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This paper deals with the simulation, and design of a trajectory-tracking control law for a physical system under parameter uncertainty modeled by a bond graph. This control strategy is based on the inversion of the system through their causal Input/Output (I/O) path using the principle of bicausality to track the desired trajectory. The proposed control strategy is validated with the use of a simple mechanical mass-spring-damper system. The results show that the bond graph is a very helpful methodology for the design of control laws in the presence of uncertainties. This proposed control can be applied in several applications and can be improved to ensure robust control.

This paper focuses on the modelling and control of an electromagnetic suspension using the bond graph tool. This technique combines graphical and relational aspects to establish connections between bond graph elements, particularly in deducing junction relationships and employing bicausal inversion for trajectory tracking controller design. To determine the controller parameters, we utilized a meta-heuristic method called Firefly for optimization, thus avoiding the need for trial and error. The simulation was conducted using 20-Sim software and a Matlab/Simulink script, which yielded improved results. This paper presents an initial contribution that demonstrates the integration of meta-heuristic optimization and the bond graph tool for parameter selection in 20-sim simulation software.

The outcomes of this research significantly contribute to the existing body of knowledge on metaheuristic optimization techniques for active suspension systems. By conducting thorough investigations and analyses, the study effectively demonstrates the remarkable advantages of the Firefly algorithm in optimizing the performance of both conventional and intelligent controllers for active suspension systems. These findings highlight the algorithm's potential to revolutionize the field and pave the way for more efficient and robust control strategies. The demonstrated effectiveness of the Firefly algorithm in minimizing the error between the car's displacements and the disturbances of the road is particularly noteworthy. This achievement ensures a more precise and accurate tracking of the desired trajectory, regardless of the input signal used, whether it be an impulse, sine wave, or step-wise graded signal.