Optimum Structural/Control Design with Robustness Constraints

An integrated approach to the design of a minimum weight structure with optimum robust control is presented. The two control design approaches used for illustration are based on the LQR and the H 2 – H ∞ theory for multi-input multi-output systems. The problem is formulated as a nonlinear optimization problem with structural design and control design variables being treated as independent design quantities. In the LQR control design approach, a constraint is imposed on the spectral radius of the closed loop transfer matrix. In the H 2 – H ∞ control design approach, constraints are imposed on the singular values of the transfer function. For both control design approaches, constraints are also imposed on the structural frequency distribution. The application of the integrated approach is illustrated by designing two idealized structures. The actuators and sensors are assumed to be collocated and embedded in structural elements. The structural design variables are the cross-sectional areas of bar elements and the thicknesses of membrane elements. The control design variables are the elements of the weighting matrix of the controller and the matrices used in the parameterization of uncertainties.

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