The Control Algorithm Of Dynamic Vibration Absorber For Vibration Control Of Marine Equipments

Vibration control is all along an important issue addressed by engineers and scholars, which covers vibration isolation and shock resistance of marine electromechanical equipments, the wind and earthquake protection of civil structures, vibration cancellation of automobile suspensions, etc. The advancement of modern military industry leads marine diesel engines to develop towards high power and high rotating velocity, which may cause more severe undesirable vibration of ship skull and equipments. Dynamic Vibration Absorber (DVA) can work as an effective strategy, which is discussed thoroughly in current study. Based on vibration control of marine equipments, some conclusions about passive and active DVA's optimum designs in vibration suppression or isolation are drawn; moreover, the Virtual DVA control law is demonstrated experimentally. The main content and novel results are listed as following:1. The marine equipment is simplified as a SDOF mass block, and then the optimum designs of DVA attached to the SDOF primary mass are derived by the Lyapunov Equation and Matrix Kronecker Product. Firstly, using Lyapunov Equation the objective function is transformed from integration quadric form to matrix quadric one, secondly the matrix quadric form are expanded as polynomial expression under initial velocity or displacement, finally the polynomial coefficient are expressed with the Frequency Tuning Ratio and Damping Ratio using Kronecker Product. Minimizing the objective function, the optimum Frequency Tuning Ratio and Damping Ratio can be obtained. If the damping of primary structure is ignored, the closed-form analytical solution can be given. If the damping is taken into consideration, the 2-order perturbation solutions, expressed as the power series about the damping ratio, can be acquired. These optimum designs are composed of initial velocity or displacement ratio; hence various initial states can produce corresponding optimum designs, which differentiate them from previous studies. Especially, given the initial velocity ratio 0 or 1, these analytical solutions can produce the classical optimum designs under external force or base acceleration excitation. The comparison between the 2-order perturbation solutions and numerical optimum solutions by gradient search are demonstrated too, which prove that the 2-order perturbation solutions are stable enough.2. The Multiple Tuned Mass Dampers (MTMD) have been already applied for vibration cancellation of marine diesel engines, and consequently the calculus tools are proposed for performance index and iteration search of MTMD composed of infinitely multiple TMDs. In the previous study, the performance of MTMD made up of many TMDs can only be conjectured based on lots of data observation, at the same time, the iteration search is time-consuming. In current study, every single TMD, i.e. a small feedback component with independent Transform Function (TF), receives the displacement signal of the primary mass and exerts the control force on the primary mass, so the small TMD element can be regarded as an infinitesimal when the total number of TMD approaches infinity. Integrating all infinitesimal TMD elements, the TF of Infinitely Multiple Tuned Mass Damper (IMTMD) can be acquired, with the help of which the best and critical performance can be obtained. Moreover, the IMTMD method has excellent efficiency of iteration and it can give correct optimum parameters numerically for MTMD composed of more than 20 TMDs.3. The Two-Stage Vibration Isolation (TSVI) is widely used for vibration isolation of marine equipments, however, it's well known that TSVI causes a steep resonant peak (i.e. the second resonant peak) in the middle frequency band, and hence the Multiple Small Middle Mass Vibration Isolation (MSMMVI), i.e. the MTMD introduced into vibration isolation, is proposed to address this issue in the present study. An infinite-dimension dynamic system is adopted to approximate a finite-dimension one, i.e. MSMMVI. When the number of small middle mass approaches infinity, the TF of MSMMVI can be obtained by integration, and then based on constrained static deflection of gravity, the optimum stiffness ratio and starting frequency ratio is derived for the single Two-Stage Vibration Isolation (TSVI), MSMMVI and Infinite Multiple Small Middle Mass Vibration Isolation (IMSMMVI), finally the performance in high frequency band is analyzed, by which the optimum frequency distribution bandwidth is acquired. Although introducing decentralized small middle masses blocks causes a little shift-up of Transform Ratio (TR) curve in high frequency band, the MSMMVI can flatten the second resonant peak of TSVI. Moreover, the TR curve can be improved obviously at the cost of an almost ignorable shift-up.4. It seems that the active DVA technique is rarely used for vibration suppression of marine equipments in current ship engineering, hence two active control algorithms, i.e. the Sliding Mode Control and Robust control, which both have excellent disturbance or error resistant ability, are selected for being discussed theoretically in the present study. The direct-current component of active control force in Sliding Mode Control (SMC) is explained, at the same time, some mistakes in the previous study are clarified. Finally a sufficient and necessary standard is given to avoid the direct-current component. For the Robust Control, some skills are given about weight function selection, which is of great value for industry application.5. The performance of Virtual DVA algorithm is studied experimentally, which is proved to be effective in vibration suppression. The algorithm is stable even if modeling error for the controlled system exists, more importantly, it can receive the local signal and feedback the control force to the local part, which is especially suitable for the Decentralized Control (DC) of the massive or complex structure.Confronted with various new issues appearing in ship industry field and development in modern control theory, research concerning the vibration control of marine equipments and Active/Passive DVA are advancing, as a result, some important problem, which may have great influence on the future of DVA, are listed.