Singularity-free practical finite-time force control for a compliant grinding mechanism subject to hysteresis nonlinearity and asymmetric time-varying air pressure constraints

In this paper, a “planning and control” scheme combining asymmetric hysteresis compensation and a command-filtered finite-time controller is developed for the force control of a compliant grinding mechanism (CGM) driven by a double-acting cylinder (DAC) with asymmetric time-varying air pressure constraints (ATAPCs). In the planning section, a novel hysteresis model that can be employed to characterize asymmetric hysteresis loops is developed by fusing higher-order polynomials, deadband operators, and play operators. Moreover, its inverse model is constructed successfully via a modified inverse multiplicative structure (MIMS) for planning the desired air pressure from the desired contact force. In the control section, a reduced-order state observer (ROSO) and a disturbance observer (DO) are proposed to observe the rate of change of air pressure (RCAP) and external disturbance, respectively. By introducing an asymmetric time-varying barrier function (ATBF), the problem that the time-varying output constraint function must be strictly positive or strictly negative in the nonlinear state-dependent transformation method is eliminated while realizing the ATAPCs. With the help of a \({c^1}\) $c^1$ continuous switching function, a practical finite-time command-filtered controller is established, which avoids the singularity problem arising from the derivation of the virtual controller in the finite-time backstepping approaches. Finally, hardware experiments verify the effectiveness of the presented practical finite-time command-filtered controller.