## 4 Hydropneumatic Suspension Controller's Design and Parameter Optimization
### Controller's Parameter Optimization  
Based on the driving road conditions and the results of the road surface grade identification, the three types of road surfaces correspond to the ride comfort mode, stability mode, and comprehensive adjustment mode, with different suspension controller parameter settings for each mode. Traditional manual parameter selection is inefficient and prone to errors and lacks adaptability. Therefore, this paper uses the Hiking Optimization Algorithm (HOA) to optimize the FSMC parameters. The HOA [24] simulates human decision-making behavior during hiking, adjusting strategies based on the natural environment, paths, and difficulty. As a nature-inspired metaheuristic algorithm, the HOA is mainly used for function optimization and global optimization problems. It can perform a global search across a broad solution space, avoiding local optima, thus improving the optimization effect of the controller. By adaptively adjusting the search strategy, the HOA enhances the controller's adaptability and robustness and is particularly suitable for nonlinear and uncertain problems, aligning with the needs of the FSMC. The core process of the HOA applied in this study consists of three key phases. First, the population is randomly initialized, and the fitness is assessed within the parameter boundaries. Second, during the iterative optimization process, (1) the current optimal and worst individuals are identified; (2) the base velocity component is computed based on random slope generation; (3) a new velocity vector is synthesized by combining the base velocity, the learning term toward the optimal individual, and the term away from the worst individual (the intensity of the learning is regulated by a random sweep factor); (4) the individual positions are updated, and boundary constraints are processed; and (5) a greedy strategy is used to decide whether or not to accept the new solution. Finally, the optimal solution and its fitness are recorded at each iteration. The algorithm achieves the global optimal search of parameters through a slope-driven velocity mechanism and an elite learning strategy of sweep factor regulation. The HOA optimizes the FSMC's parameters for each type of road surface. Given the complexity of the road surface types, B-, D-, and F-grade road surfaces are selected for optimization. The selected parameters for the SMC include \(c_{1}\), \(c_{2}\), \(c_{3}\), and two scaling factors (\(K_{bs}\) and \(K_{bsc}\)), along with a quantization factor (\(K_{le}\)). The optimization goal function is the weighted sum of the following three objectives: the sprung mass's acceleration, the suspension's dynamic deflection, and the tires' dynamic load. The optimization model is expressed as follows:  
\[\min f=w_{1}\frac{rms(a)}{rms(a_{0})}+w_{2}\frac{rms(f_{d})}{rms(f_{d0})}+w_{3 }\frac{rms(F_{t})}{rms(F_{t0})} \tag{20}\]  
where \(a\) and \(a_{0}\) represent the body's accelerations for the HOA-FSMC and passive suspension, respectively. \(f_{d}\) and \(f_{d0}\) represent the suspension's dynamic deflections for the HOA-FSMC and passive suspension, respectively. \(F_{t}\) and \(F_{t0}\) represent the tires' dynamic load for the HOA-FSMC and passive suspension, respectively, and \(w_{1}\), \(w_{2}\), and \(w_{3}\) represent the weights for the sprung mass's acceleration, the suspension's dynamic deflection, and the tires' dynamic load, respectively. The optimization weights for the different road surfaces are shown in Table 6. During underground mine operations, the auxiliary transport vehicle's suspension controller should dynamically adjust the weighting coefficients of the performance metrics based on road roughness levels. Under favorable road conditions, it should focus on comfort and give more weight to the spring load's acceleration. Under moderate road conditions, it should take into account comfort and durability, appropriately reduce the weight of the spring load's acceleration, and increase the weight of the tires' dynamic load.