Data-driven modeling and control framework under partial state measurements with experimental validation on multi-fuel engines

Abstract

Physics-based modeling approaches have traditionally been employed for development of mathematical models to represent system dynamics. This in turn, enables designing control strategies that ensure desired system performance. However, these modeling methods are not always realizable primarily due to limited understanding of the system’s underlying physics, significant nonlinearities, and the potential introduction of high-order state dynamics. In such scenarios, data-driven approaches offer a viable alternative for modeling. However, data-driven methods often depend on the availability of full-state measurements to ensure model development and control design. This requirement is often unattainable in real-world applications. Thus, these challenges necessitate development of an advanced data-driven modeling and control framework, capable of handling complex systems under such practical constraints. In this context, this paper derives a multi-step predictor form of model using input-state-output data, where the unknown initial conditions are labeled in terms of measurable quantities. Subsequently, a data-driven controller is designed that computes control by performing model inversion of the surrogate model through minimizing a cost function which captures the desired objective. Thus, this proposed framework is applicable to systems subjected to partial state measurements, enabling system representation and desired operations in real-world environments. Further, to validate the effectiveness and versatility of the proposed framework, it is first implemented on a benchmark toy problem where it achieves a modeling accuracy on the order of 10⁻³ and a control tracking accuracy on the order of 10⁻¹. Then the framework has also been experimentally demonstrated on a real-world problem of combustion phasing control of a multi-fuel compression ignition engine which is a complex dynamic process, that is affected by change in operating conditions including varying fuel properties. Thus, across cetane numbers of 25 to 48, the controller maintains combustion phasing (CA50) within $\pm 1$ degCA, adapting ignition-assist power and injection timing in real time.