The present application relates to the technical field of ultra-precision
machining control, and particularly relates to a
modal controller generation method for a nano-positioning platform, a medium and equipment. The present application performs zero-pole
decomposition on a
transfer function of a controlled object, separates stable zero points, unstable zero points, non-resonant poles and resonant poles, constructs a desired
inner loop closed-loop
transfer function, retains the stable zero points, the unstable zero points and the non-resonant poles, and replaces the resonant poles as a whole with high-damping desired poles, inversely solves to obtain a
modal controller structure, introduces zero-pole cancellation constraints to eliminate controller
instability caused by unstable zero points, introduces order constraints to ensure causal
realizability, applies constraints with a
damping ratio greater than 0.1 to the desired poles and the introduced new zero points respectively, and outputs an
inner loop modal controller. The present application realizes simultaneous suppression of multiple resonant peaks, gets rid of dependence on a low-order model, ensures stability,
realizability and smoothness of a
control signal of the controller, and significantly improves control bandwidth and dynamic performance.