Vibration Control Of MIMO Systems Based On H₂ And H_∞ Control Theories

The structural vibration control has been widely used in many fields such as aviation, machinery manufacturing, vehicle engineering, shipping and marine project, bridge and building engineering and so on. Research and application on vibration control algorithm is of great importance both in vibration reduction and the use of the good vibration. The key problem which needs to be solved is the control method when deal with the control problems. The classical control algorithms such as the PID control and the LQR (LQG) control theory have played a big role in control field. But they also have many demerits. For example, the PID control is just suitable for frequency domain control of the single-input-single-output (SISO) systems. Though the LQR (LQG) control method can be used in time domain control of the multiple-input-multiple-output (MIMO) systems, the accurate state space model must be obtained. To eliminate the problems in classical methods from the root, new vibration control theory and technology must be introduced. The pathways for solving structural vibration control are broadened by the continuous improvement of the H₂ and H∞control theory.In the background of research and development of multi-shaker control system, the paper extensively discusses and studies the aspects of structural control problems using the new methods in advanced modern control theory. Many new control strategies are proposed to solve the application problems of vibration control. Based on multiple-input-multiple-output (MIMO) linear system theory, theoretical analysis, numerical simulation and experimental research are performed in the dissertation. The main tasks of the dissertation are presented as follow:Profound research has been made of the H₂ norm and the H∞norm in vibration control. A new optimization algorithm for the H∞norm computation is set forth. The H₂ norm and the H∞norm spaces to describe the properties of vibration systems are summarized as well as the computation methods and the detailed calculation procedure. Then the difference between the H₂ norm and the H∞norm in engineering application is performed. At last, the traditional calculation method for H∞norm is recounted and a new optimization algorithm is set forth. A cantilever beam is used to verify the new algorithm. The simulation result shows that the proposed algorithm is feasible and valid.Research on the application of the LQG/H₂ control algorithm in structural vibration control is recounted. The traditional LQG problem is actually output feedback control theory, which is the combine of optimal state feedback and optimal state estimation. The application of the LQG control algorithm in structural vibration control is studied. At last, a cantilever beam is used to verify the LQG control algorithm. Based on the control results obtained from different exciting forces on the beam, the conclusion is drawn that the LQG algorithm is suitable for dealing with the structural vibration problems with random exogenous disturbances.Profound research has been made of the H∞control algorithm in structural vibration control. Many specific control methods based on H∞control algorithm are introduced, which include signal-based H∞control, mixed-sensitivity H∞control, two-degrees-of-freedom H∞control, H∞loop-shaping design and the H∞filtering theory. The specific design procedures are summarized. A summarization of the selection methods for the weighting function matrix in mixed-sensitivity H∞control is presented. A new idea for the weighting function matrix selection is proposed for the vibration control of high order flexible structures. The simulation results show that the technique for the weighting function matrix selection is effective to meet the specifications of robust stability and the performance of external disturbance rejection. A new approach is presented for dual-shaker random vibration test using H∞-based optimal decoupling method with two degrees-of-freedom controller. The results demonstrated that, in the frequency range from 20 Hz to 2000 Hz, the controller could make the error between the output PSD (power spectrum density) and the reference PSD within±1dB and the root mean square error within±10%, which is perfect for the dual-shaker random vibration control test.The dual-shaker random vibration control test is firstly implemented by using the two-degrees-of-freedom H∞control algorithm. The control system is developed on a computer with the VXI modules and so on as hardware platforms for signal acquisition and generation. The two-degrees-of-freedom H∞control algorithm is verified and corrected by lots of tests with a small cantilever beam in the laboratory. The test results demonstrated the feasibility of this method. Every specification of the test results has met the requirements of application in engineering.