Vibration Control Methods Of Engineering Structures Under Random Excitations

Randomness is one of the most fundamental laws in nature. Many militarian equipment and civil engineering structures are subjected to random environmental loads, such as earthquakes, wind gusts, ocean waves, drift ices or road irregularities. Random vibration induced by these environmental excitations may lead to structural fatigue damage, abnormal facility operation, uncomfortable ride, or safety problems for workers. How to control such harmful random vibrations within acceptable levels has long been a common target for engineering communities. Unfortunately, achievements so far obtained in this field are still quite limited, far beyond the requirements of engineering societies. In this dissertation, aiming at some urgent requirements in building earthquake-resistance and vehicle vibration, the author uses some recent achievements in mathematics, mechanics and control theory, combine and further develop them to generate a series of innovative and effective approaches in order to deal with such random vibration based structural control problems. These approaches and the conclusions drawn by using them in the study of the above civil and vehicle engineering problems have been fully justified in this dissertation. And they are also useful for the random vibration control in other engineering fields.Earthquakes and road irregularities are random and they can reasonably be treated as stochastic processes in the controller designs. However, as the usual random vibration methods are too complex and lack of efficiency, in the past time-domain based direct integration methods were usually adopted in the simulations, with very small time step and simplified structure model.In it a substantial number of earthquake acceleration records or excitation samples of the road inputs must be used in order to get statistical characteristics of the system's responses, which greatly increases the required computational effort. In this dissertation, some symplectic conservative, guaranteed cost and high robust methods are introduced in the field of random vibration control. Random responses of the uncontrolled and controlled structures are calculated with pseudo excitation method (PEM) and precise integration method (PIM) used. PEM is a highly efficient and accurate probabilistic method, in it the power spectral densities (PSDs) of the structural responses are calculated directly and conveniently from the ground acceleration or road surface elevation PSD. This yields accurate root mean squares of the structural responses, including the frequency-weighted acceleration root mean squares of the vehicle body. In a word, one feature of this dissertation is the application of stationary/non-stationary random vibration theory to the structural vibration control with PEM and PID used.Linear matrix inequality (LMI) approach has emerged as a powerful formulation and design technique for a variety of linear control problems, for which the existing convex optimization techniques such as interior-point algorithms, can be used effectively and conveniently. For new control strategies proposed in this dissertation, LMI optimization approach has been widely used. These strategies, including robust H_∞control, guaranteed cost control, robust H₂/H_∞control and constrained H_∞, control, are applied to building's aseismic control or active suspension design.Main research work of this dissertation can be summarized as follows:(1) Field of application of LQG method and its solutions are expanded. LQG regulators have been used in many engineering fields, however, as the low efficiency of usual random vibration analysis methods, LQG control technique still requires further development especially when the disturbances are non-stationary. In this dissertation, a new attempt is studied in which the LQG control is applied to adjacent tall buildings subjected to non-stationary seismic random excitations. With interval mixed variable energy introduced, the Riccati differential equation is solved precisely via the combination of interval matrices. With PEM and PIM used, such difficult transient LQG control process is solved with high precision and efficiency.(2) Based on LMIs, a new robust H_∞control approach, a new guaranteed cost control approach and a new robust H₂/H_∞control approach are presented, which are applied to aseismic structures or active suspension with uncertainties in model parameters. Uncertainties in the modeling of structures always exist. Neglecting these uncertainties may cause degradation and even instability of controlled structural systems. In this dissertation, based on LMIs, sufficient conditions for the existence of such output feedback controllers are derived, while the specific steps for controller designing are suggested. Numerical results show that whether the variation of the structural stiffness, damping, mass parameters or sprung mass of the vehicles exists or not, the proposed robust controllers behave very satisfactorily.(3) Based on LMIs, a constrained H_∞output feedback control method for active suspensions is proposed. Usually, requirements for advanced vehicle suspensions are conflicting in order to improve driving safety and ride comfort. This dissertation formulates the active suspension control problem as a constrained H_∞, output feedback control problem by choosing body accelerations as the controlled output and specifying the suspension stroke, dynamic tire load and control force as time-domain hard constraints. Such constrained H_∞, output feedback controllers are investigated for continuous-time system and discrete-time system respectively. Sufficient conditions for the existence of the controllers, as well as the detail steps for the controller designing, are given.(4) Based on the precise integration method and symplectic conservative perturbation method, a new precise algorithm is proposed for linear quadratic Gaussian (LQG) control of time-varying systems, which is applied to the vertical vibration suppressing of a rail carriage moving on a simply supported girder bridge. Vehicle-bridge coupling systems are time-dependent, which lead to the time-varying Riccati differential equation and the time-varying Kalman-Bucy filter equation, both of them need be solved in the LQG controller design. In this dissertation, the original time-varying Hamiltonian system, which corresponds to the time-varying Riccati differential equation, is decomposed into two Hamiltonian systems, i.e. a zero-order system and a residual perturbation system via the canonical transformation. With interval mixed variable energy introduced, the Riccati equations are solved recursively via combinations of interval matrices, as well as the state transfer matrices of the Kalman-Bucy filter equation. Its superiority has also been justified via numerical simulations of the random vibration control of a vehicle-bridge coupling system caused by irregular bridge surfaces.