Preactuated Multirate Feedforward Control for Independent Stable Inversion of Unstable Intrinsic and Discretization Zeros

A plant with unstable zeros is known to be difficult to be controlled, because of the initial undershoot of its step response and the unstable poles in its inversion system. There are two reasons why a plant has unstable zeros in the discrete-time domain: 1) noncollocation of actuators and sensors; and 2) discretization by the zero-order hold. Addressing problems 1) and 2) simultaneously, approximate and discrete-time stable inversion methods have been proposed as model-based feedforward control for unstable zeros. However, the approximated inversion methods compromise tracking performance, and the discrete-time stable inversion methods obtain oscillatory control inputs owing to the direct cancellation of discretization zeros. Therefore, this paper proposes a preactuated multirate feedforward control, which is an independent stable inversion of the two types of zeros: unstable intrinsic zeros from noncollocation and unstable discretization zeros from the zero-order hold. The proposed method combines both a state trajectory generation based on a time- and imaginary-axis reversal to address problem 1) and a multirate feedforward implementation to address problem 2), independently. Moreover, this study verifies the tracking performance improvement by performing simulations and experiments in comparison with well-known model-based feedforward control methods using a high-precision motion stage. The role and importance of multirate feedforward control are also demonstrated by comparing it to a continuous-time domain approach with preactuation.