A new optimal control scheme with adjustable gain featured by saturation function and its switching models for non-smooth vibrations - Do, Xuan Phu (Vietnam Journal of Mechanics, 2026)
In this study, a new optimal control scheme with two proposed theorems is presented. Two optimal control theorems are developed: (i) the first scheme uses the conventional adaptive gain with a new proposed saturation function, and (ii) the second scheme utilizes a new adaptive switching saturation function based on the first model (i). In the first model, the derivative result is derived in a new form of exponential function of the saturation function. The adaptive gain for this model includes system states with a chosen matrix of the Hamiltonian equation. In the second model, a new switching saturation is adopted. The constraints related to the system states and the chosen matrix are then applied. Unlike the first control scheme, the second scheme uses the required boundary of the system state for choosing the adaptive gain. The properties of the saturation function used in the first model are still applied in the second model. The main advantage of this second model is to provide flexibility in computing the gain under severe disturbance through the initial boundaries and adjusting the energy consumption of the control system. After the formulation, the proposed controllers with the new adaptive gains are applied to a vehicle seat suspension system with non-smooth vibrations. Two existing controllers are also chosen for this simulation to compare with the proposed models. The simulation results show that the proposed control schemes can provide better control performances in terms of the PSD index (power spectral density), displacement, and control input signal.