25. Active Vehicle Suspension with a Weighted Multitone Optimal Controller: Considerations of Energy Consumption

Vibration reduction is a significant problem in the design and construction of vehicle suspensions (Lozia and Zdanowicz, IOP Conf Ser Mater Sci Eng 148:12014, 2016; Konieczny et al., J Low Freq Noise Vib Act Control 32:81–98, 2013). Passive semi-active and active methods are used in order to reduce vibrations. Considerations related to active and semi-active vibration reduction and the influence of disturbances on such objects can be found in many publications. In the case of these systems, the aim is always to find a compromise between their efficiency and energy consumption. The control law for such systems is usually determined as a solution to the optimisation problem with quadrant quality indicator. Energy limitation is taken into account by selection coefficients of the weighting matrix associated with the control signals vector. The efficiency of vibration reduction is able to be improved in the entire useful frequency range of the system operation but this generally results in an increase in the demand for external energy. An additional problem in the case of vehicle suspensions includes the need for increased vibration reduction for selected frequencies. This is related to the internal vibration frequencies of the driver’s internal organs. The paper presents the synthesis of a weighted multitone optimal controller (WMOC) for an active vibration reduction system. The control signal in this case is determined on the basis of the identified sinusoidal disturbances vector. The vibration transmissibility function and the energetic indicators for the active suspension were determined while taking note of nonlinearities occurring in the actual vehicle. The analysis of energy indicators (e.g. energy, maximum power) is presented, depending on the level of vibration reduction efficiency. The results were compared with analogous linear-quadratic regulator (LQR).