A general framework for solving inverse dynamics problems in multi-axis motion control. (December 2019) - Zhu, Bohan; Farouki, Rida T.
Abstract: An inverse dynamics compensation (IDC) scheme for the execution of curvilinear paths by multi-axis motion controllers is proposed. For a path specified by a parametric curve r ( ξ ), the IDC scheme computes a real-time path correction Δ r ( ξ ) that (theoretically) eliminates path deviations incurred by the inertia and damping of the machine axes. To exploit the linear time-invariant nature of the dynamic equations, the correction term is computed as a function of elapsed time t, and the corresponding curve parameter values ξ are only determined as the final step of the IDC scheme, through a real-time interpolator algorithm. It is shown that, in general, the correction term for P, PI, and PID controllers consists of derivative, natural, and integral terms (the integrand of the latter involving only the path r ( ξ ), and not its derivatives). The use of lead segments to minimize transient effects associated with the initial conditions is also discussed, and the performance of the method is illustrated by simulation results. The IDC scheme is expressed in terms of a linear differential operator formalism to provide a clear, general, and systematic development, amenable to further adaptations and extensions. Highlights: Real-time compensation for machine inertia and damping is achieved. The procedure is essentially exact for P, PI, and PID controllers. The method can result in significantly improved contouring accuracy. A comprehensive treatment of the mathematical model is presented. Simulation results are used to demonstrate the improved performance.