Numerical approach for partial eigenstructure assignment problems in singular vibrating structure using active control

In the paper, the partial eigenstructure assignment problems are investigated using acceleration–velocity–displacement active control in a singular vibrating structure. The problems are transformed into solving matrix equations using the receptance matrix method. Iterative sequences are constructed, and the iterative feasibility is presented for solving the matrix equations. The partial eigenvectors of the closed-loop system are reassigned by imposing modal constraints. An algorithm is proposed to get numerical solutions of the derived matrix equations. The initial value condition is discussed to obtain the minimum norm solution of the partial eigenstructure assignment problems. The designed acceleration–velocity–displacement active control can solve the partial eigenstructure assignment problems depending only on original vibrating structure information. The proposed numerical algorithm can obtain the minimum norms of controller gain, which implies minimum energy consumption. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Applying Eigenstructure Assignment to Inner-Loop Flight Control Laws for a Multibody Aircraft

Unmanned aircraft used as high-altitude platform system has been studied in research and industry as alternative technologies to satellites. Regarding actual operation and flight performance of such systems, multibody aircraft seems to be a promising aircraft configuration. In terms of flight dynamics, this aircraft strongly differs from classical rigid-body and flexible aircraft, because a strong interference between flight mechanic and formation modes occurs. For unmanned operation in the stratosphere, flight control laws are required. While control theory generally provides a number of approaches, the specific flight physics characteristics can be only partially considered. This paper addresses a flight control law approach based on a physically exact target model of the multibody aircraft dynamics rather than conventionally considering the system dynamics only. In the target model, hypothetical spring and damping elements at the joints are included into the equations of motion to transfer the configuration of a highly flexible multibody aircraft into one similar to a classical rigid-body aircraft. The differences between both types of aircraft are reflected in the eigenvalues and eigenvectors. Using the eigenstructure assignment, the desired damping and stiffness are established by the inner-loop flight control law. In contrast to other methods, this procedure allows a straightforward control law design for a multibody aircraft based on a physical reference model.