Reduced Order Controller Design And Experimental Study Of A Flexible Beam

Large space flexible structure is characterized by lightly damped modes. The free vibration will last a long time if the modes of the structure are excited by certain disturbance. The operation precision of the equipments will be greatly influenced by the vibration if it is not suppressed effectively, and under some circumstances it is possible that the whole spacecraft lapsed. So it is very important to suppress the undesired vibration of flexible structures.Several major problems in active vibration control of flexible structures are investigated in this dissertation. These problems are: modeling of the piezoelectric beams, spillover prevention, reduced-order controller design and thermally induced vibration suppression.Flexible structures are distributed parameter systems and can be modeled using partial differential equations. Controller design techniques based on partial differential equations are not well established. Flexible structures can also be modeled using finite element analysis (FEA) method. The model obtained using FEA is often the one with high order and model reduction is often needed before designing a controller. Mathematical models of flexible structures can also be obtained using system identification methods.Modeling of the flexible beam with PZT actuator and sensor bonded on its surfaces is studied in chapter 2. Firstly, finite element model is obtained and compared with the experimental results. Secondly, in order to obtain a better description of the plant, system identification in the frequency domain is investigated. A frequency response curve fitting method is proposed based on the characteristic of the piezoelectric beam. Transfer function models of the piezoelectric beams are then obtained using the forenamed method.Modern control design techniques provide controllers of order equal to or greater than the order of the plant. However, for large-order systems such as flexible structures these controllers are difficult or impossible to implement owing to cost, reliability and hardware implementation constraints. So the reduced order controller design problems are emphasized in this dissertation. Vibration suppression of the piezoelectric beam using H₂ controller is studied in chapter 3. Reduced order H₂ controllers are designed based on the transfer function models obtained in chapter 2 and the experimental results are reported.Controllers designed using the standard H₂ control technique can't guarantee the stability of the closed loop system and the spillover instability may happen. A new method called "H₂ control with an augmented filter" is proposed to prevent spillover instability. Experimental results verified the proposed method.To guarantee the stability of the closed loop system, vibration suppression of the flexible structure is studied using H_∞control technique in chapter 4. Firstly, mixed sensitivity approach is considered. To prevent lightly damped pole zero cancellation, regional pole constraints are adopted. Secondly, reduced order H_∞controller design problems are studied. The experimental results show that the reduced order H_∞controller can suppress the vibration of the flexible beam effectively.Thermally induced vibration is one of the typical causes of the space structure failure. Thermally induced vibration suppression of a flexible beam is investigated in chapter 5. The finite element model of the thermally induced vibration of a flexible beam is obtained. Then the simulation result of the thermally induced vibration suppression using H₂ controller with an augmented filter is given.