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Time-varying feedback stabilization of systems with input saturation actuators in complex mode space

Complex modes are often present when structural damping and gyroscope effects are included in systems. With the presence of unsymmetric matrix in governing equations, states of systems should be decoupled in complex mode space. This paper considers design and analysis of control for systems expressed in complex mode space. In the category of Lyapunov stabilization, sufficient conditions of state feedback controller for such systems are established. Under the condition that actuators suffer from the problem of saturation, a new control law which introduces a time varying coefficient for feedback gain into the nested controller is developed. The coefficient is dependent on the convergence rate of the system and utilizes actuators’ capacity and meanwhile, guarantees the asymptotical stability of the system. Numerical examples of a spinning smart beam structure with single input and multiple inputs are given. It is found that the strategy investigated can be used to control systems with complex modes. And the new low-and-high gain controller which consists of a time varying coefficient for high gain can efficiently reduce the vibration and utilize actuators’ full potential at a high level.