Control of smart structural systems using multi-objective optimization techniques

Application of Linear Matrix Inequalities for design of multi-objective robust controllers for smart structural systems is investigated. Procedures are developed to obtain linear fractional representations (LFRs) for models of smart structural systems for different types of uncertainties due to unmodeled dynamics, model reduction and modal parameter variations. Robust controllers are designed for these uncertainties while ensuring that control input constraints due to actuator limits are not violated. Two different approaches for incorporating control input constraints, anti-windup methods and reachable sets are developed. The compensator design for the anti-windup design is formulated as a simultaneous stabilization problem. Multi-objective robust controllers are designed for uncertainties due to unmodeled dynamics and parameter variations. Two different designs for eliminating the spill-over problems due to unmodeled dynamics are formulated. The first design incorporates pole-placement requirements and control input limits for a given set of initial conditions. The second design incorporates disturbance minimization while ensuring control input constraints. Also, two different designs are formulated for robust control design incorporating real parametric uncertainty due to modal parameter variations. The first design is based on circle criterion in which the uncertainty due to unmodeled dynamics is incorporated. The second design utilizes Popov stability analysis to design controllers for disturbance minimization while ensuring prescribed control input limits. The designs are applied on two smart structural test articles designed and fabricated with piezo-electric actuators and sensors. A single-board two-input two-output fixed-point digital controller is also developed using a Field Programmable Gate Array (FPGA). It has been shown through this work that LMI optimization can be used as an effective tool for multi-objective controller design for integration in smart structural systems.