Learning control system and method for nano-precision motion stage

A learning control system for a nano-precision motion stage, comprising a closed-loop feedback section Sfb and a feedforward section Sff;

• wherein the closed-loop feedback section Sfb comprises a motion trajectory generator Cr, a feedback controller Cfb a motion stage P, and a first Fourier transformer Cfft1;
• the motion trajectory generator Cr generates a desired motion trajectory r(t);
• the desired motion trajectory r(t) minus a position measurement signal yj(t) results in a motion error signal ej(t);
• the motion error signal ej(t) added to a feedforward signal uff,j(t) results in a feedback input signal efb,j(t);
• the feedback input signal efb,j(t) is input into the feedback controller Cfb to generate a feedback control signal ufb,j(t);
• the feedback control signal ufb,j(t) added to a disturbance signal dj(t) results in a total control signal uall,j(t);
• the total control signal uall,j(t) is transmitted to the motion stage P to generate an actual position signal yp,j(t);
• the actual position signal yp,j(t) added to a measurement noise signal vj(t) results in a position measurement signal yj(t);
• and the position measurement signal yj(t) is transformed into a frequency domain position measurement signal γj(w) by the first Fourier transformer Cfft1;
• the feedforward section Sff comprises a second Fourier transformer Cfft2, a learning controller CILC, an iteration backward shift operator Cz, and a Fourier inverse transformer Cifft;
• the second Fourier transformer Cfft2 is configured to transform the motion error signal ej(t) to a frequency domain error signal ζj(w);
• the frequency domain error signal ζj(w) and a j-th frequency domain feedforward signal μff,j(w) are jointly input to the learning controller CILC to obtain a (j+1)-th frequency domain feedforward signal μff,j+1(w);
• the (j+1)-th frequency domain feedforward signal μff,j+1(w) is input into the iteration backward shift operator Cz to generate the j-th frequency domain feedforward signal μff,j(w);
• and the j-th frequency domain feedforward signal μff,j(w) is transformed into the feedforward signal uff,j(t) by the Fourier inverse transformer Cfft1;
• and
• j represents an iteration experiment count, j≥1, t represents time, and w represents frequency.