# A Novel Hybrid Harris Hawk-Arithmetic Optimization Algorithm for Industrial Wireless Mesh Networks
## 3 Problem Formulation
### Pressure Process Control  
Figure 3 illustrates the schematics of the real-time pressure process plant, which operates in real-time. The primary buffer tank, VL 202, was designed to withstand up to 10 Bar of pressure from the centralized air compression system that supplies air to it. The pressure inside the tank can be controlled using the hand valve, HV 202, while the process control valve, PCV 202, ensures that the pressure inside the tank is maintained at the desired level. The pressure transmitter, PT 202, is utilized to measure the pressure, which is then converted to digital voltage signals ranging from 0 to 5 V. These signals are sent to the pressure indicating controller PIC 202, which transmits the control signal to the host PC via I/O interface boards. For safety purposes, there is an analog pressure gauge that displays pressure changes inside the tank. In case of an emergency, there is a hand-operated valve at the bottom of the buffer tank that releases compressed air from the VL 202 if the valve PCV 202 fails. The hand valve can also be used as an external disturbance injection channel during experimentation. The pressure inside the buffer tank is regulated by releasing excess air through an outlet on the top of the process tank, which is connected to another process control valve (PCV 203). This valve is kept at a 50% opening during the experiment to prevent excessive pressure  
Figure 3: Real-time schematic of the pressure process plant. build-up inside the VL 202. The host PC sends signals to the control valve actuator PCV 202 based on the set-point value. Figure 4 displays the piping and instrumentation diagram of the pressure process plant. The plant operates in \"Remote Desktop Connection\" mode for safety, controlling processes from the central control room. The communication between the mainframe PC and field devices, such as the control valve actuator, flow sensors, and pressure transmitter, is established with PCI cards. These cards provide isolation protection of 2500 V DC between the PCI bus outputs. The process plant's analog input is received by a 32-channel analog input card called PCI-1713U. It has a 12-bit resolution and a sampling rate of 100 k samples. The PCI-1720U module, a crucial component of the PCI card, employs a high-quality 12-bit, 4-channel analog output port to transmit precise control signals to the host PC. Furthermore, the PCI-1751 card allows for remote control of the pressure process plant by facilitating data transmission of digital signals from the PT 202 to the host PC and vice versa, with 48 bits of parallel digital input/output. Obtaining the transfer function of the pressure process plant is achievable through mathematical modeling using the open-loop response for the step input signal. By applying the characteristic equation of the first-order plus dead-time system, the final transfer function of the plant is equated as given below. \[G_{p}(s)=\frac{K}{1+Ts}e^{-sL_{p}}=\frac{0.866}{1+1.365s}e^{-s}; \tag{13}\]  
where, \(K\) is the process gain, \(L_{p}\) represents system dead-time, and \(T\) is the system time constant. Fractional-order predictive PI controller is a dead-time compensating control mechanism proposed by [PERSON] et al. to overcome the limitations of conventional PI controllers [54]. The FOPTI controller's design is characterized by its simplicity and effectiveness, and it boasts the impressive capability to compensate for dead-time and is exceptionally adept at rejecting stochastic disturbances. The FOPTI controller integrates the dead-time compensating ability of the Smith predictor with the robust nature of fractional-order controllers. The FOPTI controller is particularly useful for non-linear, fast response, and sensitive applications such as pressure processes. The controller produces an adequate robust control signal unaffected by load changes or plant uncertainties. However, the controller parameters that are identified through analytical techniques may not be enough to create an effective control signal.