# Sliding Mode Integral Separation PID Control for Hydrogen Fuel Cell Systems
## 1 Introduction  
The development and use of renewable energy has emerged as a popular study issue in several sectors due to the effects of global warming and the challenge posed by traditional fossil fuels [1]. Among the many renewable energy sources, hydrogen energy, as a recognized renewable energy source, has been widely favored by society and industry. Hydrogen combustion releases a lot of energy and produces only water, which is completely friendly to the environment, making it a new energy source ideally suited to power the future. Because of its benefits, which include low operating temperature, high energy conversion rate, zero carbon emissions, and a simple construction, hydrogen energy is regarded as one of the most promising energy sources for the future [2, 3]. In this context, fuel cell systems efficiently convert hydrogen energy, providing an efficient power generation technology by directly converting hydrogen energy into electricity through anelectrochemical reaction. Proton exchange membrane fuel cell (PEMFC), for example, is an advanced, clean, and efficient power generation technology. PEMFC, a kind of fuel cell, not only has the characteristics of clean and non\(-\)polluting hydrogen energy, but also has the advantages of fast cold\(-\)start, high power density, etc., and consequently it has been strongly supported by many countries. The stack, gas supply modules (which include oxygen and hydrogen), heat exchanging module, and control module are all parts of the PEMFC, and they are all essential to the fuel cell system's output power and efficiency [4]. Ensuring the effectiveness of the chemical process within the cathode requires rigorous regulation of the oxygen flow rate. One crucial metric for quantifying oxygen availability is the oxygen excess ratio (OER) [5]. Oxygen deprivation happens when there is not enough oxygen available, which can permanently lower the PEMFC system's overall performance or furthermore reduce power generation efficiency [6]. The air compressor will use more energy if there is an excess of oxygen available, which will raise the mechanical losses in the PEMFC system. The temperature of the electric stack is also a crucial element impacting the capability of the output of the electric stack. If the temperature is low, the catalyst activity will be weakened, and the conductivity will be reduced, which will decrease the output performance. If the temperature is exceedingly high, the water content decreases, leading to dry cracking of the membrane electrode and damaging the internal structure of the electric stack [7]. In addition, excessive stack pressure or cathode and anode pressure differentials will damage the proton\(-\)exchange membrane, reduce system output performance, and even affect electric stack life. For the PEMFC to operate safely and perform properly, the cathode and anode pressure differentials must be controlled [8]. Accordingly, the control strategies of the key variables of the PEMFC are investigated as a way to guarantee the system's steady operation and improve the system's output performance. At present, in commercial or industrial applications, the fuel cell system level control commonly uses proportional-integral-derivative (PID) control. The PID control design structure is simple, however, and for multi\(-\)input and multi\(-\)output nonlinear fuel cell systems PID control is not suitable to meet the requirements of the fuel cell system's rapidity, stability, real\(-\)time demands, robustness, and so on. Therefore, the controller adopts modern advanced control strategies such as fuzzy control, neural network control, and model predictive control, etc., to realize more efficient, accurate, and adaptive system management. These control strategies utilize complex algorithms to optimize the control process, improve system performance, and enhance robustness to uncertainty and changing conditions.