Since the microactuator model is assumed stable, so is the error dynamics
(equation 3.177). Thus we have
k→∞ y M (k) − y M (k) = lim
k→∞ H M x(k)=0.
P M = P M ,
Hence, we have that if P M is stable and
k→∞ y M (k)−y M (k)=0.
It should be noted that for MEMS based microactuator with relative po-
sition error signal , y M is available and thus can be used in the control
scheme directly instead of y M .Incasey M is not available, its estimation y M
can be used as in Figure 3.96. In general, an open loop estimator does not
guarantee asymptotic stability of the error dynamics .
Next, we prove using an example that even with a reduced order PZT
actuated suspension model and parameter uncertainty, y M is still a close esti-
mate of y M , and hence the modified algorithm is effective in dealing with the
Figure 3.96: Dual-stage control with microactuator saturation taken into con-
3.7.5 Experimental Results
Althoughthedesignprincipleshowninthe previous section applies to various
types of dual-stage actuators, experiment using an actuated suspension is used
here to show the effectiveness of the proposed nonlinear control scheme. against
the original linear control scheme.
The nominal control loops, i.e., VCM path, microactuator path and overall
dual-stage open-loop are shown in Figure 3.97 with
P V (s)= 2.04 × 10 21
s +3.14 × 10 4
s 2 + 301.6s +2.58 × 10 5
s 2 + 2073s +4.3 × 10 8
s 2 + 1508s +3.55 × 10 8