# Complex-Order Models: A System Identification Point of View
## 4 A Use Case in System Identification  
In past decades, researchers have developed many investigations, and industry has implemented several technologies, to model and control automotive systems (such as innovative combustion engines, fuel injection, air-fuel ratio control, spark-timing control, exhaust-gas recirculation, common-rail injection systems, electric and hybrid powertrains, fuel cells, energy management systems, cruise control, idle-speed control, antilock and differential braking, active/semiaactive suspensions, collision avoidance, autonomous vehicles, etc. ), but there is still space for the improvement of performance, fuel-efficiency management, intelligent transportation and congestion reduction, and finally, environmental impact, if advanced robust control systems are employed [29]. In this context, internal combustion engines have been the most common source of propulsion in automotive vehicles because of the high energy density of diesel/gasoline fuels, which offer the best compromise among fossil fuels in terms of cost, safety, and pollution in a \"well-to-wheel\" cycle [30]. However, cleaner compression ignition engines and more efficient spark ignition engines can be designed. This improvement can be especially provided by control system technology, especially in increasingly complex systems, which can also be affected by imperfections and hidden dynamics [31]. Namely, electronic control is most responsible for reducing fuel consumption and pollutant emissions, while also taking the assignment of other tasks such as increasing stability, safety, comfort, drivability, etc. Therefore, this paper is based on a control-oriented approach, in which the mathematical representation of the physical processes occurring in the system is preliminary to the model-based control system design and optimization [30]. This is fundamental in the design of innovative internal combustion engine control systems and control strategies. In this field, injection systems still require optimization (e.g., by approaches that could be similar to those developed for flow monitoring and control in other applications [32; 33; 34]), although the technology used for fuel delivery to the intake manifold through a typical common rail, and the technology for fuel combustion, can be considered mature. Namely, government regulations continuously increase the demand for systems with a lesser impact on the environment, such as with the very limited emission of polluting gases, particulate matter, noise, etc. Note that this requirement fueled the growth of electric or hybrid vehicles, and other types of engines, even in prototype form [35]. In such cases, although energy management is complex, control plays a crucial role in applying suitable strategies to split the power demand between the engine and the battery of hybrid vehicles, and in coordinating the interacting subsystems [35]. In this work, however, a peculiar injection system is considered. It employs compressed natural gas (CNG) as fuel because gas is cheaper and more equally distributed than conventional fuels, and possesses other good characteristics, e.g., the possibility to achieve an optimal air-gas mix, a good knocking resistance, the prevention of particulate matter emissions, the reduction of energy consumption, etc. Problems arise because the reduction of emissions and the optimization of energy consumption requires accurately metering the mix between air and gas [36; 37]. To address this issue, the control of the injectors delivering gas to the intake manifold is coupled with the control of gas pressure in the common-rail volume of the injection system. Namely, the timing of the injectors (i.e., their opening and closing time intervals) can be regulated in a very precise manner due to electronic commands to the available electro- injectors.