Design of robust adaptive controller

The model structure used for control design is obtained by reducing the full actuation model. First, the actuation bandwidth of a conjugated polymer actuator is low with respect to its first-mode natural frequency. For example, a sample of 20 x 5 x 0.17 mm has a natural frequency around 

70 Hz while its actuation bandwidth is typically below 10 Hz. Therefore, we can ignore the mechanical dynamics and represent the model for the tip bending displacement as 

By ignoring terms associated with n 2 in the summation, one reduces (5.10) to a third order system  

Despite its simple looking, (5.12) captures the dominant structure of the actuator dynamics and, as shown in experimental results, is instrumental in effective control design. 

An adaptive controller can be designed based on the model structure (5.12), to deliver consistent performance in the presence of actuator behavior changes. Fig. 5.8(a) illustrated the indirect adaptive control paradigm [loannou and Sun (1996)], where the model parameters are estimated online 

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