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Điều khiển kết cấu - Chương 8

Dynamic Control Algorithms - Time invariant systems Chương này mở rộng các chiến lược kiểm soát hoạt động được giới thiệu trước đó chương để đối phó với thời gian tải phụ thuộc. Thảo luận được giới hạn thời gian hệ thống bất biến, ví dụ, trường hợp các thuộc tính hệ thống và lực lượng phản hồi thuật toán là liên tục trong thời gian của thời gian đáp ứng. | 545 Chapter 8 Dynamic Control Algorithms - Time invariant systems 8.1 Introduction This chapter extends the active control strategy introduced in the previous chapter to deal with time dependent loading. The discussion is restricted to time invariant systems i.e. the case where the system properties and force feedback algorithm are constant over the duration of the time response. The material presented here is organized as follows. Firstly the state-space formulation for a SDOF system is developed and used to generate the free vibration response. This solution provides the basis for establishing a criterion for dynamic stability of a SDOF system. Secondly linear negative feedback is introduced and the topic of stability is revisited. The primary focus is on assessing the effect of time delay in applying the control force on the stability. Thirdly the SDOF state-space formulation is specialized to deal with discrete time control where the feedback forces are computed at discrete time points and held constant over time intervals. Stability for discrete time feedback with time delay is examined in detail and a numerical procedure for determining the time increment corresponding to a stability transition is presented and illustrated with examples. Fourthly the choice of the optimal magnitudes of the feedback 546 Chapter 8 Dynamic Control Algorithm - Time Invariant Systems parameters is considered. Optimality is related to the magnitude of a quadratic performance index LQR which is taken as a time integral involving weighted response and control force terms. This approach is referred to as the linear quadratic regulator problem and leads to a time invariant linear relationship between the control forces and state variables. Fifthly the state-space formulation is extended to MDOF systems. The modal properties for an arbitrary damping scheme are derived and used to generate the governing equations expressed in terms of the modal coordinates. The last section deals with .