Abstract: The active deformation control technique for aerospace flexible structures based on smart materials has been proven effective in improving surface accuracy, control performance, and task adaptability.However, the deformation control process can generate unexpected transient dynamic responses and residual vibration phenomena, which severely degrade the control effectiveness.Taking the parabolic antenna reflector driven by piezoelectric actuators as an example, a dynamic deformation control law based on the traditional finite-time optimal terminal control algorithm is designed.The research analyzes the reasons for generating input jumps and residual vibration phenomena at the terminal moment and proposes an optimal dynamic deformation control strategy and solution algorithm based on the acceleration performance index and two-stage optimization strategy.The results show that the use of a quadratic objective function based on acceleration can effectively ensure dynamic balance at the terminal moment and avoid input jumps and residual vibration phenomena under the premise of achieving smooth state transition, thus achieving continuous and smooth deformation effect throughout the entire time domain.

Key words: active reflector, piezoelectric drive, vibration suppression, quadratic programming, acceleration