers, which are designed to handle time delays. A control pump is specifically engineered to modulate the water level or elevation by means of electricity. The control structure at the beginning is a feedforward proportional-integral controller (FF-PI), as shown in Figure 2.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Description** & **Symbol** & **Value and Unit** \\ \hline Constant of Pump Flow & \(K_{p}\) & 3.3 cm\({}^{3}\)/s/V \\ Gravitational constant & \(g\) & 981 gg \\ Tank 1 and 2 Outlet Areas & \(a_{1}=a_{2}\) & 0.1781 cm\({}^{2}\) \\ Tank 1 and 2 Inside & \(A_{1}=A_{2}\) & 15.5179 cm\({}^{2}\) \\ Cross-Section Areas & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Liquid level system parameters.  
Figure 2: Feedforward PI control block diagram for Tank 1 experiment.  
For zero steady-state error, the water level in Tank 1 is controlled through a positive proportional-integral (PI) closed-loop scheme with the addition of feedforward action, as shown in Figure 2.  
\[V_{p_{ff}}=K_{ff_{1}}\sqrt{L_{r_{1}}}, \tag{19}\]  
\[V_{p}=V_{p1}+V_{p_{ff}}, \tag{20}\]  
The mathematical equation for the voltage feedforward controller is presented in Equations (19) and (20). While the feedforward action compensates for water withdrawal (due to gravity) through the bottom outlet of Tank 1, the PI controller compensates for dynamic disturbances.  
\[G_{1}(s)=\frac{L_{1}(s)}{V_{p1}(s)} \tag{21}\]  
The transfer function of the feedforward PI control indicated in Figure 2 can be expressed as in Equation (21). After conducting the liquid level experiment in Tank 1 with the feedforward PI controller, the CNPIR controller was used, considering the system dynamics. Thus, both control structures were compared through real-time experiments.  
The second tank, which is designed with a feedforward proportional-integral controller, is shown in Figure 3.  
\[T_{1}(s)=\frac{L_{1}(s)}{L_{r_{-}1}(s)} \tag{22}\]  
In the designed block diagram, the closed-loop transfer function, named \(T_{1}(s)\), represents the water level of the 1 st tank and is mathematically expressed in Equation (22).  
\[L_{ff\_{-1}}=L_{r\_2}K_{ff\_2} \tag{23}\]  
The feedforward effect is mathematically expressed by the above Equation (23). The input signal for the liquid level in Tank 1, \(L_{r\_1}\), is equal to the sum of \(L_{11}\), which is called the small increase in liquid height calculated by the proportional-integral (PI) controller, and \(L_{ff\_1}\), which is obtained from the feedforward effect.  
\[L_{r\_1}=L_{ff\_1}+L_{11} \tag{24}\]  
According to Equation (24), the desired liquid level control of the tank is achieved as a result of the feedforward effect and the values calculated by the PI controller. To calculate the transfer function of Tank 2, the output value of Tank 2 needs to be divided by the input value of Tank 1 as follows:  
\[G_{2}(s)=\frac{L_{2}(s)}{L_{1}(s)} \tag{25}\]  
Figure 3: Feedforward PI control block diagram for Tank 2 experiment.