The Fast Model Predictive Control For Structure Vibration With Nonlinear Factors

In the practical application of civil engineering,physical limitations,time delays,uncertain disturbances,non-linearity and other problems can be found frequently in an active structural vibration control.Thus,there is significant value to study on the control methods with these factors.In recent years,the model predictive control(MPC)has received much attention because of its advantages of dealing with constrained control problems.In this thesis,a novel fast model predictive control for structures with input constraints / local nonlinearity is proposed.The specific work of this dissertation is listed as follows:For the nonlinear factor of input constraints: a novel fast model predictive control with input constraints for large-scale structures is proposed.First,based on the second-order structural dynamic equation,the explicit expression form of the Newmark-β method is derived.Then,according to the parametric variational principle,a linear complementary problem for the proposed fast MPC saturation controller is developed,replacing the quadratic programming problem for the original MPC saturation controller.The optimal control input can be achieved by solving one linear complementarity problem and one transient analysis problem.Particularly,the physical meaning of the explicit expression form of the Newmark-β method is discovered and applied for increasing computational efficiency and saving memory.Finally,numerical simulations of a plane adjacent frame building subjected to earthquake ground motion demonstrate that the proposed fast MPC method with input constraints is robust,highly efficient and it can observably suppress the vibration responses,especially for large-scale structural dynamic control problems.For the local nonlinear factor of the structure itself: a fast model predictive control with local nonlinear factor for the structural vibration is proposed.Firstly,the time-domain recursive expression of the dynamic responses for local nonlinear structures is derived by using the Newmark-β method.Then,based on this recursive expression,on the one hand,a time-domain explicit dimension-reduced iteration method for local nonlinear structures is obtained,and when the initial state values in each predictive period need to be computed,this iteration method is applied to avoid the full iteration of all dimensions for the nonlinear dynamic equations,it will improve the iterative efficiency significantly;on the other hand,the predictive model of the local nonlinear structural vibration is founded on the above recursive expression,then,combining with the core concept of optimal control and the variational principle,the optimal control input can be achieved successfully.Lastly,numerical simulations of a local nonlinear mass-spring system subjected to harmonic excitation and an adjacent frame building with viscous dampers subjected to the seismic excitation show that the proposed MPC method with local nonlinearity for structural vibration is quite accurate and satisfactory in control effect.