Stability control of suspended monorail vehicles based on PID and quadratic programming allocation

Suspended monorail vehicles are susceptible to coupled lateral-vertical vibrations under multi-source disturbances, such as track irregularities and fluctuating crosswinds, which can degrade operational stability and passenger comfort. To address this issue, this study develops an actuator-constrained hierarchical control framework for suspended monorail vehicles. The main methodological contribution is a vehicle-specific constrained control-allocation procedure. This procedure links measurable lateral-vertical acceleration feedback to physically bounded multi-actuator forces through sensitivity-based actuator configuration, data-identified control-effectiveness mapping, and QP-based allocation. Specifically, a high-fidelity vehicle dynamics model calibrated using measured data is subjected to track irregularities and Simiu-spectrum fluctuating wind loads. Sobol sensitivity analysis is then used to determine the actuator installation locations and acting directions, and a local control-effectiveness matrix is identified through single-actuator excitation simulations and linear regression. In the inner loop, a genetic-algorithm-optimized fixed-parameter PID controller and a fuzzy self-tuning PID controller are designed to generate virtual control commands. In the outer loop, a quadratic-programming-based allocation problem distributes these commands among the actuators while enforcing amplitude constraints. An LQR-QP controller is also introduced as a classical linear optimal-control benchmark. Under identical disturbances and actuator constraints, the fuzzy self-tuning PID-QP controller achieves the best overall performance among the compared methods. Relative to the uncontrolled case, it reduces the lateral and vertical acceleration RMS values by 21.15% and 20.80%, the corresponding acceleration peaks by 28.54% and 32.42%, and the RMS values of the lateral and vertical stability indices by 6.55% and 6.84%, respectively. These results indicate that the proposed hierarchical cooperative control framework can effectively improve the lateral and vertical stability of suspended monorail vehicles while satisfying actuator amplitude constraints.