Robust Vibration Suppression of Resonant Modes by Feedback Compensation Realized Using Allpass Filters

Vibration Suppression in Position Control System by Pole Zero Cancellation using Limited Pole Placement Method

“…The characteristic polynomial, γ(z), is expressed by the fixed part and the parameter part in Eq. (8).…”

“…Modern control theory and H-infinity control theory are remarkably effective in suppressing vibrations (4)- (6) . The use of phase shifters in high-frequency areas makes a system robust despite the presence of several resonance modes (7) (8) . Additionally, two-degree-of-freedom (2DOF) controllers can suppress vibrations with their feedforward controllers (9)- (11) .…”

Efficient autonomous feedback controller parameter design considering robust stability for galvanometer scanner

“…In the diagram, C PID ( s ) is PID controller, C APF ( s ) is all‐pass filter, P ( s ) is galvano scanner (controlled plant including a rigid body mode and one or more resonant modes), r is command, u is control input, and y is output. The controller C ( s ) formulated below is a cascaded FB controller composed of PID controller for rigid body mode and all‐pass filter for resonant modes 6 $$\begin{equation} C(s)={C}_{\mathrm{PID}}(s){C}_{\mathrm{APF}}(s) \end{equation}$$ $$\begin{equation} {C}_{\mathrm{PID}}(s)={K}_{\mathrm{P}}+\frac{{K}_{\mathrm{I}}}{s}+\frac{{K}_{\mathrm{D}}s}{{\tau}_{\mathrm{D}}s+1} \end{equation}$$ $$\begin{eqnarray} {C}_{\mathrm{APF}}(s)=\prod _{i=1}^{{N}_{\mathrm{APF}}}{C}_{\mathrm{APF}}^{(i)}(s)=\prod _{i=1}^{{N}_{\mathrm{APF}}}\frac{{s}^{2}-2{\zeta}_{\mathrm{APF}i}{\omega}_{\mathrm{APF}i}s+{\omega}_{\mathrm{APF}i}^{2}}{{s}^{2}+2{\zeta}_{\mathrm{APF}i}{\omega}_{\mathrm{APF}i}s+{\omega}_{\mathrm{APF}i}^{2}}\nonumber\hskip-10pt\\ \end{eqnarray}$$…”

“…In this context, FB controller design based on gain and phase stabilization is reported to be effective not only for galvano scanners but also for various control plants with resonant modes. [6][7][8][9] With this technique, a broad control band can be obtained with stabilized resonant modes through appropriate parameter setting in PID controllers or cascaded controllers using multiple compensators. However, the number of controller parameters usually grows with the number of resonant modes, and parameter design becomes complicated.…”

“…High‐speed high‐accuracy control of galvano scanners used in position control of laser irradiation is critical to meet these requirements, and aggressive R&D is carried out in industry and academia 1–5 . Particularly, perturbations of plant parameter (below referred to as “plant perturbations”) like resonance frequency and torque constant of galvano scanner caused by frequency variation, heat release, and time‐dependent changeability lead to band narrowing and instability in feedback (FB) control, thus impairing positioning speed and accuracy 6,7 . Realization of FB control robust against plant perturbations is necessary to maintain high level of productivity and precision in laser machining systems.…”